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Complex Analysis,2 Edition
The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted.
The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required.
More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex |
Number theory concerns itself with the properties of the positive integers 1, 2, 3, ..., and related objects that arise in their study. It is tempting to assume that something as simple as the counting numbers must be rather well understood. But this is far from the case! Indeed, number theory owes much of its charm to the wealth of easily-stated problems -- possible to explain to middle-school age children -- which have so far defied solution, despite hundreds of years of effort by great mathematicians.
This course is designed to introduce you to the foundational results, with particular attention paid to some the pathbreaking accomplishments of the 18th and 19th centuries. We will start with the basic theory (factorization into primes) before turning to Gauss's theory of congruences. The theory of congruences culminates with a proof of Gauss's Aureum Theorema (golden theorem), the law of quadratic reciprocity.
More advanced topics will be discussed later in the course. Possibilities include theorems about sums of squares, results on arithmetic functions, and results on the distribution of prime numbers.
Number theory, more than some other areas of mathematics, is largely an experimental science. It is recommended (but not required) that you download software that allows you to play with very large numbers. This is a great way to get an intuitive handle on the results we discuss.
Commercial packages of this sort include Maple and Mathematica, but there are also free (even open source!) options, such as gp/PARI.
HW assignments will contain problems required of all students, as well as more challenging problems required only for MATH 6400 students. Undergraduate participants may do these additional problems for extra credit.
You are expected to participate in class. In particular, attendance in this course is
required. More than four unexcused absences may result in you receiving a WF. Keep me posted whenever you have a conflict that requires you to miss class and this should not be an issue.
All exams are in-class, closed book and closed notes.
Homework will be collected in class, about once each week. Late homework will not be accepted. (If you have a need to turn in HW early, that can be arranged.) Your lowest HW score will be dropped at the end of the term.
On homework, collaboration is allowed and in fact is very much encouraged. Mathematics wouldn't be nearly as much fun if we couldn't talk about it with other people! However, copying (from a textbook or another student) and web searches are not allowed, and you must write your own final solutions independently. Keep in mind that by entering UGA, you have already agreed to abide by the UGA Honor code described in detail at <URL:
In practice, what this means that you may discuss homework problems and their solutions with your classmates, but you may not turn in a solution unless you understand it yourself. A reasonable rule of thumb is that you should be able to explain your solutions verbally to me (in all their gory detail) if requested to do so.
The withdrawal policy for this course is that if you withdraw within a week of the date the first midterm is handed back, you automatically qualify for a WP (assuming you are eligible by UGA's standards). After that point, it is at the discretion of the instructor (i.e., me) who will take your performance in the class to-date into account.
Special accommodationsDisclaimer
This course syllabus provides a general plan for the course;
deviations may be necessary. |
This is a lecture course in elementary algebra with a review of Pre-Algebra that will meet for a total of six hours per week with a focus on student-centered learning techniques. Review topics include whole numbers, operations of whole numbers and order of operations, fractions and mixed numerals, decimals, and percent notation. Topics include the real number system, operations of real numbers, simplification of algebraic expressions, and Polynomials. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC. Students must achieve a C- or better to pass the course. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
Topics include the real number system, operations with real numbers, simplification of algebraic expressions, solving equalities and inequalities graphing linear equations, slopes, equations of lines, and graphing inequalities in two variables. Additional topics are systems of linear equations integer exponents and scientific notation, introduction to polynomials and operations with polynomials. This is a developmental course. Credit for this course will not be counted toward fulfilling graduations requirements. A grade of C- or better is required. PREREQUISITE: ALGB-082 This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
Topics include the real number system, operations of real numbers, simplification of algebraic expressions, polynomials. A grade of C- or better is required. PREREQUISITES: ARTH-073, ARTH-078 or math placement of ALGB-081. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
This is a lecture course in elementary algebra with a review of topics that will be used in science and engineering classes. This class will meet for a total of six hours per week with a focus on student-centered learning techniques. Review topics include fractions and mixed numerals, operations with polynomials, scientific notation, ratio and proportion, basic statistical measures, geometric formulas and unit conversions.
Students must achieve a C- or better to pass the course.
This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
Topics include factoring polynomials, solving quadratic equations by factoring, with applications and problem solving. This is a developmental course. Credit for this course will not be counted toward fulfilling graduations requirements. A grade of C- or better is required. PREREQUISITE: ALGB-083, ALGB-087, or placement of ALGB-091 This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
Topics include operations with rational expressions, solving rational equations, applications and problem solving, and simplifying complex rational expressions. This is a developmental course Credit for this course will not be counted toward fulfilling graduations requirements. A grade of C- or better is required.
PREREQUISITE: ALGB-091 This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
Topics include radical expressions and equations and applications. Additional topics are the quadratic formula, graphs of quadratic equations, and functions. This is a developmental course. Credit for this course will not be counted toward fulfilling graduations requirements. A grade of C- or better is required. PREREQUISITE: ALGB-092 This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
A grade of C- or better is required. PREREQUISITES: ALGB-083, ALGB-087 or math placement of ALGB-091. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
This is a unique course with a format that allows the student to progress at his or her own pace. New students are assigned a beginning math level and textbook based on their placement test results. Returning students pick up wherever they ended the previous semester. Students may study on their own, with instructors and tutors available to answer questions on an individual basis. Each student is assigned an instructor and a particular class time, and may use the Testing Center and Tutor Center Monday-Friday 8:00 a.m. - 3:00 p.m. Students take tests whenever they feel ready and the test center is open. Tests are computer generated, and corrected and graded immediately for the students. Students are then given a copy of the original test and a copy of the correct answers to take with them.
Single credit grades are issued for completed credits only. It is impossible to earn three or more credits or fewer than three credits in one semester. Students who earn more than three credits in one semester will not be charged for more than three in any given semester. These credits are below college level, do not carry graduation credit, and are non-transferable. |
Spreadsheets in Mathematics: Accessibility, Creativity, and Fun
A spreadsheet, such as Microsoft Excel, provides educators with a creative tool for the study and teaching of mathematics, mathematical modeling, and mathematical visualization. It enables students to gain mathematical insights into a diverse range of interesting and significant applications in an engaging setting while they simultaneously acquire practical skills in using the principal mathematical tool of the workplace. This paper illustrates novel ways to use this powerful and accessible tool and its outstanding graphic features creatively in teaching a surprising number of mathematically oriented topics. Illustrations come from such disciplines as the physical and social sciences, statistics, mathematics, computer sciences, and the arts. |
2This course prepares students who want to strengthen computation and problem-solving skills before proceeding to an elementary algebra course. Includes the concept of variables, using rational numbers, solving simple equations in one variables, percent, and word problems.
9. Course Pre-Requisites
10. Course Co-Requisites
11. Course Recommended Preparation
12. Contact Hours (lecture, lab, lecture/lab)
2 |
Mathematical Asset Management presents an accessible and practical introduction to financial derivatives and portfolio selection while also acting as a basis for further study in mathematical finance.
Assuming a fundamental background in calculus, real analysis, and linear algebra, the book uses mathematical tools only as needed and provides comprehensive, yet concise, coverage of various topics, such as:
Interest rates and the connection between present value and arbitrage
Financial instruments beyond bonds that serve as building blocks for portfolios
Trading strategies and risk performance measures
Stochastic properties of stock prices
The difference between expected return and expected growth and the geometric Brownian motion
Diversification through the creation of optimal portfolios under various constraints
The use of the Capital Asset Pricing Model to accurately estimate the difference between the return of the market and the short rate
To further demonstrate the reality of the discussed concepts, the author analyzes five active stocks over a four-year period and highlights the different methods and portfolios that exist in today's economic world. Exercises are also provided throughout the text, along with the solutions, allowing readers to measure their understanding of presented techniques as well as see how the methods work in real life.
Mathematical Asset Management is an excellent book for courses in mathematical finance, actuarial mathematics, financial derivatives, and financial engineering at the upper-undergraduate and graduate levels. It is also a valuable reference for practitioners in banking, insurance, and asset management industries. |
The purpose of this book is to help students in calculus1 get a good practice for the midterms and final exams during their school year in calculus1. All the finals and midterms are real exams (with little changes) from several Universities around America ( USA, Canada, Puerto Rico, Mexico).
We believe to get a good grade in the midterms and final, the student should after reviewing his/her homework and notes pick some real midterms and final and do them.
We tried this idea with several students and it works very well.
We wish you all success in your studies.
Muslim Mathematical Society and Salah Abdel Hamid
Preview coming soon.
Mumas "Muslim Mathematical Society" is a group graduate Muslim students who are master in different field in mathematic and decide to get together and write a collection of practice books for the students in different area in math.
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Kirk's Tutoring Blog
Ideally, if you have prepared well, the last 24-48 hours should be dedicated to adequate rest. However the world isn't quite a perfect sphere, and we do not always have the perfect situation. If you haven't fully study yet, the volume of material to cover in these last 24-48 hours may be too much, therefore we need a survey strategy. The following works best for computational subjects such as math, physics, chemistry or disciplines such as engineering.
If this is a college prep/standardized test, take the practice test again...
The summer months are all but gone, withered into a faded memory, like an old black and white photo. Lets hope that it was as enjoyable as it was productive. Its time to turn a new leaf in the chapter of life. New challenges, new faces, new subjects and more tests. So what did you do in the summer to keep motivated, or practice new habits?
Here are my suggestions to staying motivated throughout the summer.
* Read a new book/s.
* Volunteer.
* Apply the knowledge gained through the school year to a project that you wanted to do but never completed. * Research something you were interested...
Proof techniques are fun. They are mathematical arguments of sufficiency. The feeling you get from arguing your point logically to completion is always exhilarating. Let us put our mathematical reasoning power to the test. Now since this is our first of many proof techniques. I will start with something elementary.
1. Prove the following:
(a) Given that the average of y and z is odd, then z is an odd integer when y is odd.
When doing proofs it is best to do so in algebraic and generalized form. A way to represent all possible cases. Using only examples would be trivial, since we know...
Students often ask me how do Mathematicians come up with various formulas in Trigonometry, Algebra and Calculus? By method of Proofs and Derivation I would exclaim, which in my opinion is becoming a lost art. I found deriving formulas helped to seal the understanding of the concepts and theories in Math. I believe it is thus fitting as an end to our talk on polynomials, to derive the equation of the quadratic formula. We will do so by using the last method we discussed, "Completing the Square".
It has been a while since my last post, but as promised I am back. Recently a reader of one of my blogs commented on how helpful they were in helping her explain a concept to her HS Junior. I was indeed very glad to hear. It certainly is an encouragement to see parents, not only sign their child up for tutoring but also willing to follow through the covered material as well. Expanding on the purpose of the blog page, would be a forum board where students/parents can post short questions and have tutor respond and perhaps even have their answers rated on helpfulness. This I believe would make...
Horizontal Shifts:
Let f be a function and c a positive real number.
* The graph of y = f (x + c) is the graph of y = f (x) shifted to the left c
units.
* The graph of y = f (x - c) is the graph of y = f (x) shifted to the right c units.
Reflection about the x-Axis:
* The graph of y = - f (x) is the graph of y = f(x) reflected about the x-axis.
A student got 50% of the questions on an algebra test correct. If he answered 10 out of the first 12 questions asked correctly but missed 3/4 of the remaining questions, how many questions were on the test?
So algebraically we need to setup an equation here. The sum of the 10 correctly answered questions and the remaining questions that were answered correctly divided by the total number of questions is 0.5. Let y represent the number of remaining questions answered correctly. Let x represent the number of questions in total. Then;
We have reviewing the six pillars of a good study habits, skills and strategies. Now I will talk about basic study techniques in assimilating the material. There are many self help books on how to study but to be honest the approach could vary based on the individuals learning abilities, the subject content at hand as well as the intent of the study session. There is no one size fits all approach. Studying is a discipline and as such, do start early, make a commitment at the beginning of the semester/the school year. Don't wait until it is too late and be overwhelmed with...
Throughout the school year I have worked with several students from diverse economic and social backgrounds. In the sessions I had the chance to observe their study habits, their improvements and successes. From these observations I gathered some interesting and useful information that I believe will help others avoid the pitfalls of bad study habits, ill preparation and last minute cramming for tests/exams. These suggestions may be self evident but if followed will contribute to improvement in learning, retention, and finally the...
Today I was working with a student preparing him for the upcoming SAT in June. We came across an interesting question, which I will share with everyone here. Here is the question:
(Q) There is a number 'WXYZ', (where W,X,Y and Z are integers), such that
x = w + y + z [equation(1)]
w = y + 1 [equation(2)]
z = w – 5 [equation(3)]
Find this number 'WXYZ'?
In order to solve a system of equations involving four unknowns, we need four equations (relationships). We are only given three relationships, "Houston we have a problem." Do not worry, we have another approach. Let us find x in terms of... |
2013-2014 University Catalog
A course presenting mathematical techniques used in physics and engineering. The course will survey, at a brief introductory level and from a physics perspective, numerous mathematical techniques from areas such as infinite series, integral transformation, applications of complex variables, matrices and tensors, special functions, partial differential equations, Green's functions, perturbation theory, integral equations, calculus of variations, and groups and group representations. Prerequisites: PHYS 2326/2126 and MATH 3330. |
Description Physics The course is a 2 DVD series, 11 full You
How are the MathTutorDVD.com line of DVDs different from others? The answer is simple. Most math instruction involves a lengthy discussion of the abstract theory behind the Math before instructing the student in how to solve problems. While there are some merits to this style, in the vast majority of the cases the student quickly gets bored and frustrated by the time he or she starts to solve the problems. This DVD, in contrast, teaches all of the concepts by working fully narrated problems step-by-step, which is a much more engaging way to learn.
Exceptional value and affordability. MathTutorDVD.com believes in providing value for our customers. This is a 11 Hour DVD course. We could have easily split this content into many DVD courses costing the same price but instead chose to keep the cost down so that this content is affordable to all.
What is our teaching style like? All topics on this DVD are taught by working example problems. There are no traditional lectures of background material that won't help you solve problems and improve your skills. We believe in teaching-by-doing and that is what you will receive by watching this DVD. The Equations Of Motion are explained, for example, by working many problems in step-by-step detail. We begin with the easier problems and work our way up to the harder problems. The student immediately gains confidence, does not get bored, and quickly feels like he or she can conquer the material. This method is extremely powerful and has proven itself time and again. Perhaps most importantly, problem solving skills are honed early on that will help with homework and taking exams even after watching the very first lesson. |
Calculator: Calculators may come in handy during class or in
your homework from time to time, but I will not require you to have
one. They will be allowed on tests and homework, though on tests you
will find them to be of limited value. If you intend on sharing a
calculator with a friend, keep in mind that sharing calculators is not
permitted on exams.
Ideally, a calculator should be able to do ordinary arithmetic operations,
as well as some additional functions like exponentiation (powers) and
square roots. It need not be able to graph or be programmed.
Note that cell phones and laptops are not allowed during exams, so if
your only calculator is a calculator program on your cell phone or
laptop, you will want to get a stand-alone calculator, or you will not
have one during the exams. In general, nothing that will permit
electronic communication with another student or people outside the
room may be used on exams.
Web page:
Email list: [email protected] (when you fill out your information
you may elect to be on this list)
Prerequisites: None.
Well, what math background are you expected to have? I realize that the
range of math classes taken by students in math 102 varies widely, and
this includes the extent to which students remember various facts.
This course, however, is not in sequence with the standard math sequence,
and so mastery of past math subjects is not as relevant in this class
as compared to what you might be used to.
Most of the course is based on concepts rather than specific skills,
though some skill will come in handy at some points. Though these
times are relatively rare, the strong reaction some students feel when
they do not know the relevant skils may make it loom large in their
minds. Most of these skills, when they come up, are at the
pre-algebra and algebra level: using variables, understanding
algebraic expressions, and sometimes solving simple equations. It is
assumed that students have had exposure to algebra and geometry at
some point, but it is not assumed that they have a strong mastery of
either subject.
If you find you need some review on some topic like this that is used
in class, come by my office hours or use the tutoring service mentioned
above.
The Idea of this class: This is most likely a very different kind
of math class than you have ever had. Most math classes you have
experienced emphasize skills: how to solve a quadratic equation, or
how to find an unknown side in a triangle. This class will emphasize
ideas and concepts. ``How to do it'' will take a back seat to
``Why does it work?''
This is also a course where we seek to discover math together. I'm
not here to tell you the answer; I'm more of a guide to help you
explore a mathematical concept. Through this course, I hope to show
you the big picture: what mathematics is all about. This is something
that many students don't see in high school courses, or even some
college level courses. Once you see math from this point of view, I
hope you will be able to see why mathematicians feel that mathematics
is beautiful, or how creativity, imagination, and logical thinking can
work together in mathematics. I hope you will see how mathematics is
part of what our civilization is all about: where we have been and
where we are going, and why, to be a truly educated person, one must have some
facility with mathematics.
Beyond this, we will see ten {\em Lessons For Life} as they apply to
mathematics. These lessons are to be found throughout the textbook, though
they are also at the end on p. 619 for ready reference. I hope these
{\em Lessons For Life}, illustrated through mathematical problem solving,
will serve you as you face other kinds of problems in your life.
Goals: The student should develop:
An ability to translate a problem which is well-suited to mathematical
solutions into mathematical language;
An ability to think and reason in a structured logical manner;
An ability to use mathematical reasoning to understand problems;
An appreciation for what mathematics is all about, and what
mathematicians do;
An idea for the logical structure of mathematics, and proof;
An appreciation for the applicability, subtlety and beauty of
mathematics;
an ability to approach problems in life analytically.
Objectives: The specific objectives of this course will partly
be determined by the students in one of the first assignments. Students
will select topics from the book that are of greatest interest to them,
and the course will be based on what topics are most popular.
The point is that these subjects are merely a vehicle to introduce the student
to mathematics: logical thinking, quantitative sense, great and profound
ideas, and creative problem-solving. These cannot be taught in the
abstract, but must be carried by more concrete examples, and these
examples will be the occasion for us to discover mathematics together.
Homework: Homework will be assigned twice a week; homework
assigned on Tuesday will be due on Thursday, and homework assigned on
Thursday will be due on Tuesday. Homework should be turned in at the
beginning of class.
The two lowest homework scores will be disregarded.
Remember that the primary purpose of the homework is to learn the material,
so if you miss one, or do not take it seriously, you will fall behind
in the course material and will not do well on exams.
Late assignments: No late homework is accepted. Exceptions can
be granted, if you must give me notice that you are going to turn in
an assignment late at least the class before the assignment is due.
You must also have a good reason. These reasons will be treated on a
case-by-case basis. When you obtain permission to turn in an
assignment late, we will discuss a new due date for that homework.
Collaboration: You are encouraged to collaborate on all homework
assignments, unless otherwise specified. This means you work on it
independently before discussing it with each other, and it means you
must thoroughly understand how to do the problem before writing it up.
You must write up your answers separately; you cannot turn in one
homework for more than one person, nor can you simply include
photocopies of other students' work. There is no limit to the size
of a group for collaboration, although 3-5 people tends to be an efficient
size.
You should also use these groups to ask questions of each other to
better understand the material. If you do not see each other
frequently, you should set up a regular time and place to meet to work
on assignments. If you do not have a group, talk to me and I can
place you in a group. If you do not wish to work in a group, that is
your prerogative but this will be a disadvantage to you.
Comments: You should include comments about the class at the top
of your homework assignments. These comments can be ``This class is
going too fast'', ``I like this section'', ``This is too easy/hard'',
``Can we have more connections to music'', ``Everything's
okay'', and so on. You will not be graded on these comments, but they
will affect how I teach the class, and may make the class more
enjoyable for you.
Class participation: You are expected to actively participate in
class. Many students view learning as a passive act, where the
teacher takes the only active role, and the student simply listens, or
at most takes notes. This view is not advisable in this class. Here,
you will need to take an active role in learning the material. {\em
You} are in charge of your education, and {\em you} should take
responsibility to learn the material as thoroughly as you can.
This is especially true in this class. As you will discover, this
class is not a lecture-style class, where I simply proclaim information
to you and you record the information in your notes. Rather, we will
be engaged in mathematics discovery together.
Ten percent of your grade is based on my estimate of your class
participation throughout the term. Mostly this is easy points: you
don't have to get the ``right answer''; you just have to be engaged
in the class as evidenced by the questions and comments you make.
In fact, making ``wrong statements'' is a pretty important part of this
course, and you will get more points for boldly guessing than for
waiting until you are sure you are right before speaking.
Attendance: Attendance is important. The whole point of the
class is for us to discover mathematics together, and you cannot do
that if you are not here. Skipping even a single class will mean you
will not likely be able to do the work or know what is happening in
the next class period. This is not the sort of class where just
reading the material in the book will allow you to do the work. And, of
course, if you don't attend, you can't get class participation points. In
short, skip class at your peril.
Exams: There will be three midterms, and one final. Each
midterm counts for 16% of your grade, and the final counts for 22%.
Homework counts for 20% and class participation for 10%. the final
exam grade will substitute for your lowest midterm grade if this is to
your advantage. Borderline grades could go either way, depending on
the effort I see you put into the class.
There are no make up exams. If you must miss an exam due to a major
emergency, you must make arrangements with me beforehand, and
exceptions may be granted on a case-by-case basis. If granted, your
final exam score will be used to calculate the score for the missed
exam.
Midterms will be during the normal class period. Both midterms and
final will occur in the normal classroom for the class. Dates for
these tests are as follows:
Midterm 1
Sep 29
during class
Midterm 2
Oct 27
during class
Midterm 3
Dec 1
during class
Final (sec. 3)
Dec 13
1:30 p.m.--4:00 p.m.
Final (sec. 4)
Dec 14
1:30 p.m.--4:00 p.m.
I will hold review sessions before each, at a time that is popular with the
class.
Holidays:
Labor Day
Sep 5
Conference
Oct 7
Thanksgiving
Nov 24--25
Grading: A grade of C indicates an ability to do homework-like
problems, and memorization of all techniques and definitions. In
order to receive a B, a student must demonstrate a deeper knowledge of
the material, being able to apply the course material to new
circumstances where applicable. An A student must demonstrate this
kind of deep understanding in all of the covered topics, as well as be
able to draw new conclusions from known facts in a logical manner, and
must also demonstrate persistence and dilligence. In the other
direction, a grade of D shows only superficial understanding of the material,
and shows inconsistency to do straightforward problems. An F
grade indicates that the student has severe gaps in even superficial
understanding of the material in the course.
Although this is the philosophy, grading will be done by counting points
received on each problem, as usual. But the difficulty level of the problems
will be arranged in order to achieve the above grading scale.
Christian attitude: Although not part of the grading for this
course, you are expected to approach this class with a Christian
attitude, being willing to help your fellow classmates to understand
the material outside of class, being willing to be corrected by your
fellow classmates when you see they are right, but firm in your
conviction otherwise, being bold to ask questions without feeling
ashamed of looking foolish, encouraging one another in love, being
patient with those who are asking questions, and preferring a grasp of
the material, which is enduring and becomes part of you, over a grade,
which is transient, external, and shallow. You should diligently
devote the time you spend on this class as to the Lord. As cheating
harms both the cheater and the rest of the class (though in different
ways), you should not cheat, nor should you provide temptations for
others to cheat.
For my part, I commit to approaching this class with a Christian
attitude, viewing my role as that of a servant, being concerned first
for your personal, especially intellectual, development. I
will also seek to produce an environment of encouragement and love,
that fosters a sense of community and understanding. I commit to reporting
grades that accurately and honestly reflect the level of work done in the
class, as described in the paragraphs above. I also commit the time I
spend preparing for this class as to the Lord, and I will pray for all
individuals in the class on a regular basis, understanding that even as I
may seek to educate, God provides the true transformation. |
Mathematics Department Handbook
Welcome to the Department of Mathematics at the University of Rochester.
We have compiled these notes in order to assist you, the first year
student, in making the transition from high school to university. This
is sometimes a difficult process for various reasons. As far as first
year mathematics courses go, there are two main difficulties:
First, the Department of Mathematics expects students who take courses
in mathematics to take the responsibility for mastering the course
material. There is lots of assistance offered, all detailed in these
notes, but it is your responsibility to use these resources. Second,
many talented students have been able to do well in their high school
math courses in spite of not having regular work habits, but now the
situation is very different. It is almost impossible to pass first
year university mathematics courses without developing these habits.
We hope this Guide will help you learn how.
We have also included in these notes some hints on study techniques and
writing examinations, expanded descriptions of first year courses, and a
reading list for students interested in expanding their knowledge of
mathematics in a general way.
Again, welcome, and we wish you every success in your academic
endeavors. |
Essential Math With Application - 8th edition
Summary: The latest book from Cengage Learning on Essential Mathematics As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing ...show morethem with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the concepts53.71 +$3.99 s/h
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Journals and books
Journals and books
A central part of the NCM enterprise is the Nämnaren Project. The project is aimed at teachers, teacher trainers, researchers and the staff responsable for basic education, further education and development work - and consists of different parts:
Nämnaren the journal for mathematics education, publishes four issues annually. Plans are made for a fifth issue in English. In December 2000 a new book was published, "Matematikk & undervisning, Norden 2000". On the occasion of the World Mathematics Year, 2000, the editors for the Nordic journals have decided to publish a book about "Mathematics education in the Nordic classroom. Year 2000". Studies at different ages are described - from six-year-olds to trainee teachers. The purpose is to stimulate communication concerning the development of mathematics as a subject in the Scandinavian countries. The book has been forwarded to all subscribers of Nämnaren as a gift to mark the occasion of the World Mathematics Year 2000.
Nämnaren on the web inclusive of Nämnaren's data base, a searchable data base which can be located via the NCM web site. The data base contains an outline of approximately 2300 articles published since the start in 1974.
NämnarenTEMA began with some smaller projects followed up by the National Agency for Education project for support and stimulance material for teachers (1993-95). The aim was to analyse the news, facilitate interpretation of the curriculum and evaluation, deal with the area of weaknesses in the field of Swedish mathematics education in compulsory and upper secondary schools documented in Swedish and international studies. The responsibility for this work was transferred in 1995 to the Nämnaren project. So far, four books have been published, and three more are in preparation. The series is a result of cooperation between researchers, teacher educators and teachers.
The Mathematics Biennial 2000 - Time For Mathematics One of the first assignments of the NCM was to organise and implement the 11th mathematics biennial in Göteborg 27-29 January, 2000 - up to now the biggest biennial. 280 lecturers provided 334 programme points for 5000 participants. Three students were invited from every teacher training area; in return they brought exhibition materials about their own education. Special seminars were built into the programme for the exchange of experiences between 170 students from different universities, and between students and the NCM. A Research conference for 130 participants in collaboration with the Swedish Association for Mathematics Education Research, SMDF and NCM started. International researchers from 16 different countries participated and took part later in the biennial. The documentation is produced by SMDF with support from NCM. Ten discussion groups with a total of 500 participants were initiated within chosen problem areas where the possibilities for improvement are considerable. The conference site on the NCM web site will be available. The discussions will hopefully lead to a mapping of the needs of competence development and development work within the respective areas. |
Math for Elementary Teachers II
Welcome to Mth126: "Continued study of the mathematical
concepts and techniques that are fundamental to, and form the
basis for, elementary school mathematics. Topics include:
use of probability and statistics to explore real-world
problems; representation and analysis of discrete mathematical
problems using counting techniques, sequences, graph theory,
arrays and networks; use of functions, algebra and the basic
concepts underlying the calculus in real-world-applications."
News and Updates - Spring 2011
See the Homework and Handouts table
below to download or print the syllabus, calendar, and all
homework sets and class notes. |
. Premise: Mathematical results are expressed in a foreign language.
This course teaches mathematical symbolism and reasoning as if it were
expressed
in a foreign language (It is!). Like other languages, the language of
mathematics
has its own grammar, syntax, vocabulary, word order, synonyms,
negations,
conventions, idioms, abbreviations, sentence structure, and paragraph
structure.
It has certain language features unparalleled in other languages, such
as
representation (For example, when "x"
is a dummy variable it may represent
any real number or any numerical expression, including "2x - 1" and "b").
The language also includes a large component of logic. The Language
of
Mathematics emphasizes all these features of the language (Esty,
1992
discussion
of how to read, write, speak, and think mathematics.
Fortunately, mathematical sentences and paragraphs are generally
written in a limited number of easily distinguishable patterns.
Students who are taught
to recognize these patterns find mathematics far more comprehensible
than
those who are not. Furthermore, their abilities to solve problems and
do
proofs are much enhanced (Esty and Teppo, 1994).
Most examples come from algebra, functions, and set theory (not trig
or
calculus), but the material is the language itself, which is essential
for
all areas of mathematics. Since this material is not emphasized in any
other
course, the course level is hard to peg. Some parts look like a
"transition
to advanced mathematics" course, but, with this unique approach, many
students
who regard themselves as "terribly math anxious" do very well with the
material
(Esty and Teppo, 1994).
For a thorough explanation of how the language is essential to
mathematics,
see "Language Concepts of Mathematics" (Esty) in FOCUS on Learning
Problems
in Mathematics 14.4 (Fall, 1992) pp. 31-54. For the effectiveness
of
this course, see "A General-Education Course Emphasizing Mathematical
Language
and Reasoning" (Esty and Teppo) in FOCUS on Learning Problems in
Mathematics
16.1 (Winter, 1994) pp. 13-35. For an article on grading in the context
of
this course, see the Mathematics Teacher, 85.8 (Nov. 1992)
pp.616-618
"Grade assignment based on progressive improvement" (Esty and Teppo),
reprinted
in Emphasis on Assessment, NCTM, 1996.
Because the organization and emphasis of the material is radically
new, the use of the text is not (yet) widespread. Idaho State and
Montana State have decided that it will be necessary for Elementary
Education majors (It
was not designed for them, but they seem to have special difficulties
with
abstract symbolism and this course can cure that). At Montana State it
has
been successfully offered twelve years to general students and four
times
in the summer to secondary math teachers (who knew the procedures of
mathematics,
but were not so comfortable with expressing them symbolically. A
research
paper on this will eventually appear). The course was actually designed
with
freshman math majors in mind, but, general-education students in it
found
that they could "finally" understand mathematics, so, when the word got
around,
they became the majority of the audience.
Equivalent courses: Probably no other text yields an
equivalent course. At MSU the course number is Math 151. The level
would be about equivalent
to a basic logic course -- but, it is only partly logic and, in The
Language
of Mathematics, the logic is illustrated by and selected for
mathematics.
The course is more sophisticated (abstract) than Algebra II, but the
content
is not at all like "College Algebra" or "Precalculus." Surprisingly,
many
students who fail algebra in college (even remedial Algebra I) learn
very
well in this course if they are mature enough to actually do the
reading
and the work. It counts as a "core" course in mathematics at Montana
State
and Idaho State. It is somewhat above the level of "Finite Math." |
Course Requires a Media Kit to be Purchased by Course Sponsor
(see additional details below):
No
Description:
No matter what you plan on majoring in once you go off to college, you will have to take at least one math course before you graduate. Statistics is required by just about every major. Business, science, and technology degrees need basic calculus. Even many education and liberal arts programs require a course in graphical analysis and/or trigonometry.
That is why Math You Can Use In College was developed. We will spend time on concepts you could possibly use again and not on the concepts you will probably never see after high school. This course is application-based and focuses on important real-life topics including:
A common thread throughout the course is the use of spreadsheets to help evaluate these mathematical explorations. Students should have, at a minimum, a fundamental understanding of how spreadsheets work. All students are required to have access to Microsoft Excel, or an alternative spreadsheet based program. An online graphing calculator will also be used during the coursegovhs.org.
14 Intro to Calculus
-Basic differentiation
-Applications of the derivative
15 Final Assessment
-Summative Assessment
-Course evaluation survey
Course Objectives: -Learn to navigate and work cooperatively in this environment
-Become familiar with the graphing calculator and its applications
-Introduce and use basic trigonometry
-Explore concepts of graphical analysis
-Discuss basic skills and concepts used in statistics
-Use concepts learned to solve practical applications
-Learn what math classes you can expect to take in college. |
To understand and connect concepts of the calculus with real
world problems and other scientific disciplines.
To value mathematics and develop an ability to communicate mathematics,
both in writing and orally.
To develop mathematical reasoning, and an ability to solve problems.
To attain computational facility in integral calculus, and sequences
and series.
WITHDRAWAL:
The last day for undergraduates to withdraw from a full-session couse is
Friday, March 8.
GRADING:
Grades for 230 will be assigned on the basis of 650 points,
as follows:
3 one-hour exams worth 100 points each
Quizzes and/or homework, 150 points total
Final exam, 200 points
ADVICE:
Perhaps the single most important factor in your success
in this course is your study habits .
Think of learning math as "working out" in the gym.
Study at least 3 times per week; do not wait until the day before the exam.
Learn mathematics like you would learn a language.
Work on the concepts until they make sense.
Don't just memorize facts and then forget them a few weeks later.
You will need to know this stuff for Calc III and other courses.
Master each homework problem - beyond just getting a correct answer.
Be on the lookout for mistakes in algebra and trig.
Always come to class!
While you're there, listen, think, and ask questions. |
Dyslexia, Dyscalculia and Mathematics will be an essential resource for teachers, classroom assistants, and SENCOs who help dyslexic and dyscalculic children with their understanding of mathematics. Written in an accessible style with helpful illustrations, this practical book reveals helpful ways in which to tackle both simple and complex concepts... more...
This book (along with vol. 2) covers most of the traditional methods for polynomial root-finding such as Newton's, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent's method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation... more...
Mathematicians is a remarkable collection of ninety-two photographic portraits, featuring some of the most amazing mathematicians of our time. Acclaimed photographer Mariana Cook captures the exuberant and colorful personalities of these brilliant thinkers and the superb images are accompanied by brief autobiographical texts written by each mathematician.... more...
The Clemsons' clear and readable book takes the reader from debates about how children learn and what children know and can do when they start school; through to a discussion of how mathematics can be managed, assessed and evaluated in the school and classroom. Linking these two parts of the book is a section on the subject of mathematics itself, from... more... |
(cur | prev) 19:15, 29 December 2011Barta(Talk | contribs)(3,042 bytes)(Created page with "Many institutions have liberal arts courses in mathematics. Creating a mathematics course that satisfies the math requirement and at the same time shows students how mathematics ...") |
This full-year course is designed for those students who scored in the basic performance level on the Mathematics portion of the NJPASS and for those students who may be identified as needing to focus on math skills. This class will be devised to help students improve mathematics proficiency to carry them into future classes class is required for those students who have been identified as needing additional instruction in the mathematical concepts which will be tested on the eleventh grade HSPA test. Emphasis will be on mastering the New Jersey Core Curriculum Content Standards as tested on the HSPA test.
This course is designed for those grade 9 students who may not be ready to be introduced to a traditional Algebra I course. Topics will include set theory, operations on signed numbers, combining like terms, solving basic linear equations, performing basic operations on matrices, graphing, and probability and statistics including data analysis. Students will also learn the functions of the scientific calculator. After successful completion of this introductory course students will take Algebra I. |
Question Bank With Sample Papers based on the New CBSE Curriculum. An exhaustive coverage of all types of questions on each topic. Questions have been well classified as per their weightage in the examination. Fully solved exercises to make you aware of h
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Very simple language and vocabulary/terminology is used for the better understanding of students of all categories like-outstanding, bright, average and weak. An exhaustive coverage of all types of questions on each topic as per the examination pattern quAs per New Examination Pattern CCE (Continous and Comprehensive Evaluation)This is the Main Course Book text book according to NCERT / CBSE syllabus for class I. The empahsis is laid on practical rather than theoretical approach to fundamental concepts of
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This a main text book strictly according to NCERT/CBSE syllabus for classes I to V. The emphasis is laid on practical rather than theoretical approach to fundamental concepts of Mathematics. The children over the years from numeracy skills to analytical a
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> Main textbook strictly according to NCERT/CBSE syllabus for classes I to V. > The emphasis is laid on practical rather than theortical approach to fundamental conecpts of Mathematics.> The children over the years move the numnercy skills to analytical a
read more
This is the main textbook strictly according to NCERT/CBSE syllabus for classes I to V. The emphasis is laid on practical rather than theoretical approach to fundamental concepts of Mathematics. The children over the years mover from numeracy skills to an |
The objective of this tutorial is to acquaint the student with the basic tools needed to use the SIMULINK package. SIMULINK is an extension to MATLAB which uses a icon-driven interface for the construction of a block diagram representation of a process. Submitted: Jun 26, 2002
This video demo gets you started with Simulink. It takes you through many key concepts in building and simulating a model. We will build up a model from scratch while taking you through a number of features of Simulink. Submitted: Apr 14, 2008
Provides examples on how to create vectors, matrices, functions, polynomials. Also includes sections on plotting and printing. Tutorial allows for users to view tutorial in one window while running MATLAB in another window. Submitted: Jun 19, 2002
This page indexes a number of pages that can be used to test you skill at using MATLAB. Answers are available on request. In almost all cases, there is more than one way to solve a particular exercise. Some of the exercises presented here are taken (in modified form, usually) from the text, Essential MATLAB for Scientists and Engineers by BD Hahn, Arnold Publishing, 1997. Submitted: Jun 26, 2002
Wavelets are interesting mathematical basis functions with applications to many areas of science and technology. The Wavelet Digest is a free electronic newsletter available to researchers with a standing interest in wavelets and their applications. Its primary role is to link together the wavelet community, which is extremely diverse. Submitted: Mar 11, 2003
These Web pages attempt to provide a concise on-line guide to using MATLAB. The information is organized in outline form to enable users to see the interelationship of topics. Most of the common MATLAB commands are demonstrated by example. Many of the MATLAB scripts, m-files and data files used in the examples have links so that they may be easily downloaded. The information in this reference is geared toward new MATLAB users. Intermediate and expert MATLAB users will find probably find some useful tidbits too. Submitted: Jun 19, 2002
MATLAB Tutorial from the University of New Hampshire. The tutorials are broken up into some of the basic topics. The first includes a few examples of how Matlab makes it easy to create and manipulate vectors. The tutorials move from the simple examples and get tougher. Submitted: Jun 19, 2002
The information presented in these pages generally applies to version 5.x of MATLAB though most of the basics have not changed since version 3.5. The discussion does assume you know how to use and read the on-line help facilities in MATLAB (help, helpdesk and helpwin) and are familiar with how MATLAB handles things like vectors and arrays. Submitted: Jun 19, 2002
Math+Fun.com offers online tutorial and testing for subjects such as arithmetic, algebra, trigonometry, geometry, ACT and SAT testing, and much much more. Our online tests allow your kids to test their math skills while our practice sessions offer page after page of fun ways to prepare for taking the tests. We make sure that your kids are having fun while studying by combining testing and practice sessions with cleverly designed math games. Easy ways for parents to monitor their kid's progress. Submitted: May 08, 2006 |
Math Anxiety
What is it?
Math anxiety has been defined as a feeling of tension and apprehension that arises when someone is faced with manipulating numbers and solving mathematical problems. It is not just associated with academic settings. It can show its ugly head in many ordinary life situations.
In academic settings, though, math anxiety can cause students to perform poorly on math tests, homework, and just in class generally. Very often, a studentís poor performance in a mathematics class is not just the result of a lack of knowledge. It can be tied to math anxiety as well. Someone with math anxiety is not mentally deficient. But, it can cause a student to lose focus and to lose confidence in mathematical situations, thus impacting future success in mathematical requirements.
What causes it?
Math is linear in nature. In most classes it is possible to skip one chapter and still understand the other material covered. Not so with mathematics. In this discipline a student must learn and understand a process before moving on to the next one. In other words, what you learn in Chapter One is the foundation of what will be taught in Chapter Two.
Math is like a language. It has many symbols that appear foreign until you really understand what each means. You canít expect to take Spanish, for example, one week and be fluent in it the next week. It is the same in mathematics. Practice makes perfect. Doing one or two homework problems is simply not enough practice to fully grasp the concepts covered in the chapter. Do all the problems assigned. Try doing a few of the ones not assigned, as well. You can be ďfluentĒ in math if you work at it.
Donít expect your college math classes to mirror those you had in high school. In a secondary setting, you went to math class every day and were saturated with the materials covered that semester. In college, however, you are expected to learn the same amount of material but in a shorter amount of time with less contact, often, with your instructor. What you had a year to learn in high school will now be covered in about 14 -16 weeks, and you are expected to fully understand it before exiting the class.
Remember, math requires a different mindset. In other classes you may just need to listen, take notes, and then learn the material without really applying what you learned. In math, you will be taking what you have learned and using it to solve equations or a set of problems.
Donít despair! You can do mathematics. In fact, you probably use more math daily than you realize. Balanced a checkbook lately? Doubled a recipe? If math begins to get you down, come to the Learning Assistance Center and let the tutors get you back on track. You can succeed in your math classes!
How do I know that I have Math Anxiety?
Ask yourself these questions:
1. Do I become anxious and forget important concepts during a math test?
2. Do I blame the instructor if I donít do well on math assignments and tests?
3. Do I stop taking notes in class when I get confused?
4. Am I afraid to ask questions in math class?
5. Do I stop working a problem as soon as I get stuck?
6. Do I feel like it is impossible for me to understand math?
If you answered ďyesĒ to several of them, then you probably do suffer from Math Anxiety.
Strategies for reducing math anxiety:
1. Go to every math class, without fail.
2. If you must miss a class, ask the instructor if you can attend another section so you can keep up with the work.
3. Make sure you read the text carefully. Donít skip over the explanations. They are there for a reason.
4. Try making a vocabulary list or an outline of the material in the chapter. Math does have its own vocabulary, and you need to be familiar with it.
5. Get tutoring as soon as you recognize a problem.
6. Always ask your instructor if you have a question about your assignment.
7. Copy everything on the board. Repeat the steps mentally and try to work the problem. Make note cards with the steps to remind yourself of the process to solve problems.
8. Study as soon as possible after your class. If you wait too long, you will forget what was covered in class. Try to make consistent study times at a point during the day when you are alert and focused. Have a set start and stop time and stick to it.
9. Find a place that is relatively free of distractions and make that your consistent place to study.
10. Turn off the phone, TV, and music while you study. It does make a difference.
11. Form a study group from your classmates. Make sure you choose students who are motivated and disciplined so you can support each other.
12. Donít study for extended periods. Take a break every 30 minutes or so.
13. If you are frustrated with a concept, stop. Get up. Get some fresh air. Come back to it in a few minutes when your mind is clear.
14. Watch the video tapes that accompany your text. You can find them in the LAC and in the library.
15. Do some math work every day.
16. Review your notes and homework before you go into class. That will give you a reference point when the instructor begins the lecture for that class session. |
Description
The
Features
Engaging applications and real-world data put learning into context. Bob Blitzer is on a constant search for data that can be used to illustrate algebra applications. He has used this research to update the chapter- and section-opening applications, examples, and exercises in the text.
Additional study skills support is available to students through two new in-text features and the new Learning Guide:
NEW! Great Question! takes the content from each Study Tip from the previous edition and presents it in the context of a student question. Answers to the questions offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions.
NEW! Achieving Success boxes offer strategies for success in math courses, along with suggestions to help developmental students achieve their full academic potential.
NEW! TheLearning Guide helps students learn how to make the most of their textbook and its companion learning tools, including MyMathLab. Organized by the textbook's learning objectives, this workbook provides additional practice for each section and guidance for test preparation. Published in an unbound, binder-ready format, the Learning Guide can serve as the foundation as the student's course notebook.
Extensive exercise sets offer several types of exercises. This variety makes it easy to create well-rounded homework assignments from the text or in MyMathLab. Exercise types include the following:
NEW! Concept and Vocabulary Checks provide fill-in-the-blank and true/false exercises that assess students' understanding of the definitions and concepts presented in the section. These are also assignable in MyMathLab.
Practice Plus Problems are more challenging exercises that require students to combine several skills or concepts.
Writing in Mathematics exercises ask students to explain terms and concepts in their own words, helping them to develop a mathematical vocabulary.
Critical Thinking Exercises stretch student thinking by taking concepts one step further while asking students to draw conclusions and justify answers. Make Sense and True/False exercises also fall under this category.
Preview Exercises help students prepare for the following section by previewing the concepts that they will soon encounter.
Mid-Chapter Check Points allow students to stop and assess the skills and concepts they've learned separately over several sections. The Mid-Chapter Check Points will now be available as a pre-made assignment in the Blitzer MyMathLab courses.
Check Point exercises after every example make the text more interactive by offering students the opportunity to test their understanding of the example by working a similar exercise. Answers to all of the Check Points are in the answer section.
Chapter Summaries are organized by section and highlight important concepts and topics with side-by-side examples to make it easy for students to study and check for mastery of important chapter content.
Author
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. When not secluded in his Northern California writer's cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters. |
Title
Authors
Comments
This lesson focuses on a topic that deals with the relationship between two quantities, known as independent and dependent variables.
Document Type
Lesson Plan
Abstract
This lesson occurs towards the beginning of a unit on functions, a mathematical topic that deals with the relationship between two quantities, known as independent and dependent variables.The goal for this lesson will be to draw upon students' intuitive awareness of cause and effect, and to apply this knowledge to authentic, real-world situations. This will give students the theoretical and conceptual foundations they will need to grasp more complex and formulaic ideas in the unit. It will also promote meaningful learning as it will show students how mathematics is relevant to their everyday lives. Through this lessons tudents will be able to identify independent and dependent variables in the real world and express the relationship between specific independent and dependent variables |
Examines currents in the development of mathematics and throughout ancient Egypt, Babylon, China, and the Middle East. It studies math's influence on society through the major events of Europe, contemporary developments, and some projections into the future, including the women and men who played key roles in evolution of mathematics.
Course Learning Outcomes:
Discuss some of the major milestones in the development of mathematics and how public thought was influenced by them: from early mysticism to the sixteenth century desire to classify and categorize that introduced Arabic numerals to England and forever altered commerce, navigation and surveying; From the belief in the power of rational, logical thought expressed by Newton or Boole to the loss of certainty expressed in Godel's Theorem. From a sense of the individual soul to the attitude of becoming a statistics and to the possibility that the human brain state can be modeled with a fairly sophisticated computer.
Do some mathematics of various time periods.
Discuss current directions in mathematics education.
Specified Program Learning Outcomes:
BACHELOR OF ARTS IN MATHEMATICS EDUCATION
Employ a variety of reasoning skills and effective strategies for solving problems both within the discipline of mathematics and in applied settings that include non-routine situations
Employ algebra and number theory ideas and tools as a base of a fundamental language of mathematics research and communication
Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines
MAJOR IN MATHEMATICS
Employ a variety of reasoning skills and effective strategies for
solving problems both within the discipline of mathematics and in
applied settings that include non-routine situations
Model real world problems with a variety of algebraic and
transcendental functions
Use advanced statistics and probability concepts and methods
Use current technology tools, such as computers, calculators,
graphing utilities, video, and interactive programs that are
appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate
mathematical ideas in the connections and interplay among
various mathematical topics and their applications that cover
range of phenomena across appropriate disciplines
MAJOR IN MATHEMATICS WITH A PRELIMINARY SINGLE SUBJECT TEACHING CREDENTIAL (CALIFORNIA)
Employ a variety of reasoning skills and effective strategies for
solving problems both within the discipline of mathematics and in
applied settings that include non-routine situations
Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate
mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines |
CBSE Board Textbook for Math
As we all know there are so many students who have problems in Math subject as they found Math as a difficult subject that is the reason we have introduced CBSE Board Math Text Books to the students. CBSE uses NCERT book for the students of all classes but for more practice and to increase the knowledge of students, you will find information about the reference books on our web site which are according to CBSE Pattern and Syllabus. CBSE Board Text book Math is really helpful to increase the knowledge about the subject. On our website you will find some question papers, Solved questions and answers, Question banks, Sample papers for all classes of students. The Math subject in school starts from Class 1 to Class 12th. We have given information about all classes but we have primary focus on Board exams as it is very important. In Board exams to score good marks, students need to do study from CBSE Board Math Text Book. For more practice of the questions, they can also study from references books, previous year sample papers.
You will find guess papers, question banks, Test Series which are made by our experts according to CBSE patterns. You will also get to know from our website about the marking system of the CBSE Board exams. We have the facility of online assistant about CBSE Board Math Text Book on our website. Our motive is to give all information about the CBSE Board Text books for Math to our students so that students will have complete knowledge about the books, syllabus, and pattern. It is also helpful in decreasing the fear of exams during the exams and it minimizes the stress level of the students and they can concentrate more in the studies to score good marks in examination
CBSE Board Textbook for Math by Class
CBSE Board Best Sellers
In order to keep pace with technological advancement and to cope up with CBSE Board examinations, Pearson group has launched Edurite to help students by offering Books and CDs of different courses online. |
Introductory Physics with Algebra as a Second Language: Mastering Problem-Solving
Many students find it difficult to master the fundamental skills that are essential to succeeding in physics. Now with this helpful book, they'll quickly learn how to break physics down into basic steps. Author Stuart Loucks presents the material in a way that will motivate and empower them. He offers clear explanations of key concepts while examining the fundamental topics and approaches needed to solve algebra-based physics problems.
Understand the basic language of physics Introductory Physics with Algebra as a Second Language™ will help you make sense of your textbook and class notes so that you can use them more effectively. The text explains key topics in algebra-based physics in clear, easy-to-understand language.
Break problems down into simple steps Introductory Physics with Algebra as a Second Language™ teaches you to recognize details that tell you how to begin new problems. You will learn how to effectively organize the information, decide on the correct equations, and ultimately solve the problem.
Learn how to tackle unfamiliar physics problems
Stuart Loucks coaches you in the fundamental concepts and approaches needed to set up and solve the major problem types. As you learn how to deal with these kinds of problems, you will be better equipped to tackle problems you have never seen before. |
Description
This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs.
Table of contents
Preface
PartI. ONE-DIMENSIONAL THEORY
1. The Real Number System
1.1 Introduction
1.2 Ordered field axioms
1.3 Completeness Axiom
1.4 Mathematical Induction
1.5 Inverse functions and images
1.6 Countable and uncountable sets
2. Sequences in R
2.1 Limits of sequences
2.2 Limit theorems
2.3 Bolzano-Weierstrass Theorem
2.4 Cauchy sequences
*2.5 Limits supremum and infimum
3. Continuity on R
3.1 Two-sided limits
3.2 One-sided limits and limits at infinity
3.3 Continuity
3.4 Uniform continuity
4. Differentiability on R
4.1 The derivative
4.2 Differentiability theorems
4.3 The Mean Value Theorem
4.4 Taylor's Theorem and l'Hôpital's Rule
4.5 Inverse function theorems
5 Integrability on R
5.1 The Riemann integral
5.2 Riemann sums
5.3 The Fundamental Theorem of Calculus
5.4 Improper Riemann integration
*5.5 Functions of bounded variation
*5.6 Convex functions
6. Infinite Series of Real Numbers
6.1 Introduction
6.2 Series with nonnegative terms
6.3 Absolute convergence
6.4 Alternating series
*6.5 Estimation of series
*6.6 Additional tests
7. Infinite Series of Functions
7.1 Uniform convergence of sequences
7.2 Uniform convergence of series
7.3 Power series
7.4 Analytic functions
*7.5 Applications
Part II. MULTIDIMENSIONAL THEORY
8. Euclidean Spaces
8.1 Algebraic structure
8.2 Planes and linear transformations
8.3 Topology of Rn
8.4 Interior, closure, boundary
9. Convergence in Rn
9.1 Limits of sequences
9.2 Heine-Borel Theorem
9.3 Limits of functions
9.4 Continuous functions
*9.5 Compact sets
*9.6 Applications
10. Metric Spaces
10.1 Introduction
10.2 Limits of functions
10.3 Interior, closure, boundary
10.4 Compact sets
10.5 Connected sets
10.6 Continuous functions
10.7 Stone-Weierstrass Theorem
11. Differentiability on Rn
11.1 Partial derivatives and partial integrals
11.2 The definition of differentiability
11.3 Derivatives, differentials, and tangent planes
11.4 The Chain Rule
11.5 The Mean Value Theorem and Taylor's Formula
11.6 The Inverse Function Theorem
*11.7 Optimization
12. Integration on Rn
12.1 Jordan regions
12.2 Riemann integration on Jordan regions
12.3 Iterated integrals
12.4 Change of variables
*12.5 Partitions of unity
*12.6 The gamma function and volume
13. Fundamental Theorems of Vector Calculus
13.1 Curves
13.2 Oriented curves
13.3 Surfaces
13.4 Oriented surfaces
13.5 Theorems of Green and Gauss
13.6 Stokes's Theorem
*14. Fourier Series
*14.1 Introduction
*14.2 Summability of Fourier series
*14.3 Growth of Fourier coefficients
*14.4 Convergence of Fourier series
*14.5 Uniqueness
Appendices
A. Algebraic laws
B. Trigonometry
C. Matrices and determinants
D. Quadric surfaces
E. Vector calculus and physics
F. Equivalence relations
References
Answers and Hints to Exercises
Subject Index
Symbol Index
*Enrichment section
New to this edition
Changes to the Exercises
Computational exercises have been rewritten so that answers are simpler and easier to obtain.
Calculus-style exercises at the beginning of the book have been revised to be more conceptual, emphasizing the same ideas, but at a higher level.
Theoretical exercises of medium difficulty have been added throughout the book.
New True/False questions in the first six chapters confront common misconceptions that students sometimes acquire at this level.
Content Updates
A new section 1.1, Introduction, combines introductory material that was previously scattered over several sections. This section includes two accessible examples about why proof is necessary and why we cannot always trust what we see.
The number of axioms has been reduced from four to three by introducing the Completeness Axiom first, and using it to prove the Well Ordering Principle and the Principle of Mathematical Induction.
The material on countable sets and inverse images of sets has been postponed to Chapter 3, making it possible to begin discussing limits of sequences even earlier than before.
Coverage of Taylor's Formula has been moved from Chapter 7 to Chapter 4 to offer another example of the utility of the Mean Value Theorem.
The Heine-Borel Theorem now has its own section and includes several exercises designed to give students practice in making a local condition on a compact set into a global one.
Section 12.1, Jordan regions, has been organized to simplify the presentation and make it easier to teach.
Features & benefits
Flexible presentation, with uniform writing style and notation, covers the material in small sections, allowing instructors to adapt this book to their syllabus.
The practical focus explains assumptions so that students learn the motivation behind the mathematics and are able to construct their own proofs.
Early introduction of the fundamental goals of analysis Refers and examines how a limit operation interacts with algebraic operation.
Optional appendices and enrichment sections enables students to understand the material and allows instructors to tailor their courses.
An alternate chapter on metric spaces allows instructors to cover either chapter independently without mentioning the other.
More than 200 worked examples and 600 exercises encourage students to test comprehension of concepts, while using techniques in other contexts.
Reorganized coverage of series separates series of constants and series of functions into separate chapters.
Consecutive numbering of theorems, definitions and remarks allows students and instructors to find citations easily.
Author biography
William Wade received his PhD in harmonic analysis from the University of California—Riverside. He has been a professor of the Department of Mathematics at the University of Tennessee for more than forty years. During that time, he has received multiple awards including two Fulbright Scholarships, the Chancellor's Award for Research and Creative Achievements, the Dean's Award for Extraordinary Service, and the National Alumni Association Outstanding Teaching Award.
Wade's research interests include problems of uniqueness, growth and dyadic harmonic analysis, on which he has published numerous papers, two books and given multiple presentations on three continents. His current publication, An Introduction to Analysis,is now in its fourth edition.
In his spare time, Wade loves to travel and take photographs to document his trips. He is also musically inclined, and enjoys playing classical music, mainly baroque on the trumpet, recorder, and piano. |
This textbook includes all the features of the longer book, but is designed for a course in which the time available limits the number of topics covered. The book is written for general beginning statistics courses with a basic algebra prerequisite. Solutions are worked out step-by-step where appropriate and generally follow the same procedures used in the examples in the textbook.
This textbook offers instructors an effective solution to teaching the fundamentals of statistics within a more limited time frame. The book use a non-theoretical approach, explaining concepts intuitively and teaching problem solving through worked examples step-by-step. |
Catalina ACT Math has found its way into all the sciences including the daily weather reports, biology and even theoretical physics, and that is why you need to know about it. Linear algebra is the study of simultaneous linear equations. They can be solved with one of two methods: substitution or elimination of a variable |
*—"Core" math modules (PRE, ALG,
GEO, TRI) are sold in packages. Buy any three for $395, or
all four for $495.
Algebra II / Trigonometry (TRI)
Algebra II / Trigonometry is another of Acces' core instructional
modules. It provides teachers with 16,000 free-response problems covering
advanced algebra, trigonometry, and some pre-calculus topics. The module is very
thorough in its coverage, provides lots of challenging problems, and is a good
supplement to most advanced algebra textbooks.
The following list provides an overview of the module's 161 categories (topics):
Algebra review
Radical expressions, rational exponents
Complex numbers
Quadratic equations and inequalities
Linear equations in two variables
Linear systems
Theory of roots
Introduction to functions
Polynomial and rational functions
Conics
Exponential and logarithmic functions
Sequences and series
Right triangle trigonometry
Arcs, angles, and the wrapping function
Circular trigonometry
Trigonometric functions and graphs
Trigonometric identities and equations
As one of EducAide's core modules, Algebra II / Trigonometry is
useful for both instruction and Assessment. Though designed for math classes in
grades 11–12, it would be quite appropriate for an introductory algebra
course at the college level. Much of the database that covers functions, systems
of equations, and right triangle trigonometry could also be used in grades 9–10,
and the more advanced topics would be suitable for review in a calculus course.
The principal author of the Algebra II / Trigonometry module is
Janet Fortney, a high school and community college math teacher, currently at
Charlotte Country Day School (NC). |
Mathematics & Science Computing
and Distance Learning
The Math Sciences provides a variety of online support services for P-20 programs in the STEM areas across the commonwealth of Kentucky.
Webclass is a website providing an interactive environment for UK class homework and diagnostic testing (
The Kentucky Center for Mathematics receives technology support for mathematics coaching and intervention programs statewide. (
The Web Homework System (WHS) distributes homework assignments with immediate feedback for the results of student work as well as providing an authoring and class management environment for the assignments themselves. (
The Kentucky Early Mathematics Testing Program (KEMTP) provides on-line testing to help high school students determine their level of preparedness for learning college level mathematics. (
The Kentucky Mathematics Placement Examinations are scheduled proctored on-line examinations, the results of which are shared amongst the participating schools for the purpose of placing students into classes appropriate to the level of preparedness of the student. (
The Access to Algebra/CATSbusters program, which originated as a service for students who had exhausted the mathematics available at their local school, affords high school students the opportunity to take a college algebra course at no cost for tuition, fees, or materials. In the program, participating teachers sponsor small numbers of students and then mentor them as they take a UK college algebra course on the same schedule, with the same text, the same online homework, and the same uniformly, hand-graded examinations as an on-campus, comparison group. The program uses a modified distance-learning format in which the teachers meet online weekly to formatively evaluate the course and confer on the content. ( The textbook for the course may be found at
~sohum/ma109_fa07/fa07_edition/ma109fa07.pdf |
A typical maths module common to many business courses is "Introduction to
Business Mathematics".
Introduction to Business Mathematics.
In this module four of the six learning outcomes relate directly to mathematics topics:
1) Use a calculator to perform common commercial percentage calculations.
2) Perform simple and compound interest calculations
3) Perform basic depreciation calculations
4) Apply the principles of linear equations to do break-even analysis.
The Victoria University of Technology TAFE provides a Business Mathematics module in
two departments.
Marketing and Public Relation Department, including International Trade.
The module " Introduction to Business Mathematics" is part of
Certificate IV in Business (Sales, Marketing). This certificate is Stage 1 of the
Advanced Diploma of Business (Marketing)). The diploma aim to provide career
opportunities in Marketing Officers, Marketing Researchers, Product/Sales Managers, and
Assistant Marketing Managers. After successful completion of Stage 1, Certificate
IV in Business (Sales and Marketing), participants should be able to undertake positions
as assistant Marketing Officer, Market research field workers and Assistant Product/Sales
Manager. The module is also part of the Advanced Diploma of Business (International
Trade) of which Stage 1 us Certificate IV in Business (International Trade). The
objective of this course is to provide participants with the opportunity to gain knowledge
skills relation to international marketing which includes: market research, strategic
planning communications, use of computer facilities and the Australian and international
legal systems.
Financial Services Department.
The module "Business Mathematics" is part of Diploma of Business (Accounting)
which is Stage 1 of the Advanced Diploma of Business (Accounting)). The Advanced
Diploma of Business (Accounting) aims to provide participants with the skills required to
carry out the duties and tasks of a para-professional accountant. The Diploma of
Business (Accounting) aims to provide participants with the skills required for employment
as payroll clerks, cost clerks, audit clerks, assistant accountants and related
occupations. |
Applied Mathematician
Applied mathematicians use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, and engineering and in the physical, life, and social sciences. Applied mathematicians start with a practical problem, envision the separate elements of the process under consideration, and then reduce the elements to mathematical variables. They often use computers to analyze relationships among the variables and solve complex problems by developing models. |
Edurite CBSE Class 11 MathematicsEdurite CBSE Class 11 Mathematics (CD) Price: Rs.464
Mathematics is a subject that requires a through understanding of concepts. Edurites CDs work on building concepts and also give students a lot of practice with questions on each Mathematical topic. Our CDs include chapter wise coverage of each topic with a clear voice over, A glossary of Mathematical terms commonly used and a synopsis of all chapters, Tips and techniques and easy learning techniques for scoring well in exams and online courses on each topic |
Find a Dania CalculusIt includes the study of transformations and right triangle trigonometry. Inductive and deductive thinking skills are used in problem solving situations, and applications to the real world are stressed. It also emphasizes writing proofs to solve (prove) properties of geometric figures. |
Search Digital Classroom Resources:
Flash Tools for Developers (AS3): Graphing curves in the plane
Flash CS3 (Actionscript 3.0) templates and classes for graphing functions in one variable as well as parametric curves in rectangular or polar coordinates.
Digital Classroom Resources
Actionscript 3 Tutorials
by Doug Ensley, Barbara Kaskosz
Overview
Doug Ensley
Shippensburg University
Barbara Kaskosz
University of Rhode Island
ActionScript 3.0 is new; it is exciting, fast, and fully object-oriented. Flash CS3 authoring environment and ActionScript 3.0 provide a great tool for educators in mathematics and sciences to create their own, custmized web-based learning aids. Most of available samples, books, and articles on ActionScript 3.0 (AS3) are not written with mathematical applications in mind and Flash's great potential in that respect is only now being realized. This is where our MathDL Flash Forum and this collection of tutorials come in. You will find here a collection of ActionScript 3.0 and Flash CS3 tutorials prepared with a mathematics educator in mind. We will help you learn AS3 through creating mathematical objects and applets. |
Calculus : Easy Way - 4th edition
Summary: This ingenious, user-friendly introduction to calculus recounts adventures that take place in the mythical land of Carmorra. As the story's narrator meets Carmorra's citizens, they confront a series of practical problems, and their method of working out solutions employs calculus. As readers follow their adventures, they are introduced to calculating derivatives; finding maximum and minimum points with derivatives; determining derivatives of trigonometric functions; ...show morediscovering and using integrals; working with logarithms, exponential functions, vectors, and Taylor series; using differential equations; and much more. This introduction to calculus presents exercises at the end of each chapter and gives their answers at the back of the book. Step-by-step worksheets with answers are included in the chapters. Computers are used for numerical integration and other tasks. The book also includes graphs, charts, and whimsical line illustrations. Barron's Easy Way books focus on both practical and academic topics, presenting fundamental subject matter in clear, understandable language. Equally popular as self-teaching manuals and supplementary texts for classroom use, they are written to help students improve their grades and review subject matter before tests. They are also useful for introducing general readers to a new career-related skill. Easy Way titles cover virtually all subjects that are taught on advanced high school and college-101 levels. New subjects are periodically added, and existing titles are frequently updated to keep them timely and relevant to students' needs. Subject heads and key phrases are set in a second color5.16 +$3.99 s/h
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Personal Math Companion
Synopsis
This quick reference guide is suitable for students in middle school, grades 6-8. The book will serve as a true companion by providing quick access to the metric system, basic algebra, geometry, exponents, probability, mathematical formulas, intro to statistics, and much more. This is truly the ultimate companion for students who wishes to excel in math. The Personal Math Companion will have all the answers to the tough math questions that are frequently asked by students in the 6th, 7th, or 8th grades. "« Do you want to know how to find the third angle of a triangle? "« How to use and understand a number line for better assistance when handling real numbers? "« Classifying the different types of polygons? Well, it has all these answers and more, plus helpful tips that will help your children to understand the different concepts of mathematics |
Find a Picacho
...Start any word problem with labeling the unknown, "Let x = the number of ...." It is this great art that has so greatly advanced all the modern sciences. Think of it as the art that supports the sciences! Algebra 2 comes after Algebra 1,which is the science of linear and quadratic equations (the building blocks of all polynomials)in order to solve problems.
...It is important to understand the basic concepts of algebra before continuing to Algebra II. Students will learn to solve equations and inequalities. They will become proficient in factoring and simplifying algebraic fractions |
Helping Students Pre-AlgebraFacilitate students transition from arithmetic to algebra! Includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. Supports NCTM standards. |
Survey of Mathematics With Applications
9780321112507
ISBN:
0321112504
Edition: 7 Pub Date: 2004 Publisher: Addison-Wesley
Summary: The sixth edition of this best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical ideas as they relate to varied disciplines. This book provides an appreciation of mathematics, highlighting mathematical history, applications of mathematics to the arts and sciences across cultures, and introduces students to the uses of technology in mathematics. Exercise sets are now organ...ized into Concept/Writing, Practice the Skills, Problem Solving, Challenge Problems/Group Activities, Research Activities. An updated Consumer Math section including updated material on sources of credit and mutual funds. Motivational, chapter-opening material demonstrates connections between math and various other disciplines. KEY MARKET For those who require a general overview of mathematics, especially in the fields of elementary education, the social sciences, business, nursing and allied health fields |
Suggested Project Topics
Here are a few ideas for project topics for final year, higher diploma, and
Masters students. The only common thread is that they combine some
mathematics with compuation.
1. Program a LEGO Robot using Matlab
The goal will be to learn how to programme real-time systems,
model-based design, and develop
object oriented Matlab code. These can be applied to
contoling LEGO Mindstrom NXT robot.
2. The Singular Value Decomposition, and it's applications.
The singular value decomposition (SVD) is an important
factorization of a matrix with interesting applications to
a wide variety of areas such as image and signal processing,
data compression, computational tomography, etc..
For one example of the the SVD can be applied to problems involving in face
recognition, see Singular Value Decomposition, Eigenfaces, and 3D Reconstructions by Neil Muller, Lourenco Magaia,
B.M. Herbst
You should consider this project if you like Linear Algebra. Some
computing will be essential, but not necessarily
anything too difficult.
3. Numerical Algorithms for Parallel Computers
Many classical numerical methods were designed for single-processor computers.
Examples include Gaussian elimination
or Numerical Integration. With the advent of parallel,
multiprocessor and distributed systems, there is a need to revisit
many of these methods and to see how they can be adapted for parallel
computation.
A different example is Schwarz Methods for linear boundary
value problems. These have existed for over 100 years, but are being
``rediscovered'' because they are so suitable for parallel computers
A project on this topic would mainly involve programming and algorithm
design. Code could be tested on some Linux computers running software to
emulate parallel and distributed systems.
The student who does this project should like programming.
It would be useful
to have studied numerical analysis.
4. Simulating Small-World Networks
Many networks that occur naturally have two properties: clustering and
short average path-lengths. This is called the small world
phenomenon and is related to research activities in very diverse
areas. To verify this, check a web search engine for such topics as
Six Degrees of Separation and The Kevin Bacon Game
A student working on this project will, at the very least, read
a number of articles on the topic, learn enough mathematics to
understand some of the theorems and conjectures in the area, and write
some computer programs to simulate these networks.
The project would suit a student with interests in programming and
graph theory. Some knowledge is stochastic processes and Markov chains
would be useful.
5. Topics in Numerical Analysis
Numerical Analysis is the area of mathematics that is concerned
with the design and analysis of methods and algorithms for obtaining
useful solutions to mathematical problems. Two of the main sources of
problems are differential equations and linear algebra. The
applications are far too numerous to mention.
The interested student should browse a few books in the library. For
example
Afternotes on Numerical Analysis and
Afternotes goes to Graduate School
(G.W. Stewart),
Introduction of Numerical Analysis (Stoer and
Bulirish),
Depending on the students' interests, projects may have little or no
computing aspects, or may be strongly focused on computational
problems, or something in between.
6. Some topic of mutual interest
Why not come up with your own idea? A good place to start
would be the Education articles in
SIAM
Review. Or you could go to the
library and have a look at such titles as |
Windows Software
equationsThis bilingual problem-solving mathematics software allows you to work through 19292 trigonometric equations with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. The software includes all trigonometr...
Qds Equations - equation editor is a set of visual components for Delphi that allow to enter and display formulas of any complexity, from simple Greek symbols to matrixes and complex integral expressions. You can use the equation editor in your projects written in the Delphi environment, for example... ...
This bilingual problem-solving mathematics software allows you to work through 84102 trigonometric problems with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. The software offers tasks on simplific ...
MatBasic is a calculating, programming and debugging environment using special high-level programming language designed for solving mathematical problems. MatBasic programming language allows execution of difficult mathematical calculations, involving an exhaustive set of tools for the purpose of cr ... |
Math and Science Workbook
This study guide provides students with review and practice of the math and science questions they're sure to see on the ACT exam. Each section ...Show synopsisThis study guide provides students with review and practice of the math and science questions they're sure to see on the ACT exam. Each section begins with review and is followed by a 17-question practice set with complete answers and explanations to help students improve their scores.Hide synopsis
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Description:Good. Paperback has been read, but remains in clean condition....Good. Paperback has been read, but remains in clean condition. All pages are intact, and the cover is intact. There is light highlighting or handwriting through out the book |
Module Description
This course revises ideas associated with continuous functions, including the idea of an inverse, differentiation and integration, and sets them in a more fundamental context which permits a better understanding of their properties. Differential equations are introduced, and methods for solving them are studied. The properties of inequalities are reviewed. Complex numbers in Cartesian form are introduced.
Syllabus
Geometry and Trigonometry:
- Pythagoras' theorem; trigonometric functions.
- Basic manipulation of inequalities
Functions of one variable:
- the functions exp, ln, xa, |x|, trigonometric and hyperbolic functions; their domains and their graphs;
Learning & Teaching Methods
This course consists of 30 contact hours given at 3 hours per week commencing in week 2 (the first teaching week). There will be a test at the end of term and five assessed problem sheets throughout the term. Three revision lectures will also be given in the summer term.
Assessment
25 per cent Coursework Mark, 75 per cent Exam Mark
Other details: Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework Information
Exam Duration and Period
1:30 hour exam during Summer Examination period.
Other information
'A' level Maths or equivalent normally required. Available independently to Socrates/IP students spending all relevant terms at Essex. |
MATHEMATICS AT EUREKA
Mathematics, more than any other human endeavor, relies on deductive reasoning to produce new knowledge from the investigation of natural events, whether they occur in our immediate environment or in the immensity of space. It serves as a universal language which represents, interprets, and integrates all such knowledge.
The subject of mathematics is divided into algebra, geometry, analysis, and probability. Some of the concepts of each of these subdivisions are particularly useful in helping to discuss or solve problems in other fields. These concepts are frequently called Applied Mathematics.
REQUIREMENTS FOR A MAJOR IN MATHEMATICS –
38 hours of coursework, consisting of the following:
All of the following:
MAT171
Calculus with Analytic Geometry I
4
MAT271
Calculus with Analytic Geometry II
4
MAT272
Calculus with Analytic Geometry III
4
MAT275
Differential Equations
3
MAT280
Discrete Mathematics
3
MAT310
Probability and Statistics
3
MAT315
Linear Algebra
3
MAT320
Abstract Algebra
3
MAT340W
Foundations of Geometry
3
MAT415
Real Analysis
3
S&M286
Problem Solving in Science & Mathematics
2
One of the following:
CSC135
Computer Science I
3
CSC165
Computer Science II
3
TOTAL:
38
REQUIREMENTS FOR A MINOR IN MATHEMATICS –
20 hours of coursework in Mathematics numbered 171or above, including at least six hours at the 300-level or higher.
REQUIREMENTS FOR A MAJOR IN MATHEMATICS WITH TEACHER CERTIFICATION –
42 hours of coursework, consisting of the following:
1. The Mathematics major outlined above.
2. One additional course from the following: PHS110 (Introduction to Physical Science), PHS111 (Introduction to Earth Science), or any PHY course
Plus Professional Education Course Requirements. For a list of these courses, please refer to the Education section of the catalog concerning requirements for certification in Secondary Education. To qualify for Student Teaching, a student must have a cumulative 2.50 GPA and a 2.75 GPA in the Mathematics major outlined above.
REQUIREMENTS FOR A MAJOR IN ELEMENTARY EDUCATION WITH A MATHEMATICS SPECIALIZATION –
28 hours of coursework. Please refer to the Education section of this catalog for a listing of required courses.
Get to Know...
Mrs. Rachel Gudeman
Lecturer in Mathematics. Mrs. Gudeman received her B. S. from Illinois State University, and is currently attaining her M.S. in Mathematics from Illinois State University. She has taught all levels of highschool mathematics especially for the home-schooled population. She has taught at Eureka College since Fall 2012. Mrs. Gudeman enjoys teaching and helping students learn and understand mathematics in order to achieve their goals and earn a college degree.
Mrs. Elisha VanMeenen
Lecturer in Mathematics. Mrs. VanMeenen received her B. S. in Mathematics from Illinois Wesleyan University, M.B.A. from the University of Illinois, M.S. in Mathematics from Illinois State University, and is currently working on her Ph.D. in Mathematics Education from Illinois State University. She teaches full time at ISU, and is in her third semester teaching part-time general education mathematics for Eureka College. She is interested helping students learn and understand mathematics in order to achieve their goals and earn a college degree.
Mr. Kevin Brucker
Lecturer in Mathematics, came to Eureka College in 2004. His teaching focuses on Statistics and Mathematics for Elementary Teachers. He holds a B.S. in Mathematics from McKendree College and an M.A.S. (Master of Applied Statistics) from The Ohio State University. In addition to his teaching duties, Mr. Brucker works as the Teacher Education Assessment Coordinator and Transfer Advisor. |
Intro to Geometry: Grades 5-8 by Instructional Fair
This revised edition of Intro to Geometry links all the activities to the NCTM Standards. The activities were designed to provide students with practice in the skill areas required to understand basic geometry concepts. Activities that focus on congruence and similarity, classifying various kinds of angles and triangles, transformations, parallel and perpendicular lines, properties of geometric figures, arcs and chords, and finding surface area and volume are all part of the new edition. Examples of solution methods are presented at the top of each page. New puzzles and riddles have been added to gauge the success of the concepts learned. Contains complete answer key. 128 pages |
Course Number and Title
Number of Credits
Minimum Number of Instructional Minutes Per Semester
Prerequisites
Corequisites
None
Other Pertinent Information
At least four one-hour tests, quizzes, and a two-hour comprehensive departmental final examination will be given.
Catalog Course Description
This is the first course in the calculus sequence for physical science, business, computer science, mathematics, and engineering students. Topics include: limits, the rate of a function, derivatives of algebraic and basic trigonometric functions, applications of derivatives, integration, and applications of the definite integral.
Required Course Content and Direction
Learning Goals:
Course Specific:
The student will be able to:
demonstrate understanding of the concept of limit.
evaluate limits.
demonstrate understanding of the concept of continuity.
evaluate derivatives of algebraic and trigonometric function.
demonstrate correct use of implicit differentiation to find a derivative.
Category III: Critical Thinking/Problem Solving: The student will be able to:
demonstrate an understanding of solving problems by:
recognizing the problem
reviewing information about the problem
developing plausible solutions
evaluating the results
These skills are developed in VII.B.3 and VII.B.5.
Planned Sequence of Topics and/or Learning Activities:
The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lesions required to study the topic.
Limits and Continuity (8 lessons)
Geometric Interpretation of Limits
Evaluating Limits
Limit Theorems
One-Sided Limits
Continuity
The Derivative (12 lessons)
Geometric Interpretation - Tangent Line to a Curve
Definition of Derivative
Velocity, Acceleration, and Other Rates of Change
Finding Derivatives, Using the Limit Definition
Finding Derivatives, Using the Formulas
Product and Quotient Rules
Derivatives of Basic Trigonmetic Functions
Chain Rule and Composite Functions
Implicit Differentiation
Higher Order Derivatives
Applications of the Derivative (12 lessons)
Straight Line Motion
Related Rates
Increasing and Decreasing Functions
Relative and Absolute Extrema
Concavity and Inflection Points
2nd Derivative Test
Optimization Problems
Differentials
Integration (9 lessons)
Indefinite Integrals
Differential Equations
Summation Notation
Finding Areas and Definite Integrals by Definition
Fundamental Theorem of Integral Calculus
Properties of the Definite Integral
Using Substitution to Evaluate Integrals
Applications of Integration (7 lessons)
Area Under a Curve
Average Value of a Function
Area Between Curves
Volumes of Revolution - Disk and Shell Method
Length of a Plane Curve
open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:
Departmentally selected textbook and graphing calculator. Details provided by the instructor of each course section. See Course Format. |
10. Gain competency in other areas of mathematics (which ones
and how many depends on the selected option).
11. Demonstrate basic competency in both oral and written
communication.
MS Mathematics
In the Mathematics MS program students choose one of two
options: Option 1 (General Mathematics) and Option 2 (Applied
Mathematics). The learning outcomes are somewhat different for
each as seen below.
Graduating students in both options will:
1. Have a broad exposure to advanced mathematics through
electives chosen from a wide range of topics including abstract
algebra, advanced calculus, geometry, differential equations,
linear algebra, probability, number theory, and topology.
2. Understand and devise proofs of mathematical theorems. This
includes understanding the role of definitions, axioms, logic,
and particular proof techniques such as proof by induction,
proof by contradiction, etc.
3. Be able to write a coherent, clear article on a mathematical
theme, and to present this orally.
4. Be able to search the mathematical literature to research a
topic of interest.
5. Understand and be able to apply basic results of complex
analysis including: the relationship between complex analytic
functions and harmonic functions, conformal mapping, and
applications to Dirichlet problems; Cauchy's integral formulas
and their consequences including the fundamental theorem of
algebra; series expansions, classification of singularities, and
the application of residue calculus to definite integrals and
sums.
Graduating students in Option 1 (General Math) will:
1. Have a broad understanding at the graduate level of the
content of the required courses of the option. This includes the
theory of groups, rings and fields, topology, complex analysis,
and real or functional analysis.
2. Understand the basic theories of groups, rings and fields,
including the structure of finite groups, polynomial rings and
Galois theory.
3. Understand how the main topological concepts (connectedness,
compactness, products and separation properties) are introduced
and used in abstract spaces where the topological structure is
not derived from an underlying metric.
4. Understand basic set theory including axiom of choice, basic
topological properties of the real line; properties of real
functions, sequences of real functions and various notions of
convergence such as pointwise and uniform convergence.
1. Have a broad understanding at the graduate level of the
content of the required courses of the option. This includes
numerical analysis, linear analysis, mathematical modeling and
complex analysis.
2. Be able to use a variety of mathematical tools (differential
equations, linear algebra, etc) to formulate a mathematical
model of real world problems. Understand the balance between the
complexity of a model and its mathematical tractability.
Understand the iterative process of modeling and the necessity
to test a model against data.
3. Be able to apply numerical methods to solve problems, such as
large systems of linear equations, eigenvalue/eigenvector
problems, and understand the theoretical underpinnings of these
methods.
4. Be able to solve partial differential equations numerically
and be able to analyze the stability and convergence of these
approximate solutions. This includes the understanding of the
fundamental differences among parabolic, elliptic and hyperbolic
partial differential equations, the Max/Min principle for
certain elliptic partial differential equations and the method
of characters for and second order hyperbolic partial
differential equations.
5. Understand metrics, norms, and inner products on important
spaces of functions, including Banach spaces and Hilbert spaces
and be able to use important applications including Fourier
series and solutions of integral equations by contraction. They
will be familiar with basic properties of linear operators,
especially on Hilbert spaces, invertiblity and spectrum, and be
able to apply these to solution of integral equations and
differential equations. |
Saxon Algebra I textbook is designed to differ from a
traditional textbook in three areas: (1) the text is organized into
lessons to avoid the uneven or abrupt flow of material that can result
when topics are organized into chapters, (2) Saxon uses an extensive
conversational presentation of the material rather than charts and
diagrams, and (3) only a small number of the exercises in each lesson are
on the new material, the majority are practice and drill of previously
presented concepts and skills.
Strategy: Graphing
calculator Subjects: 294 pre-university Dutch
students, 16-17 years old. Results: Students in the
treatment group made significantly more use of graphical solutions than
the students in the control group. Males used the graphing calculator
significantly more than females. The graphing calculator had a positive
effect on the weaker math students.
Description: This study utilized two experimental
conditions and one control condition in a senior high mathematics
classroom. Three classrooms used the graphing calculator throughout the
year with all topics in their textbook. Five classrooms used the graphing
calculator for only one topic for a two-month long implementation and four
classrooms (control group) covered the topics in the textbook without
using the graphing calculator Skills and concepts learned and applied
using the University of Chicago School Mathematics Project (UCSMP)
Advanced Algebra textbook Subjects: 306
students in heterogeneous classes studying second-year algebra in four
high schools. The high schools selected were in a White middle-class
suburb of Atlanta, a rural area that is becoming a suburb of Chicago, a
small semi-rural community in Mississippi, and an affluent suburb of
Philadelphia. Of the students, 19% were in Grade 10, 76% in Grade 11, and
5% in Grade 12. Additionally, 84% were Caucasian, 3% African American, 1%
Hispanic, while the remainder were classified as other or
unknown. Results: Students using the UCSMP curriculum
significantly outperformed students in the comparison curriculum
(p=0.0014) on all items of the post-test. However, analysis of
the items all students in the study had the opportunity to learn did not
indicate a significant difference (p=0.108). Performance on the
eight skill items in this last analysis was comparable for the two
curricula.
Description: UCSMP is a curriculum that uses
reading and problem solving, realistic applications, technology (graphing
calculators and/or computers), a multidimensional approach understanding,
and an instructional format featuring continual review combined with a
modified mastery-learning strategy. It emphasizes
understanding of concepts through multiple representations, realistic
contexts, and the use of technology. There is less emphasis on skills than
in a traditional curriculum. The instructional method often uses
small-group explorations and extended projects, both involving writing
about mathematics Webb.
The impact of the
Interactive Mathematics Program on student learning teachSubjects: Eighty volunteer students with
lower-middle to middle SES status enrolled in a college algebra
course.
Results: Treatment subjects achieved gains in
the concepts of modeling, translating, and interpreting as they relate to
functions. There was no significant difference in groups in regard to the
concept of reification.
Description: CIA teaches college algebra using
computer technology and with a focus on real-world
situations.
Results:
No attempt was made to verify the comparability of the
treatment and control groups prior to performing the experiment,
therefore, although students in the treatment group outscored the control
group, it is not possible to meaningfully attribute these gains to the
intervention.
Description: This strategy employs an algebra
text written to provide continuous review of four or five problem sets for
each fundamental part of a skill. Each problem set has only four or five
problems on the new facet of the skill and approximately twenty review
problems of prior facts or skills. This method provides the student a
longer period of time in which to learn a skill or develop a
concept • Number
& Operations
Math Topic(s): Computation and
concepts/application skills.
9th to 12th grade.
(Also in
Diverse Learners)
Study: Austin.
An experimental study
of the effects of three instructional methods in basic probability and
statistics.
Strategy:
The use of manipulatives and pictorial
modes. Subjects: Freshman and sophomore students
(n=71) at Purdue University who did not major in science or
mathematics. Results: Computational achievement did
not differ among the three different methods. Using pictorial figures
improved students' achievement, but there was no significant difference as
a result of using manipulatives.
Description: Students were divided into three
different treatment groups; manipulative-pictorial (MP); pictorial (P);
and symbolic (S). The MP group manipulated such things as coins, dice,
random-number tables, and marble-selection devices and used graphs,
diagrams, and figures for the pictorial portion of the experiment. The P
group looked at the data from the experiments and the same pictorial
elements of the MP group. The S group used no pictorial aids; only
mathematical symbols and words were used confront
Math Topic(s): Computation and
concepts/application skills.
9th to
12th grade.
(Also in
Diverse Learners)
Study:
R. Wertheimer.
Title: The Geometry Proof Tutor: An "Intelligent"
Computer-Based Tutor in the Classroom.
Strategy: Individualized instruction with the
Geometry Proof Tutor (GPTutor) Subjects:
Geometry students from a public high school: 10 students from one gifted
class, 18 students from one scholars class, and 9 students from each of
three regular classes. Racially mixed and with a wide range of
socioeconomic statuses. Results: All
experimental groups outperformed the control group on the
posttest:
Description:
The Geometry Proof Tutor is a computer-based tutoring software
for proof construction that provides individualized instruction. It is
composed of the following three components: 1. Expert: embodies the
knowledge (i.e. theorems, axioms, and definitions) necessary for
successfully solving problems. 2. Tutor: contains information
that is used to tutor students with messages about students' errors and
strategies to attack problems; and 3. Interface:
presents students with problems and handles students' input tutorsStrategy: Conceptually Oriented Instruction Subjects:
Two ninth grade general math classes from a Midwest suburban high
school with a population of 700 students. Subject students ranged from
14-17 years old. The average age was 15 years old. First semester: the
"conceptually oriented" class had 28 students and the "computational"
class had 19 students. Second semester: the "conceptually oriented"
class had 23 students and the "computational" class had 21
students. Results: Students in the conceptually oriented class
outperformed students in the drill and practice class on a test of
computation. Effect Size = +0.96.
Description: Conceptually oriented instruction
focuses on estimation, mental arithmetic, whole number concepts and
relationships, and arithmetic word problems. It examines set, region, and
linear models for fractions (as a part of a whole), and the connections
between fractions, decimals, and percents. The intervention uses
calculators, manipulatives, models, and illustrations. It employs
questioning strategies and encourages student communication |
Math 53 Midterm Review
On the midterm, you can use your book and notes. You cannot use
calculators, computers, or the assistance of other people.
Many of the questions will be computational, e.g. solve a differential
equation. For these questions, you should be able to check if your
answers are correct. There will also be a few conceptual short-answer
questions, e.g. true/false questions. There will be no proofs. |
An introduction to the various branches of mathematics within the historical framework of their origin. Such topics as sets, systems of numeration (ancient and modern), logic (Aristotelian and symbolic), geometry (Euclidean plane and solid, non-Euclidean, analytic), arithmetic (simple and modular), probability, statistics and computers are explored from the standpoint of their development and impact on modern living. Does not fulfill the mathematics requirement for elementary education majors. Does not satisfy the general education requirement for mathematics.
Prerequisite: Satisfactory math placement test score or a grade of P4 in DVM 0050 [DVM 005] or DVM 0070 [formerly DVM 007].
Book:
As determined by the Mathematics Department.
Outcomes:
Upon successful completion of the course, each student should be able to:
1. Compare and/or contrast the mathematics of the ancient civilizations of Egypt, Mesopotamia, Greece, India and Persia with that of the present, especially with respect to the foundations of arithmetic, algebra, geometry, trigonometry, number theory, logic and calculus. 2. Discuss the relationship between mathematics and the natural biological sciences, the social sciences and the humanities. 3. Apply mathematics to daily existence, in skill areas such as probability, statistics, calculus and analytic geometry. 4. Use the hand-held calculator and the microcomputer to solve appropriate mathematical problems. |
The Basics of Algebra
Before you can really get into Algebra 1 and understand what's going on, you have to understand the basics. These basics include a number of topics from arithmetic that will be used extensively in Algebra 1, so it's really important that you know them well. If you take the time to understand these topics before you try to tackle more complicated subjects, then you'll have a strong foundation for the rest of your education in mathematics.
One of the topics from basic mathematics that people think they understand when they really don't is the order of operations. The order of operations tells us which order we should do things in when we have complicated mathematical equations. We need this standard order of operations so that people don't get different answers for something as simple as 1 * 2 + 3. If you do it correctly, you should get 5, but if you do it incorrectly, you could get 6. If people went around getting different answers for equations, then mathematics wouldn't have much use.
Another important topic to understand is the use of variables, and this is the basis of a lot of ideas in Algebra 1. A variable is a letter that takes the place of a number that either we don't know or we want to keep open for various numbers to take its place. Sometimes we're going to be solving for a specific variable, like if we have the equation 2x – 3 = 17. Other times we're going to be looking at the nature of an equation with variables in it, like when we look at the graph created from the equation y = 3x + 2.
Exponents are another topic that should be understood before jumping into Algebra 1. While they aren't difficult to understand by themselves, doing complicated operations using exponents can be tricky. If you know the few simple rules for dealing with exponents, then they can be made fairly simple.
Understanding the distributive property is super important for learning Algebra 1. Without understanding the distributive property, you will find yourself completely lost in a lot of common situations that come up. The distributive property is definitely worth putting a lot of effort into learning.
Order of Operations – If there are no parentheses to point out what to do first, the order of operations will tell you how to make sure you get the right answer.
The Integers – Dealing with both positive and negative numbers is an important skill in Algebra 1.
Variables – We don't always know the value of numbers we're dealing with, but variables let us do math with these numbers anyway.
Exponents – Just like multiplication is repeated addition, exponents allow us to use a shorthand for repeated multiplication.
Percentages – Having an even ground for comparison between different amounts is a critical skill. |
1 : Basic Operations on whole and rational numbers 4.00.005 2 : Developments & applications 4.00.005
Mathematics program intended for High School pupils (age 15-17) This Title comprises 20 3 : Analysis, vectors, trigonometry, probabilities… 2.01.002
PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a ... mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI .... Free download of PARI/GP 2.3.4
... is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical ... of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library. YACAS comes with extensive documentation (hundreds of pages) covering the scripting language, the functionality .... Free download of Yacas 1.3.3
A Program for Statistical Analysis and Matrix Algebra MacAnova is a free, open source, interactive ... are analysis of variance and related models, matrix algebra, time series analysis (time and frequency domain), and (to a lesser extent) uni- and multi-variate exploratory statistics. The current version is 5.05 release 1. .... Free download of MacAnova 5.05.3 Windows 12.09.0 Mac OS X 12.09.0 4.2.30 for Mac 4.2.30 4.0 64bit 4.0
Algebra1 : Basic Operations on whole and rational numbers 4.00.005
... needs to solve problems ranging from simple elementary algebra to complex equations. Its underling implementation encompasses high precision, sturdiness and multi-functionality. MultiplexCalc also has the unlimited ability to extend itself by using user-defined variables. You can add your own variables to MultiplexCalc in order to convenience your work. Any instance .... Free download of Multipurpose Calculator - MultiplexCalc 5.4.8
... needs to solve problems ranging from simple elementary algebra to complex equations. In .... Free download of Innovative Calculator - InnoCalculator 1.1.8 |
Course
Number: MA.IMP2
Course Name: Interactive Math Program 2 Prerequisite: None Course Description:
This course is part of an integrated, problem-centered mathematics program designed to meet the needs of all students. Algebra, geometry, trigonometry, probability and statistics are used together to emphasize logical analysis, inference and deduction rather than drill-skill memorization. Course Length: 2
semesters Period Length: 1 Grade Level: 9-12
grade(s) Credit Per Semester: 1.0 (Math requirement or Elective) |
Speaker's Bureau
Algebra: Hints and Helps
Description:
Hints for the Algebra classroom teacher that will make teaching algebra easier and more exciting. Open discussion to address particular problems you have when teaching Algebra. This workshop also gives helps for students who have difficulty with Algebra.
Note: The speaker authored the BJU Press Algebra textbook. |
Mathematics
The Mathematics Department requires all students to take four years of mathematics. Students who take Algebra I or Honors Algebra I as freshmen and Geometry as Sophomores have the opportunity to take Calculus on the Honors or AP level as seniors if they meet the criteria for enrollment in a course entitled Honors Algebra II/Pre-Calculus as juniors. Another option is Algebra I, Geometry, Algebra II and Pre-Calculus on the Honors or Standard level. Also, any student who places into Geometry or Honors Geometry as a freshman may also take Honors Algebra II/Pre-Calculus as a sophomore if she meets the criteria for enrollment. The use of the graphing calculator and a variety of computer programs in math is an essential component of each course. Upon enrollment, all freshman will be required to have a TI84+ Graphing Calculator which they will use for all their math and science classes.
517alg IH Honors Algebra I GR 9 | QP 4.67 | 1 CREDIT | YEAR This course covers the same topics as Algebra I (515), but problems of a higher difficulty level are presented as well as theoretical explanations of greater depth. Prerequisite: Student must be invited to enroll in this course based on results from the Mathematics Placement Exam administered in May before freshman year.
524geom Geometry GR 10 | QP 4.33 | 1 CREDIT | YEAR This course is an axiomatic approach to the Euclidean geometry. Logical reasoning is used to explore the relationships between lines, planes, triangles, and polygons. Trigonometry, coordinated geometry and exploration of solid figures are also studied; theory and application are equally considered. The course has a strong integration with Algebra I. Prerequisite: Algebra I (515 or 517)
527geomH Honors Geometry GR 9-10 | QP 4.67 | 1 CREDIT | YEAR This course is an in-depth axiomatic approach to Euclidean geometry. Topics include parallel lines and planes, triangles, polygons, circles, trigonometry, constructions, solid figures, and coordinate geometry. Abstract reasoning is developed in an advanced use of theory and application. Prerequisite: [3.67 in Algebra I (515/517) and (B+ on all SHA midterm and final exams in 515/517 or departmental approval)] OR Student may be invited to enroll in this course based on results from the Mathematics Placement Exam administered in May before freshman year.
534algII Algebra II GR 10-11 | QP 4.33 | 1 CREDIT | YEAR This course stresses the structure of Algebra and the development of computational and problem-solving skills. Topics include a review of Algebra I, the real number system and its properties, complex numbers, polynomial and rational expressions, functions and relations. A theoretical approach is used with emphasis given to the application of theorems and formulas. Prerequisite: Algebra I (515 or 517) and Geometry (524 or 527)
537algIIH Honors Algebra II GR 10-11 | QP 4.67 | 1 CREDIT | YEAR This course stresses the structure of Algebra and the development of computational and problem-solving skills. Topics include a brief review of Algebra I, the real number system and its properties, functions and relations, systems of linear equations in three variables, complex numbers, polynomials, and rational expressions. An in-depth theoretical approach is used and emphasis is given to the application of theorems and formulas. Prerequisite: [3.67 in Algebra I (515/517) and 3.67 on the final exam in 515/517in Grade 9 and 3.33 in Geometry (524 or 527) in Grade 10] OR 3.67 in Honors Geometry (527) in Grade 9
539 algIIpcH Honors Algebra II/ Pre-Calculus GR 10-11 | QP 4.67 | 1 CREDIT | YEAR This course is designed to allow freshman and sophomores currently in Geometry or Honors Geometry to enroll in Calculus, AP Calculus and any other advanced math class as juniors and seniors. Sophomores who studied Algebra I or Honors Algebra I as freshmen may enroll in this class to prepare for Calculus or AP Calculus as seniors. Present freshman Geometry students may enroll in this class as sophomores to prepare for Honors Calculus as juniors and BC Calculus as seniors. The focus of this course is an extensive and in-depth study of functional analysis, mathematical analysis and analytical geometry. This integration of Algebra II, trigonometry and functional analysis intends to broaden the students' mathematical background and provide the mathematics needed for success in Calculus. Graphing calculators will be used for graphical investigations and explorations hence a TI83+ or TI84+ graphing calculator is required. Prerequisite: [4.0 in Algebra I (515 or 517) in Grade 9 and 4.33 in Geometry (524 or 527) in Grade 10] OR 4.33 in Honors Geometry (527) in Grade 9. In addition, all enrolled students must have an A exam average in Algebra and Geometry courses at SHA or departmental approval.
542func Functions, Statistics and Trigonometry GR 11-12 | QP 4.33 | 1 CREDIT | YEAR This course serves either as a transition between Algebra II and Pre-Calculus (546) or as the final course in the math sequence. This course integrates work with functions and trigonometry to introduce the student to the topics in Pre-Calculus (546). It also challenges the student to think mathematically. The Statistics part of the curriculum is done with the technology available at Sacred Heart Academy: the laptops, the internet and the graphing calculator will be utilized to complete this section of the course. The use of functions and statistics to model real world situations is a major theme, and will provide the students with the tools to see how seemingly abstract mathematical ideas are meaningful in the world around them. Required: TI83+ or TI84+ Graphing Calculator. Prerequisite: Algebra II (534 or 537)
544statAP AP Statistics (Advanced Placement) GR 11-12 | QP 5.0 | 1 CREDIT | YEAR Collecting, representing and processing data are activities of major importance to contemporary society. Topics covered in this course include the description and analysis of population distributions, change and growth of data, correlation, experiment design, probability models, linear regression, hypothesis testing and confidence intervals. Graphing calculators and computers are used as tools for the facilitation of statistical tests on significant bodies of data. Advanced Placement Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Ideas and computations presented in this course have immediate links and connections with actual events. Computers and calculators will allow students to focus deeply on the concepts involved in statistics. The TI83+ or TI84+ calculator is required and is used as the technical tool to allow the student to calculate any tests or data required. AP exam fee applies. Prerequisite: 4.0 in 534, 3.67 in 537 or 3.33 in 539. In addition, all enrolled students must have an A- exam average in Algebra II OR departmental approval.
123engnrg Introduction to Engineering GR 11-12 | QP 4.33 | ½ CREDIT | SEM 1 OR 2 This course focuses on the fundamentals of modern engineering and technology. Students explore the engineering design process as they learn and apply math and science concepts to design and test an array of high-tech digital devices. The course will show students how engineers use advanced development tools in everyday engineering work: Designing, developing, testing, debugging, and finally producing a finished product that works. Prerequisite: 3.67 in Algebra II (534, 537, or 539) Note: This course may be used to fulfill the science or math graduation requirement.
545finance Personal Finance GR 11-12 | QP 4.33 | ½ CREDIT | SEM 1 OR 2 This course explores the mathematics of personal and business matters with an emphasis on rational decision making. Topics in personal finance include analyzing budgets, banking, insurance, credit, taxes, real estate and investments. Students research a range of investment opportunities and financial instruments from a variety of sources including the Internet. Book fee applies. Note: This course counts toward the four-credit math requirement.
546precalc Pre-Calculus GR 11-12 | QP 4.33 | 1 CREDIT | YEAR This course covers the advanced techniques of Algebra as well as the integration of functional analysis, analytic geometry and trigonometry. The trigonometric functions are thoroughly presented, including graphing, solving identities, and applications. This course also includes an introduction to probability and counting problems. Technology allows the focus of the course to be on functional investigations and exploration. Heavy emphasis is on the use of the overhead graphing calculator-projector and digital lesson investigations with the Smart Board. Since this course includes in-depth use of hand-held graphing calculators, the TI83+ or TI84+ graphing calculator is required. Prerequisite: 2.67 in Algebra II (534, 537, or 539) Note: Students taking this course may qualify for Honors Calculus (590) or AP Calculus AB (593).
547precalcH Honors Pre-Calculus ECE(UCONN ECE MATH 1030Q) GR 11-12 | QP 4.67 | 1 CREDIT | YEAR UCONN COURSE 1030Q: 3 Spring college credits This course is an integration of an intensive study of trigonometry, geometry, and advanced algebra intended to broaden the student's mathematical background prior to the study of calculus. This course also includes an introduction to Discrete Mathematics. The three fundamental areas of functional analysis, mathematical analysis and analytic geometry are investigated in depth through the use of a myriad of technological aids such as the overhead graphing calculator, the Smart Board and digital lessons. Each student is required to have either a TI83+ or TI84+ graphing calculator since extensive use of graphing technology is incorporated as an investigative tool. Prerequisite: 4.0 in Honors Algebra II (537) AND A- exam average in 537 or departmental approval. There is an ECE change fee if a qualified student requests to be added in June. Note: All students enrolled in this course will have mandatory Spring concurrent enrollment in the University of Connecticut Early College Experience Program that allows students to earn 3 college credits. UConn will bill students separately for UConn ECE tuition in the Spring.
549stat Introduction to Statistics GR 11-12 | QP 4.33 | 1 CREDIT | YEAR The importance of Statistics in both academic and personal settings has grown at a tremendous rate recently. Intro to Statistics is designed to introduce fundamental statistical knowledge that students will be able to use in college and throughout their lives. Statistics is currently taken by over 85% of all undergraduates at the university level. Topics covered in this course include; data collection, regression, probability, sampling distributions, and inference. The student who successfully completes this course will have the tools for collecting, analyzing, and interpreting data in academic settings and her everyday life. Required: TI83+ or TI84+ Graphing Calculator. Prerequisite: Algebra II (534 or 537)
590calc Honors Calculus GR 11-12| QP 4.67 | 1 CREDIT | YEAR This course is designed for students who want to have preparation for and experience with calculus especially those planning to enter fields of medicine, nursing, business, economics, management, and the social sciences. It focuses on the development of conceptual understanding of real-life situations involving change so the material is data driven and technology based. Topics include functions and linear models, non-linear models, rates of change, derivatives, analysis of change, limits and integration. Extensive use of graphing technology is incorporated hence a TI83+ or TI84+ graphing calculator is required. Overhead graphing-calculator projectors, the Smart Board and digital lessons via the projector are used in most classes. Prerequisite: [4.0 in 546, 3.67 in 547 or 3.33 in 539] AND [For 546: 4.0 average on exams or departmental approval; For 539/547: 3.0 average on exams or departmental approval]. Students who are interested in taking Honors Calculus and exceed the exam average component but fall just short of the overall average required may be eligible subject to departmental approval. These cases will be considered on an individual basis and students should approach the respective teachers well in advance.
593calcAP AP Calculus AB (Advanced Placement and UCONN ECE MATH 1131) GR 11-12 | QP 5.0 | 1 CREDIT | YEAR UCONN COURSE MATH 1131: 4 Fall college credits This course provides an intuitive understanding of the concepts of calculus, and experience with its applications and methodology. Course content generally follows the AP syllabus for Calculus AB, which is more extensive, and of greater breadth and depth than the 590 Calculus curriculum. UCONN will grant 4 college credits for all the Calculus covered in the first semester. This two semester course includes the study of elementary functions, limits, the derivative and its applications, and integral Calculus including anti derivatives and their applications. Overhead graphing calculators, the Smart Board and digital lessons are used in most classes. The TI83+ or TI84+ graphing calculator is required. This challenging course is meant only for the serious math student. AP exam fee applies. Prerequisite: [4.0 in 539/547 or 4.33 in 546] AND [For 546: 4.0 on the midterm and final exams or departmental approval; For 539/547: 3.33 average on exams]. There is an ECE change fee if a qualified student requests to be added in June. Note: All students enrolled in this course will have mandatory concurrent enrollment in the University of Connecticut Early College Experience Program that allows students to earn 4 college credits. UConn will bill students separately for UConn ECE tuition in the Fall only.
594calcAP AP Calculus BC (Advanced Placement) GR 12 | QP 5.0 | 1 CREDIT | YEAR Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both the AB and BC courses represent college-level mathematics for which most colleges grant advanced placement and college credits. The Calculus BC exam has a Calculus AB sub-score so the students enrolled in this class will be receiving two AP scores. The content of Calculus BC is designed to qualify the student for college placement and credit in Calculus II, which is one course beyond that granted for Calculus AB. AP exam fee applies. Prerequisite: [A- on the midterm exam in 590/593 or departmental approval] AND [4.33 in 590 or 4.0 in 593].
191compsciH Honors Computer Science GR 10-12 | QP 4.67 | ½ CREDIT | SEM 1 OR 2 In today's innovation-driven economy, complex problem solving and analytical reasoning skills are important for building a foundation for numerous careers, including jobs in math, science, engineering, and technology-related fields. This course provides an introduction to the intellectual enterprises of computer science and the art of programming. This course teaches students how to think algorithmically and solve problems efficiently. Students will be able to design and implement computer-based solutions to problems in several application areas, including mobile apps for Android and iOS (for iPhones, iPod touches, and iPads), two of today's most popular platforms; to learn well-known algorithms and data structures; to develop and select appropriate algorithms and data structures to solve problems; and to code in a well-structured fashion. Prerequisite: Geometry; 3.67 in a previous full-year math class, including an A- or higher on the final exam. Note: This course counts toward the four-credit math requirement.
550mathsat SAT Math Review GR 11 | QP 4.33 | ½ CREDIT | SEM 2 This course provides juniors with the opportunity to prepare for the math section of the early spring SAT and the advanced math topics in the Subject tests SAT-I and SAT-II administered in early June. In this course, students are introduced to the content and format of the standardized test, learn fundamental test-taking strategies and are provided with ample opportunity to implement these strategies by taking multiple practice tests and correction tests. This course will provide test taking strategies for multiple choice problems and open answer questions, as well as TI 84+ and TI83 calculator tips for successful time management. The four major topics covered in this course are: Numbers and Operations, Algebra and Functions, Geometry and Measurement, and Data Analysis, Statistics and Probability. Each unit of study includes comprehensive instruction on the given topic, followed by guided practice and, finally, individual completion of timed practice tests. Note: This course counts toward the 27-credit graduation requirement. However, this course does not count toward the four-credit math requirement. |
Secondary Mathematics III [2011]
Create equations that describe numbers or relationships. For A.CED.1, use all available types of functions to create such equations, including root functions, but constrain to simple cases. While functions used in A.CED.2, 3, and 4 will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Mathematics I. For example, finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line. Note that the example given for A.CED.4 applies to earlier instances of this standard, not to the current course.
Mathematical Modeling A.CED.1 - A.CED.4 Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics III Cluster "Create Equations that Describe Numbers or Relationships" / Standards A.CED.1, A.CED.2, A.CED.3 and A.CED.4.
Optimization Problems: Boomerangs
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, and interpret and evaluate the data generated and identify the optimum case, checking it for confirmation |
Custom Classes for Mathematics in ActionScript 3
In this section we give links to Flash and Math tutorials and the MathDL Flash Forum articles that provide
custom AS3 classes and templates for building math applications. We also list AS2 articles whose AS3 version is coming soon.
All graphing applications listed below use our custom math formula parser, MathParser.
NEW! Sketching Derivatives Applet in AS3 Flash - The Code
We present a math applet for sketching derivatives with complete AS3 source code.
The applet uses a large collection of custom AS3 classes developed by the Flash and Math team
over the past few years. The newest of the classes are related to an interesting drawing
and smoothing techinique. The user draws by dragging and shaping a curve.
Function Grapher with Zooming and Panning
In this tutorial, we present a math function grapher which has a drag and drop panning
and mouse click zooming functionality. Panning has a cool easing
effect, too. All the source code including parsing and graphing
custom AS3 classes available for download.
Contour Map Plotter and 3D Function Grapher in Flash Combined
We use our custom AS3 classes in the package flashandmath.as3.*
to build an applet which combines a contour diagram plotter
and a 3D function grapher. The user's can input formulas for functions and variables ranges. The applet uses our custom classes: MathParser,
GraphingBoard, GraphingBoard3D, and many helper classes. We provide complete, well-commented source code and a pdf guide of custom classes.
Custom AS3 Math Classes, Implicit Plotter in Flash
The implicit equations grapher presented in this tutorial is another example of how
the custom AS3 math classes provided at flashandmath.com can be used to easily create
custom math applets. In this tutorial, we use our custom MathParser and GraphingBoard
classes that do all the work for you. The tutorial contains complete, well-commented source code.
The SimpleGraph class An alternate title for this tutorial could be, "How to make a functional grapher in 30 lines of code." With the custom SimpleGraph class available from flashandmath.com, creating a graph of an expression in one variable is a snap!
Visualizing Regions
for Double Integrals This article in the Sharing Area of the MathDL Flash Forum presents a mathlet for
students learning double integrals in rectangular and polar coordinates.
The mathlet draws regions of integration
corresponding to the limits entered by the user and provides many
practice problems.
We welcome your comments, suggestions, and contributions. Click the Contact Us link below
and email one of us. |
You can perform a key word search for the specific area of math that you
need: algebra, calculus, trigonometry, etc. Students can access the
catalog from any location and they do not have to log in. Students can
have books owned by other campuses sent to Loudoun using Intercampus Loan,
the process takes 2-3 days and is free. Students do need an NVCC student
ID card to check out materials.
Resources available in the Math
Center (LR room 204) are included below by course.
Click on your course:
Video tapes for Basic Mathematical Skills with Geometry
The tapes contain a short video lesson for each section of the textbook.
See the Video Index Binder for the table of contents.
Streeter-SMART CD
This interactive tutorial and testing software is keyed specifically to your
textbook. Look for the Streeter-Smart icon on the desktop of the computer.
You will need the CD-ROM in the computer while you run this program.
Video tapes for Fundamentals of Mathematics The tapes contain a short video lesson for each section of the textbook.
See the Video Index Binder in the Math Center for the table of contents.
Interactive Video Skillbuilder CD
This is the CD that comes with your textbook. Look for the Fundamentals of
Math icon on the desktop of the computer in the Math Center. This program
contains MathCue, the same software that is used during class sessions. It
also contains short video lessons for each section of the text.
Video tapes:Real to
Reel Video Series for Beginning Algebra
The tapes contain a short video lesson for each section of the textbook. See the Video Index Binder for the table
of contents.
Digital Video Tutor for
Beginning Algebra This set of CDs contains the same video lessons that are on the
videotapes. Find the appropriate CD in the CD rack. Then follow the
instructions that are in the box with the CD.
Pass the Test CD This CD contains practice tests, section reviews and tutorials for each
chapter in your Lial textbook. Check the Math Center Resource notebook for
instructions on how to use the CD.
Video tapes:
Steps to Success Video for Intermediate Algebra The tapes contain a short video lesson for
each section in the textbook.
Digital Video Tutor:
Intermediate Algebra, ninth editionMyMathLab: You can enroll in this tutorial if
your textbook included a CD when you purchased the book. Follow the
instructions that came with your CD and choose this course ID: serbousek91927
Thinkwell: Intermediate Algebra
This set of CDs contains video lectures by a lively, entertaining teacher.
Check the Math Center Resource notebook for instructions on how to use the
CDs.
Video tapes:
Steps to Success Video for Intermediate Algebra: Graphs and Models
The tapes contain a short video lesson for each section in the textbook.
Digital Video Tutor:
Intermediate Algebra: Graphs and ModelsThinkwell:
Intermediate Algebra
This set of CDs contains video lectures by a lively, entertaining teacher.
Check the Math Center Resource notebook for instructions on how to use the
CDs.
CD: Interactive Trigonometry The CD is linked to a different
textbook than the one you use for your class, but by looking at the table of
contents you should be able to find each topic from your textbook.
Tutorials, guided examples and quizzes are available for each section.
Video tapes: for Mathematical Ideas The tapes contain a short video
lesson for each section in the textbook.
Digital Video Tutor:
Mathematical Ideas This set of CDs contains the same video lessons that are on the
videotapes. Find the appropriate CD in the CD rack. Then follow the
instructions that are in the box with the CD.
Video tapes and DVDs: for Precalculus, A Graphing Approach The tapes contain a short video lesson for each section in the textbook.
Interactive Precalculus CD You will need the CD in the computer to use this software. Click on the
Interactive Precalculus icon the desktop of the computer in the Math Center.
The material is linked to your textbook and provides tutorials, guided
examples and quizzes for each section in the text.
Interactive Trigonometry CD You will need the CD in the computer
to use this software. Click on the Interactive Trigonometry icon the desktop
of the computer in the Math Center. The material is linked to a different
textbook than the one you use in class, but by looking at the table of
contents you should be able to find each topic from your textbook. It
provides tutorials, guided examples and quizzes for each section in the
text.
Thinkwell: Precalculus This set of CDs contains video lectures by a lively, entertaining
teacher. Check the Math Center Resource notebook for instructions on how to
use the CDs.
CD: Texas Instruments resource CD and
GraphVideo tapes: for
Stewart'sCalculus, Early Transcendentals Selected examples from each section of the text are explained.
Interactive Video
Skillbuilder CD This is the CD that comes with your textbook (5th edition). Put the CD
in the computer in the Math Center, click on "Start", then "Run" then type
the letter of the CD drive (probably D: or E:). Click on the file labeled
Start. The material is linked directly to your text and contains video
lessons and section quizzes for each section and a test for each chapter.
CD: Tools for
Enriching Calculus
This is also linked to your text and contains homework hints, exercises and
interactive demonstrations for many of the concepts in the textbook
DVD: for Calculus
This set contains video lectures for each section in several calculus
textbooks by Larson, Hostetler and Edwards. By looking at the table of
contents on the screen, you can probably find a lecture on any topic from
your text.
CD: Interactive Calculus
CD
The material is linked to Larson's Calculus, Early Transcendental
Functions textbook, but by looking at the table of contents on the
screen, you can probably find a lecture on any topic from your text. It
includes tutorials, guided examples and quizzes for each section in the
table of contents.
CD: Calculus Learning
Tools
The material is linked to Larson's Calculus, Early Transcendental
Functions textbook, but by looking at the table of contents on the
screen, you can probably find a lecture on any topic from your text. It
contains the tools to perform the open explorations that are in most
sections of the text. A copy of the text is available in the Math Center for
use in the Math Center only.
Thinkwell:
Calculus I and Calculus II This set of CDs contains video lectures by a lively, entertaining
teacher. Check the Math Center Resource notebook for instructions on how to
use the CDs.
Video tapes: for the graphing calculator
Video tapes: ELI video tapes for Mth 174 and Mth 277
Scientific Notebook: This program is a combination word processor and computer algebra
system. Access it by clicking on the Scientific Notebook shortcut on the
computer desktop. Take a quick tour from the Help menu.
Student edition of Derive: Derive is a computer algebra system, allowing you to perform algebraic
manipulations, perform the calculus operations of derivatives, integrals,
etc. exactly the way you would do them by hand. The program runs from a
floppy disk and is accompanied by a manual.
CD: Texas
Instruments resource CD and Graph-Link
Use the CD labeled TI Resource CD and click on the desktop shortcut TI
Connect in the Math Center. YouCD:Texas
Instruments resource CD and Graph |
0495391328
9780495391326
1133168663
9781133168669
Discrete Mathematics with Applications: Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. «Show less
Rent Discrete Mathematics with Applications 4th Edition today, or search our site for other Epp Discrete |
Channels: User Stories
Mathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom.
Mathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom. Includes Spanish audio.
William Meyer, the vice president of technology at Scattering Solutions, LLC, describes an example of using Mathematica's data-analysis capabilities to save time and money on drug screening. Includes Japanese audio.
This video features John Kiehl, co-owner of Soundtrack Recording Studio, who shares an example of Mathematica using powerful set theory and pattern-matching capabilities to make and produce music. Includes Japanese audio. |
Algebra 1
Description
An outstanding text that presents mathematics as a study of absolutes with a logical approach from one concept to another. Concepts are developed and mastered through an abundance of worked examples and student exercises. Many application problems relate algebra to the physical world |
Rate of change Teacher Resources
Title
Resource Type
Views
Grade
Rating
Math pupils calculate the average rate of change over a specific interval. They represent the average rate of change on a graph and examine the behavior of the graph for decreasing and increasing numerals.
In this function instructional activity, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page instructional activity contains approximately 20 problems.
High schoolers investigate logistic models by making a scatter plot of internet phone users over 5 years. They find a logistic model that fits their data and then discuss what the instantaneous rate of change means in the context of the problem. Very relevant and applicable!
In this calculus worksheet, students problem solve 8 word problems involving rates of change in association with high school students. Students work out each problem and give a short explanation of each answer.
Students, with the assistance of their TI-84 Plus / TI-83 Plus calculators, distinguish meanings from right, left and symmetric difference quotients that include rate of change and graphical interpretations. They utilize symmetric difference quotients to approximate instantaneous rate of changes.
For this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts. The twenty-two page worksheet contains explanation of the topic, numerous worked examples, and sixteen multi-part practice problems. Answers are not provided.
In this successive approximations activity, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page activity contains explanations, examples, and approximately ten problems.
Students calculate the rate of change using the derivative. In this algebra lesson plan, students identify the function over closed interval and identify the rate of change. They use correct notation and classify a function as increasing or decreasing.
Learners explore the concept of rate of change. In this rate of change lesson, students calculate concentrations, flow, and duration of ice water. Learners calculate and graph temperature over time of the ice water. Students analyze the rate of change. |
ESSENTIAL MATH W/APPL (8TH 10)
by BARKER
Annotated Instructor Edition
Our Price:
$28.51
Rent
Our Price:
$18.67
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Description
As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Students are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of "active participant" is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the concepts. To this point, simplicity plays a key factor in the organization of this edition, as in all other editions. All lessons, exercise sets, tests, and supplements are organized around a carefully-constructed hierarchy of objectives. This "objective-based" approach not only serves the needs of students, in terms of helping them to clearly organize their thoughts around the content, but instructors as well, as they work to design syllabi, lesson plans, and other administrative documents. The Eighth Edition features a new design, enhancing the Aufmann Interactive Method and the organization of the text around objectives, making the pages easier for both students and instructors to follow. |
Is All About Math - Julio Cesar de la Yncera
Main site for a mathematical Video PodCast that will cover a big range of topics in college-level mathematics accessible to the majority of the students with some mathematical inclinations. The Video PodCast will also try to be inspirational for the non-mathematicallyKarismath - CLSO Learning Systems, Inc.
Math topics, including Algebra, are presented visually, through lessons (Flash animations that explain a target concept), demos (Flash animations that explain every exercise template to be used) and worksheets (PDF format) that can be downloaded. Each
...more>>
Khan Academy - Salman Khan
Salman Khan has recorded over 1400 YouTube videos on a variety of topics, largely math and finance. The Khan Academy, which Khan founded, is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere. To keep
...more>>
Learning Math is Fun - Kevin Cornell
Learn the order of operations by watching a video of the PEMDAS song. Before becoming an elementary school principal, singer "Mister C" taught 5th grade science and served as a math coach. See also Cornell's science site at
...more>>
Learning Wave Communications - Human Relations Media
Learning Wave is a producer of videos, CD-ROMs and other supplementary materials for math education including interactive games such as Absurd Math. Under the name HRM Video it has created programs such as middle school math mysteries, applications-basedMAA Bookstore - Mathematical Association of America
A searchable list of books, with descriptions, in the following categories: Algebra; Analysis; Applied Mathematics; Calculus; Career Information; Computing and Computers; Elementary Models; Games, Puzzles, and Popular Exposition; Geometry and Topology;
...more>>
Maisonet Math - Shane Maisonet
This website provides math worksheets in pdf form for public download. Online quizzes also provide instant feedback to indicate level of mastery. Online videos of various math concepts are also available.
...more>>
Math and Soccer Video - Sharp Tack Productions
A video revealing the role played by numbers, graphs, geometry, algebra, angles, area, surveys, and chance data in the game of soccer; for example, how a goalie relies on the properties of angles to know where to stand when defending the goals, and on
...more>>
Math Dork Interactive Math
Animated algebra tutorials, on-line quizzes, and games. Animations require Flash 3. Full access to this site involves a monthly fee; free lessons include graphing points in the coordinate plane and "The Golden Rule of Algebra."heatre - Sadie Bowman and Marc Gutman
Blog of the performers starring in "Calculus: The Musical!" This comic "review" blend of sketch comedy, musical theatre, and lecture about the concepts and history of calculus emerged as a teaching tool from the classroom of Gutman, who "... found that
...more>>
Mathematics - Annenberg Media
The video, software, and print guides in the math collection show concrete examples of good teaching and active learning in all sorts of settings: public school classes, multi-age classes in rural areas, bilingual classes, magnet and charter schools,Math Learning Site
This site offers a library of over 2000 lessons in video format, as well as pretests, exams, and a performance report accessible by parents and/or teachers. Lessons are accessible by subscription, with a money-back guarantee and an online demo.
...more>>
Math Magic by the Human Calculator Scott Flansburg
Scott Flansburg, "The Human Calculator," created Math Magic to be a fun math activity that makes learning basic math skills easy. For kids, Math Magic offers an entertaining video with an easy-to-use workbook that features math worksheets which cover
...more>>
The Mathman - Don Cohen
Materials for sale for K-12 students, teachers and parents; pre-calculus. Materials include Get Ready for Calculus (Calculus By and For Young People book, CD-ROM, worksheet book, videotapes and map) and Changing Shapes with Matrices. Patterns, visualization,
...more>>
MathMol - NYU/ACF Scientific Visualization Laboratory
A starting point for those interested in molecular modeling, one of the fastest growing fields in science, from building and visualizing molecules to performing complex calculations on molecular systems. Using molecular modeling scientists will be better
...more>>
Mathnasium Math Learning Centers - Mathnasium LLC
After school learning centers where students, grades pre-K to 12, "go to boost their math skills." Browse a directory of Mathnasium tutoring centers in the US and abroad. Read about the Mathnasium Method, created by former Los Angeles teacher Larry Martinek.
...more>> |
This pre-algebra course provides basic principles, concepts and techniques that are necessary for students' success in higher level mathematics courses. Content material includes using the four operations with integers and rational numbers, algebra basics such as the order of operations, using variables and combining like terms. 1-step and 2-step equations, and inequalities, will be explored as well as multi-step equations. Designated for students with little or no algebra background. |
WileyPLUS for Mathematics and Statistics offers a wealth of assessment tools, outcomes reporting, algorithmically – generated problems, and remedial tutorials that allow you to extend the learning experience beyond the classroom and keep students on-task seven days a week. Instant feedback and automatic grading
by Maple give you more time to teach and help you be more effective in the classroom.
First course for undergraduate students, this book aims to present the fundamentals of linear algebra in the clearest possible way; pedagogies eg. more basic applications, section-end Concept Review, True/false exercises are the main considerations. Calculus and technology are not a prerequisite but included for further exploration. A concluding chapter covers 20 applications of linear algebra drawn from various disciplines.
This revision of the market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Written from the viewpoint of the applied mathematician, it focuses both on theory and practical applications with current examples of Differential Equations as they apply to engineering and the sciences.
A first course in differential equations, it emphasizes a systems approach and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Section exercises give hands-on experience in modeling, analysis, and computer experimentation. Optional projects provide additional opportunities to explore the role played by differential equations of a more serious nature.
Written from the viewpoint of the applied mathematician, this book sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications.
For a first course in differential equations, this book is intended for science and engineering majors who have completed the calculus sequence, but not necessarily a first course in linear algebra. It emphasizes a systems approach and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. It emphasizes contemporary applications to a greater extent and makes somewhat more use of graphs. |
In the words of the author: Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful. My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics. I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024). In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course. |
Why study calculus? Is it because you want to be a doctor, an engineer, a forensic scientist, a biologist, or a mathematician? Or is it because someone told you that it would be "good for you"? Well, all of those are certainly legitimate reasons. But if you aren't quite sure "Why calculus?" here is another reason: It is one of the greatest intellectual achievements of humankind, and, even more to the point, it is easily accessible to anyone who already has studied algebra, trigonometry, and geometry.
Gottfried Leibniz and Isaac Newton independently invented Calculus. Although the notation, terminology, and rigor may have changed or been standardized over the years, the concepts that we will study have not changed fundamentally since the work of the co-inventors in the 17th century.
We will begin Calculus with the study of Rates of Change and what are called derivatives. Rates of Change are all around us. For example, velocity is the rate of change of distance with respect to time; and acceleration is the rate of change of velocity with respect to time. So, we experience derivatives every time we ride in a car, or fly in an airplane. Calculus can also be used to compute areas and volumes of odd shapes with what are known as integrals. Thus, calculus has a place in architecture too.
That calculus is important in real-world applications is not in dispute. In fact, there are so many applications of calculus that studying it really is "good for you." Besides engaging in a worthwhile intellectual endeavor, you will be helping to keep your future career options open. That, from a practical point of view, is not a bad reason at all.
Moreover, studying calculus can be a lot of fun, but we will let you be the judge of that.
How to study calculus. Calculus has a lot of rules. We admit it! Find the derivative of this function, or the integral of that. However, you should train yourself to keep the rules in perspective: Always put the concepts first. When you study a given calculus concept, ask yourself three questions:
What is the picture (a graph or sketch) that I should have in mind?
What is the theorem or formula that gives a statement of the concept?
Do I know how to use the concept in different situations and with different numbers?
The above is what we might call "high-level thinking." It provides a way for you to stay oriented, to know what you are learning, and for what purpose. The rest is in the details, important though they are. The combined process is a lot like using a map to hike through the woods. Yes, you have to look at individual trees and their proximity to local landmarks to find your way, but you always want to keep the map and a compass handy to give an overview of the whole trip. So it goes with the study of calculus concepts. Always know where you are going, the direction to take to get there, and how to accomplish the task. The proof, though, is in getting there!
Practice, practice, practice. In the end, there is no other way. You cannot learn calculus by reading about it. You have to take a pencil and paper and work problems. Learning calculus, or mathematics in general, is a participatory activity. You have to do it to learn it, to make it your own.
Using Calculus on Demand to study calculus.
The Index page of COD (i.e., the page you see when you go to the web site with your Browser) has a picture of a Leibniz Wheel in the upper left-hand corner. Click on the Leibniz Wheel to find out what it is, and how it represents our philosophy of combining theory with practice in the study of calculus in a computing environment.
COD is a Calculus I course that gives an introduction to differential and integral Calculus that comprises roughly to the AB part of the AP exam. You will find the topics listed in the green left-hand sidebar of the COD index page. Clicking on a topic will take you to the Lecture-page on that topic.
Lecture pages: All the Lecture pages have the same layout. There is a short statement of the main thrust of the lecture, followed by these items:
Quick Question: This section is intended to get you thinking about the topic. Sometimes you can answer this question before studying the material of the Lecture, other times not. If you have answered the question, you can check its correctness by clicking Answer. If you don't think you know the answer to the Quick Question, it is better to wait and try the question again after you have studied the Textbook section, which should allow you to answer the question. As before you then can check the correctness of your answer by clicking Answer.
Textbook: Here you will find a link to on-line material from a textbook. At present, we are using the book Principles of Calculus Modeling: An Interactive Approach by Donald Kreider and Dwight Lahr. When you click on the topic in the Textbook section of the Lecture page, you will get a list of the material from the sections of this book corresponding to the COD topics. If you click a topic, you will launch an Acrobat Reader pdf file that will display the text on-line. You can open the link for the Lecture you are working on or for any other topic if there is something you have forgotten and want to review, or if you want to peek ahead. The textbook material will open in a separate window so that you can leave it open on your desktop while you are going through the rest of the lecture.
Today's Homework: The link here will take you to the WeBWorK login page. If you do not have a password, you can sign in as a practice user with practice1 as both the user name and password. If "practice1" is in use, try practice2, or practice3, etc. until you find one that is not in use. After logging in, you will see a page that has the option to "Begin Problem Sets." After selecting it, you will see a list of homework sets that are listed by day. For example, the homework set "Setm3f02day04" corresponds to the homework for COD Lecture 4. Similarly, "Setm3f02day13" is the homework for COD Lecture 13. Ignore the fact that the sets all say "CLOSED;" this just means that the answers are available, and that WeBWorK will not retain your answer once you log off. However, by choosing a problem set and "getting a problem" you may input your answers and WeBWorK will tell you if you are right or wrong. You could also get a copy of the problem set (in pdf).
You may not want to do the homework until you have looked at some Examples and tried the on-line Quiz. This will be true if you are studying the material for the first time. In that case, you should look at the Examples, take the Quiz, and review the Textbook material as necessary before turning to the homework exercises. For those students who have seen the material before, there is nothing wrong with going directly to the homework. You can always come back later to the examples and quiz as needed.
Quiz
: The quiz consists of a set of problems that come up in their own window. You can work out the answers on paper and check them by looking at the COD answers on-line.
Examples: Here you can find examples of problems and their step-by-step solutions on-line.
Applets: These carry out little computer programs that illustrate a calculus idea or provide a tool to implement a calculus procedure. Look at and experiment with them. They are meant to help you learn the material better, or to function much like advanced calculators. Don't be shy. Have fun with them.
Videos: Click on a video to see a calculus problem being worked out by real people. Be on the lookout for Dartmouth graduate students, faculty, and undergraduates. So far, there have been no lucrative film contracts in the offing, but who knows? How long did it take Matt Damon to be discovered?
Lecture-page sidebar: The green sidebar on the left contains links to several resources. First, there is a link to the Math 3 Course Home Page. Math 3 is the Dartmouth course for which COD is the on-line version. The Math 3 Home Page talks about all of the issues relevant to a student taking the course on campus in that particular term. We thought you might be interested. The next link on the COD sidebar gives the Syllabus for that offering of Math 3. The day-by-day syllabus corresponds to the layout of the Lectures in COD. Be careful, though, and don't be misled. If you are studying calculus on your own it may take more than one day to master the material of a given lecture: having a real live teacher does make a difference!
There is also a link to past Math 3 exams (covering Lectures 1-10, 11-19; and the course final). This link is called Practice Exams and should be used as such to test your understanding of blocks of the COD Lectures. There is also a Textbook Home Page link to the home page of the book Principles of Calculus Modeling: An Interactive Approach by Donald Kreider and Dwight Lahr. Here you will find section-pages that give links to calculus resources on the World Wide Web. And finally, there is a link to the Post a Comment page that we discuss below.
What do you do if you have a problem? If you are studying calculus in a classroom setting, you can talk to other students or to the teacher. However, if you are studying on your own, you can Post a Comment using the bottom link on the green sidebar of a lecture-page. There you can communicate with other students who also are studying calculus on-line. You could either state your problem and ask for help, or you may find that someone has already answered that or a similar question. You may even find questions that you can answer for other students. We encourage you to look at the Post a Comment section of COD on a regular basis. |
MathWorks is a developer of mathematical computing software for engineers and scientists. The company's programs cover algorithm development, data analysis, visualization and numeric computation. Many fields use MathWorks, including the aerospace, automotive, communications and electronics |
Undergraduate linear algebra is both beautiful and replete with real world applications and connections to the rest of mathematics. The purpose of the present volume is to enrich the understanding of linear algebra for a wide audience by placing a broad collection of short items in the hands of teachers, students, and others who enjoy the subject. Because undergraduate linear algebra is so fundamental to the mathematics curriculum, it is often taught by non-specialists and specialists alike. "Linear Algebra Gems" offers to all teachers clever ways in which core ideas can be presented to their students.
Most articles are accessible to those with modest preparation in linear algebra, including beginning students. However, many items will also contain pleasant surprises even to those well-versed in the subject. The editors have combed through the literature, and have selected from original submissions, to find expository articles and problems to enrich the reader's understanding. The seventy-three articles selected are organized into nine sections, with over 120 problems grouped into subject categories as a tenth section.
Contributors to the volume include experts in the field and long-time teachers of linear algebra. The book was prepared as part of a broad contract with the National Science Foundation to improve undergraduate linear algebra education. The editors hope that many readers will find enjoyment from this collection. [via]
More editions of Linear Algebra Gems: Assets for Undergraduate Mathematics:
Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topicsBuilding on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work. [via] |
Numerical Analysis, CourseSmart eTextbook, 2nd Edition
Description
Numerical Analysis, Second Edition, is a modern and readable text for the undergraduate audience. This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers—topics such as compression, forward and backward error analysis, and iterative methods of solving equations—all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB® is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.
Table of Contents
Preface
0. Fundamentals
0.1 Evaluating a polynomial
0.2 Binary numbers
0.2.1 Decimal to binary
0.2.2 Binary to decimal
0.3 Floating point representation of real numbers
0.3.1 Floating point formats
0.3.2 Machine representation
0.3.3 Addition of floating point numbers
0.4 Loss of significance
0.5 Review of calculus
0.6 Software and Further Reading
1. Solving Equations
1.1 The Bisection Method
1.1.1 Bracketing a root
1.1.2 How accurate and how fast?
1.2 Fixed point iteration
1.2.1 Fixed points of a function
1.2.2 Geometry of Fixed Point Iteration
1.2.3 Linear Convergence of Fixed Point Iteration
1.2.4 Stopping criteria
1.3 Limits of accuracy
1.3.1 Forward and backward error
1.3.2 The Wilkinson polynomial
1.3.3 Sensitivity and error magnification
1.4 Newton's Method
1.4.1 Quadratic convergence of Newton's method
1.4.2 Linear convergence of Newton's method
1.5 Root-finding without derivatives
1.5.1 Secant method and variants
1.5.2 Brent's Method
REALITY CHECK 1: Kinematics of the Stewart platform
1.6 Software and Further Reading
2. Systems of Equations
2.1 Gaussian elimination
2.1.1 Naive Gaussian elimination
2.1.2 Operation counts
2.2 The LU factorization
2.2.1 Backsolving with the LU factorization
2.2.2 Complexity of the LU factorization
2.3 Sources of error
2.3.1 Error magnification and condition number
2.3.2 Swamping
2.4 The PA=LU factorization
2.4.1 Partial pivoting
2.4.2 Permutation matrices
2.4.3 PA = LU factorization
REALITY CHECK 2: The Euler-Bernoulli Beam
2.5 Iterative methods
2.5.1 Jacobi Method
2.5.2 Gauss-Seidel Method and SOR
2.5.3 Convergence of iterative methods
2.5.4 Sparse matrix computations
2.6 Methods for symmetric positive-definite matrices
2.6.1 Symmetric positive-definite matrices
2.6.2 Cholesky factorization
2.6.3 Conjugate Gradient Method
2.6.4 Preconditioning
2.7 Nonlinear systems of equations
2.7.1 Multivariate Newton's method
2.7.2 Broyden's method
2.8 Software and Further Reading
3. Interpolation
3.1 Data and interpolating functions
3.1.1 Lagrange interpolation
3.1.2 Newton's divided differences
3.1.3 How many degree d polynomials pass through n points?
3.1.4 Code for interpolation
3.1.5 Representing functions by approximating polynomials
3.2 Interpolation error
3.2.1 Interpolation error formula
3.2.2 Proof of Newton form and error formula
3.2.3 Runge phenomenon
3.3 Chebyshev interpolation
3.3.1 Chebyshev's Theorem
3.3.2 Chebyshev polynomials
3.3.3 Change of interval
3.4 Cubic splines
3.4.1 Properties of splines
3.4.2 Endpoint conditions
3.5 Bézier curves
REALITY CHECK 3: Constructing fonts from Bézier splines
3.6 Software and Further Reading
4. Least Squares
4.1 Least squares and the normal equations
4.1.1 Inconsistent systems of equations
4.1.2 Fitting models to data
4.2 Linear and nonlinear models
4.1.3 Conditioning of least squares
4.2 A survey of models
4.2.1 Periodic data
4.2.2 Data linearization
4.3 QR factorization
4.3.1 Gram-Schmidt orthogonalization and least squares
4.3.2 Modified Gram-Schmidt orthogonalization
4.3.3 Householder reflectors
4.4 Generalized Minimum Residual (GMRES) Method
4.4.1 Krylov methods
4.4.2 Preconditioned GMRES
4.5 Nonlinear least squares
4.5.1 Gauss-Newton method
4.5.2 Models with nonlinear parameters
4.5.3 Levenberg-Marquardt method
REALITY CHECK 4: GPS, conditioning and nonlinear least squares
4.6 Software and Further Reading
5. Numerical Differentiation and Integration
5.1 Numerical differentiation
5.1.1 Finite difference formulas
5.1.2 Rounding error
5.1.3 Extrapolation
5.1.4 Symbolic differentiation and integration
5.2 Newton-Cotes formulas for numerical integration
5.2.1 Trapezoid rule
5.2.2 Simpson's Rule
5.2.3 Composite Newton-Cotes Formulas
5.2.4 Open Newton-Cotes methods
5.3 Romberg integration
5.4 Adaptive quadrature
5.5 Gaussian quadrature
REALITY CHECK 5: Motion control in computer-aided modelling
5.6 Software and Further Reading
6. Ordinary Differential Equations
6.1 Initial value problems
6.1.1 Euler's method
6.1.2 Existence, uniqueness, and continuity for solutions
6.1.3 First-order linear equations
6.2 Analysis of IVP solvers
6.2.1 Local and global truncation error
6.2.2 The explicit trapezoid method
6.2.3 Taylor methods
6.3 Systems of ordinary differential equations
6.3.1 Higher order equations
6.3.2 Computer simulation: The pendulum
6.3.3 Computer simulation: Orbital mechanics
6.4 Runge-Kutta methods and applications
6.4.1 The Runge-Kutta family
6.4.2 Computer simulation: The Hodgkin-Huxley neuron
6.4.3 Computer simulation: The Lorenz equations
REALITY CHECK 6: The Tacoma Narrows Bridge
6.5 Variable step-size methods
6.5.1 Embedded Runge-Kutta pairs
6.5.2 Order 4/5 methods
6.6 Implicit methods and stiff equations
6.7 Multistep methods
6.7.1 Generating multistep methods
6.7.2 Explicit multistep methods
6.7.3 Implicit multistep methods
6.8 Software and Further Reading
7. Boundary Value Problems
7.1 Shooting method
7.1.1 Solutions of boundary value problems
7.1.2 Shooting method implementation
REALITY CHECK 7: Buckling of a circular ring
7.2 Finite difference methods
7.2.1 Linear boundary value problems
7.2.2 Nonlinear boundary value problems
7.3 Collocation and the Finite Element Method
7.3.1 Collocation
7.3.2 Finite elements and the Galerkin method
7.4 Software and Further Reading
8. Partial Differential Equations
8.1 Parabolic equations
8.1.1 Forward difference method
8.1.2 Stability analysis of forward difference method
8.1.3 Backward difference method
8.1.4 Crank-Nicolson method
8.2 Hyperbolic equations
8.2.1 The wave equation
8.2.2 The CFL condition
8.3 Elliptic equations
8.3.1 Finite difference method for elliptic equations
REALITY CHECK 8: Heat distribution on a cooling fin
8.3.2 Finite element method for elliptic equations
8.4 Nonlinear partial differential equations
8.4.1 Implicit Newton solver
8.4.2 Nonlinear equations in two space dimensions
8.5 Software and Further Reading
9. Random Numbers and Applications
9.1 Random numbers
9.1.1 Pseudo-random numbers
9.1.2 Exponential and normal random numbers
9.2 Monte-Carlo simulation
9.2.1 Power laws for Monte Carlo estimation
9.2.2 Quasi-random numbers
9.3 Discrete and continuous Brownian motion
9.3.1 Random walks
9.3.2 Continuous Brownian motion
9.4 Stochastic differential equations
9.4.1 Adding noise to differential equations
9.4.2 Numerical methods for SDEs
REALITY CHECK 9: The Black-Scholes formula
9.5 Software and Further Reading
10. Trigonometric Interpolation and the FFT
10.1 The Fourier Transform
10.1.1 Complex arithmetic
10.1.2 Discrete Fourier Transform
10.1.3 The Fast Fourier Transform
10.2 Trigonometric interpolation
10.2.1 The DFT Interpolation Theorem
10.2.2 Efficient evaluation of trigonometric functions
10.3 The FFT and signal processing
10.3.1 Orthogonality and interpolation
10.3.2 Least squares fitting with trigonometric functions
10.3.3 Sound, noise, and filtering
REALITY CHECK 10: The Wiener filter
10.4 Software and Further Reading
11. Compression
11.1 The Discrete Cosine Transform
11.1.1 One-dimensional DCT
11.1.2 The DCT and least squares approximation
11.2 Two-dimensional DCT and image compression
11.2.1 Two-dimensional DCT
11.2.2 Image compression
11.2.3 Quantization
11.3 Huffman coding
11.3.1 Information theory and coding
11.3.2 Huffman coding for the JPEG format
11.4 Modified DCT and audio compression
11.4.1 Modified Discrete Cosine Transform
11.4.2 Bit quantization
REALITY CHECK 11: A simple audio codec using the MDCT
11.5 Software and Further Reading
12. Eigenvalues and Singular Values
12.1 Power iteration methods
12.1.1 Power iteration
12.1.2 Convergence of power iteration
12.1.3 Inverse power iteration
12.1.4 Rayleigh quotient iteration
12.2 QR algorithm
12.2.1 Simultaneous iteration
12.2.2 Real Schur form and QR
12.2.3 Upper Hessenberg form
REALITY CHECK 12: How search engines rate page quality
12.3 Singular value decomposition
12.3.1 Finding the SVD in general
12.3.2 Special case: symmetric matrices
12.4 Applications of the SVD
12.4.1 Properties of the SVD
12.4.2 Dimension reduction
12.4.3 Compression
12.4.4 Calculating the SVD
12.5 Software and Further Reading
13. Optimization
13.1 Unconstrained optimization without derivatives
13.1.1 Golden section search
13.1.2 Successive parabolic interpolation
13.1.3 Nelder-Mead search
13.2 Unconstrained optimization with derivatives
13.2.1 Newton's method
13.2.2 Steepest descent
13.2.3 Conjugate gradient search
13.2.4 Nonlinear least squares
REALITY CHECK 13: Molecular conformation and numerical optimization
13.3 Software and Further Reading
APPENDIX
Appendix A: Matrix Algebra
A.1 Matrix fundamentals
A.2 Block multiplication
A.3 Eigenvalues and eigenvectors
A.4 Symmetric matrices
A.5 Vector calculus
Appendix B: Introduction to MATLAB
B.1 Starting MATLAB
B.2 MATLAB graphics
B.3 Programming in MATLAB
B.4 Flow control
B.5 Functions
B.6 Matrix operations
B.7 Animation and movies
References |
Book Description: This book presents the basics of applied calculus through technology and practical use. Written especially for readers with an interest in business, economics, life and social sciences. Topics include the applications of first and second derivatives and the integral as well as translations among graphs, formulas, numbers, and words. KEY TOPIC: While emphasizing fundamental concepts over symbol manipulation, Applied Calculus: A Graphing Approach presents calculus in a manner that is intuitive, yet intellectually satisfying. It provides realistic applications illustrating the uses of calculus in other disciplines as well as detailed instructions on the use of the TI-82, TI-83, and TI-85 graphing calculators. Instructions on the use of Visual Calculus, an easy-to-use software package customized for the book are also given. A valuable reference book for professionals across a variety of disciplines who need to apply calculus to mathematical problems in their own businesses. |
Includes seven chapters: Number Sequences, Re-arranging Formulae, Simultaneous Equations, Quadratic Equations and Trial and Error. Each chapter contains at least one virtual laboratory, which allows students to input their own examples and produces a step-by-step solution. Main theory is general, but the plug-in question books allow for subject-specific, or harder/easier questions and examples to be incorporated. |
books.google.com - Besides... II For Dummies
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User Review - msrg - Overstock.com
Algebra for Dummies, like most of the "for Dummies" series, explains concepts in a clear, concise manner. My son and his friends did think the book was helpful in clarifying algebra. Some topics ... Read full review
Review: Algebra II For Dummies (For Dummies (Math & Science))
User Review - Jeff Sylvester - Goodreads
Great resource. Covers higher level mathematics but far beyond in depth and breadth from what I can remember taking in Gr. 12 algebra and trigonometry. If you can master the contents of the Dummies ...Read full review
Globalbook Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you ... detalles.php?ISBN=0471775819
Algebra II For Dummies:Book Information - For Dummies Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you ... WileyCDA/ DummiesTitle/ Algebra-II-For-Dummies.productCd-0471775819.html
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About the author (2006)
Mary Jane Sterling has authored Algebra For Dummies, Trigonometry For Dummies, Algebra Workbook For Dummies, Trigonometry Workbook For Dummies, Algebra I CliffsStudySolver, and Algebra II CliffsStudySolver. She taught junior high and high school math for many years before beginning her current 25-year-and-counting career at Bradley University in Peoria, Illinois. Mary Jane enjoys working with her students both in the classroom and outside the classroom, where they do various community service projects. |
Algebra Cheat SheetsAlgebra Cheat Sheets is a set of black-line masters showing examples and procedures for teaching 40 algebraic concepts. Most cheat sheets come in two versions -- one with an example and the second with space for student notes. Comprehensive instructions are given for teachers and/or parents.
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
277.7 KB | 75-20 years teaching experience in schools
-interactive and group models as well as individual pace
-Montessori Jr HS teacher and then Principal
-25 years educational software development
-25 years educational manipulative development |
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Boletin UAL: Online Mathematical Project
Submitted by Boletin on Sun, 02/19/2012 - 10:54
Optional Abstract:
The project we present here is an online free journal on the spreading of Mathematics ( mainly addressed to secondary school students, although also appropriate for a broader audience. It is a local action of the University of Almería (Spain) to promote Mathematics among secondary school students and to strengthen relationships with their Math teachers. Our leitmotiv is to provide a closer, more objective, real and positive image of mathematics and help to improve its perception and assessment. This project also includes visits to secondary schools, where the prize of the journal's mathematical contest is awarded to the winner and talks on popularization of Maths are delivered. The journal, created in 2007, is published in Spanish 3 times an academic course, and its length is around 20-25 pages. More than 30 persons are involved in its edition. Last year we had around 115,000 visits and more than 45,000 downloads.
In Spain, it is well known that secondary school students' motivation to study Science (especially Mathematics) is not very strong. This is a common problem to almost all Europe. Spanish and Andalusian governments have general policies on education to promote the study of Science. They are necessary and convenient. However, we think that local actions in the students' environment, which supplement these policies, are also needed.
For this reason, five years ago we founded at the University of Almería an online free journal called Boletín de la Titulación de Matemáticas de la UAL ( mainly addressed to those students. Our intention is to stimulate their interest in mathematics, to develop their mathematical skills, to complement their background, and to improve their perception and assessment of mathematics. Many aspects, usually out of the syllabus, are treated to provide a closer, more real and positive image of mathematics. Another aim is to encourage a closer contact between secondary schools and our university. Although these are our main goals, we do not discard a broader audience and often include articles appropriate for a general public.
It is not a customary journal or gazette but a virtual place where secondary school students and teachers, undergraduate students and university professors can write about their experience with Mathematics in their classes, read and write short articles on mathematical spreading, participate in quizzes, see real life applications of Mathematics, etc. We do not know of a similar project in Spain, and our journal is now known all over the country.
Boletín is available in a well-known free format from our web page (pdf file), and elaborated with the free software LATEX, commonly used in the scientific world.
This project is a joint experience which is carried out by people working or studying in different levels of the Spanish educational system. There are professors and students from our university and teachers from secondary schools. The secondary school students are, as said, the main target of this project, and they can participate through the mathematical contest that we pose. There exists a closer contact later in the prize award ceremony at the winner's secondary school. In such ceremonies, apart from awarding the prize, we give a talk on Maths and inform about our university degree in Maths, thus strengthening relationships with the winner's secondary school and their Math teachers. No doubt, the contest is the way that leads us from our virtual site to the live contact with the most important part of our audience. Regarding our undergraduate students, they have their own section in the journal, called "Territorio Estudiante" (Student Area).
The journal is published in Spanish 3 times an academic course (October, January and April). Its length is around 20-25 pages and papers published must be short and suitable for a secondary school level. It is divided into 5 main sections, each of which has several subsections:
Interviews, mathematical activities, and news.
From Secondary School to University, containing teaching experiences, learning Maths in a foreign language, solutions to the university entrance exam Maths problems, etc.
A mathematical contest for secondary school students.
Mathematical spreading, including short articles about History of Mathematics, applications of Mathematics, Women and Mathematics, Culture and Mathematics, etc. Books and web pages reviews about Mathematics popularization appear here as well. Mathematical quotations and puzzles are also included.
Student area, made itself by our undergraduate students and where, among other things, they speak about their experiences with mathematical studies and activities and interview Erasmus students and alumni.
The editorial committee consists of 3 main editors and 29 section editors, composed by professors of the University of Almería and teachers from secondary schools of our province, and 4 undergraduate students in charge of the student area. Although our goal is acting in our local environment, since we use a global tool such as the Internet, we usually receive experiences and articles from people from other regions, which is an indicator that Boletín is known out of our province. For example, the Spanish Royal Mathematical Society (RSME) in its nice site DivulgaMAT ( includes a link with the summaries of the Boletín issues.
To spread our project, apart from our web site and visits to secondary schools, we announce the publication of a new issue in the RSME electronic bulletin, collaborate with the local press, use Facebook (group Almería Matemática with more than a hundred members), give out merchandising (pens with our logo, mathematical T-shirts, usb memories, etc.) and publicize it among our guest professors and at the universities we visit for research purposes.
Several facts allow us to claim that this project has a very positive effect. We are very interested in knowing if our efforts to bring the Mathematics closer to young people and teachers in schools are useful. Among the methods to know this we use:
Appearance in the local newspapers to achieve more social relevance (see the additional documentation).
Number of visits that we pay to secondary schools and feedback from them since this quantity points out the interest that the Boletín arouses.
Recognition by the local academic authorities. In 2011, we received the award for Excellence in Teaching Innovation.
In conclusion, with the invaluable help of our journal we have set up a reliable atmosphere between professors from our university and teachers from secondary schools in our region of influence. This has permitted to develop other activities jointly such as meetings about mathematical education (I Jornada del Profesorado de Almería, or the group Almería Matemática in Facebook. Our Maths students at the university benefited from this and there is a growing interest among secondary school students in studying the degree in Mathematics at the University of Almería. |
and is self-contained. It is suitable both as a text and as a reference.
* A wide ranging all encompasing overview of mathematical programming from its origins to recent developments * A result of over thirty years of teaching experience in this feild * A self-contained guide suitable both as a text and as a reference less |
MATHCOUNTS® Prep
Course Description
Description
This course is intended to prepare students for future MATHCOUNTS® training and competition by strengthening their analytical and problem-solving skills. It is designed to challenge and motivate students who have had no previous MATHCOUNTS® experience. The web-based whiteboard provides interactive and team-building experiences for students.
Topics include:
averages
estimation
fractions
decimals and percents
exponential expressions
scientific notation
probability
statistics
area and volume
geometry
number theory
patterns
logic
Materials Needed
There are no required materials for this course.
List of Topics
The following topics will be covered in this course:
Integers
Fractions and Decimals
Variables, Functions & Expressions
Exponents and Radicals
Number Sense and Patterns
Algebra
Plane Geometry and Solid Geometry
Coordinate System
Probability and Statistics
Graphs and Diagrams
Transformations and Similarity
Whiteboard Session Times
The instructor will hold whiteboard sessions each week at the following times:
Wednesday from 6:45 PM ET to 7:45 PM ET
Wednesday from 8:00 PM ET to 9:00 PM ET
Whiteboard Demo
System Requirements
All CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).
This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment.(Note: iOS & Android devices cannot run Java applets.) |
Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics. Emphasizing the physical interpret... |
Goal
Introduction to advanced topics in optimization theory and algorithms. The course "Mathematical Optimization" gives the background knowledge to attend various special state-of-the-art lectures at IFOR like "Geometric Integer Programming".
Target Audience
Students with a mathematical interest in optimization. This course assumes the basic knowledge of linear programming, which is taught in courses such as "Introduction to Optimization |
Linear transformations. "Linear Algebra is the heart of applied science but there are divergent views concerning its meaning.
The field of Linear Algebra is more beautiful and more fundamental than its rather dull name may suggest. More beautiful because it is full of powerful ideas that are quite unlike those normally emphasized in a linear algebra course in a mathematics department.
Throughout the book the author follows the practice of first presenting required background material, which is then used to develop the results. The book is divided in ten chapters.
Relevant material is included in each chapter from other sources improves readability and makes the presentation "self-contained" to a large extent. All the examples
(more).
Readers will find tips on how to optimise a company's potential through articles by experts and leading professionals. The book serves as an ideal guide for concepts like people management, leadership, resource allocation, decision making, standing out amongst competition, and strategy development"A systematic procedure for attacking problems is essential for effectiveness in teaching algebra and geometry so that pupils may acquaint themselves with comprehensive knowledge of subject matter and deductive reasoning and develop habits of careful thinking, observing, comparing and problem-solving to discover new ideas, statements, truths, concepts and theorems. Therefore, in order to be effective and successful, teachers have to become well aware of these techniques.
"A Textbook of Algebra and Geometry" brings to the fore each and every aspect, concept, technique, theorem and principle of algebra and geometry to make the subject teachers successful. In this endeavour the book delves deep into basic needs and aims, course content, problem-solving, various types of equations, preparatory course, graphs, linear
"A Textbook of Algebra and Trigonometry is written to meet the requirements of students at various levels of the examples have been taken from the examination papers of various universities.
6. Gaps in understanding, sustainable use and conservation of biodiversity.
7. Strategy and action plan.
8. Constitutional and statutory protection.
Appendices. Index.
"Assam, a constituent of one of the two biodiversity hotspots of India, holds immense promise for conservation and sustainable use of its rich biological resources. Owing to alarming population growth and ramification of human aspirations and activities the area has been loosing fast its biodiversity base causing thereby irreparable harm to the state's genetic legacy and potentiality for progress.
Because of man's ever growing greed, many valuable species of plants and animals have silently disappeared before they could be identified. It is in this backdrop, this book explores the extent of biodiversity generously gifted by nature to Assam, a land with unique natural make up and
Contents: Preface. 1. Lyrics with Alif as the terminal. 2. Lyrics with Bey as the terminal. 3. Lyrics with Tey as the terminal. 4. Lyrics with They or Sey, Jeem, Chey and Khey as the terminals. 5. Lyrics with Daal as the terminal. 6. Lyrics with Zaal and Re as the terminals. 7. Lyrics with Ze as the(more)Contents: Preface. 1. customerature organizat(more) organization.
This system features five key initiatives-create a value-based vision, give customers a value proposition, align what you do with customer desires, balance "hard" and "soft" business to deliver on promises, liberate the energies of the organization's people-and explains how to implement them company-wide |
Key Message:TheLial serieshas helped thousands of readers succeed in developmental mathematics through its approachable writing style, relevant real-world examples, extensive exercise sets, and complete supplements package. Key Topics:Reviewa... MORElities, and Functions; Inverse, Exponential, and Logarithmic Functions; Nonlinear Functions, Conic Sections, and Nonlinear Systems; Sequences and Series Market:For all readers interested in Intermediate Algebra. The Lial series has helped thousands of students succeed in developmental mathematics through its approachable writing style, relevant real-world examples, extensive exercise sets, and complete supplements package. With this edition, the authors continue to provide students and instructors with the very best package for learning and teaching supporta book written with student success as its top priority, a media package that truly brings the book to life, and an expanded instructor supplements package.
Note: each chapter concludes with a Group Activity, Chapter Summary, Chapter Review Exercises, Chapter Test, and after Chapter 1, a set of Cumulative Review Exercises |
Astronomy Calculator - R.T. Back
The Astronomy Calculator provides general information about the phases of the moon and planets, and annual meteor showers. You supply the date, time of observation, and the number of hours east and west from directly overhead.
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Athena Scientific
A small publishing company that specializes primarily in textbooks written by professors at the Massachusetts Institute of Technology and used in their courses. Publications: three textbooks currently used in first year graduate courses at the Department
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Atlantis Puzzles & Games - Karl Scherer
Puzzles and games for sale; puzzle books (A Puzzling Journey To The Reptiles And Related Animals; NUTTS And Other Crackers; New Mosaics - A Book On Tilings); Fractal computer art; brain teasers (A-Maze; Globetrotter). Also ALIVE, a WINDOWS version of
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ATLAS of Finite Group representations - R. A. Wilson
Representations of many finite simple groups and related groups such as covering groups and automorphism groups of simple groups. Contents: groups: Alternating & Symmetric, Lie type, and sporadic. Includes experimental generic group pagemaker and an experimental
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ATLAST Project Forum
A National Science Foundation project to encourage and facilitate the use of software in teaching linear algebra. Includes information on the book ATLAST Computer Exercises for Linear Algebra , (Prentice-Hall, Fall 1996, featuring teacher-developed, class-tested
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Audiblox - Susan du Plessis
Audiblox is a system of cognitive exercises, aimed at the development of the skills foundational to reading, spelling, and writing. A resource for dyslexia, dysgraphia and other learning disabilities.
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Authentic Assessment Toolbox - Jon Mueller
A how-to text on creating authentic tasks, rubrics and standards for measuring and improving student learning, including an introduction to the topic with comparison to traditional test-based assessment, why and how best to use it, standards, tasks, rubrics
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AutoAbacus - Nathan Funk, Singular Systems
An equations-solving application and calculator. Any number of simultaneous equations can be solved instantly. Uses for the program range from checking results on homework assignments to setting up mathematical models of a real-life problems. A demo is
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Automated Deduction - William McCune
Research on applications of automated deduction to problems in abstract algebra and algebraic geometry, algorithms and strategies for searching for proofs and for counterexamples, high-performance implementation of automated deduction algorithms, and
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Automatic Fractal Map Generator - Paolo Guagliumi
A freeware program that generates .map files used by Winfract and Fractint, which make use of .map files that contain 256 lines of ASCII characters that describe RGB (red, green, blue) color values. Site is in English and Italian.
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Avances de Investigación en Educación Matemática
The official publication of the Spanish Society for Research in Mathematics Education (SEIEM, Sociedad Española de Investigación Matemática) welcomes contributions in either Spanish or Portuguese. Freely download PDFs of past articles,
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Averting Instant Insanity - Ivars Peterson (MathTrek)
Once called "The Great Tantalizer," the puzzle looks innocuous and sounds quite simple. It consists of a set of four cubes with one of four colors on each of their six faces. Your goal is to arrange the four cubes in a row so that all four colors appear
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Aviezri Fraenkel
Aviezri Fraenkel is an Israeli mathematician investigating combinatorial game theory. This page offers preprints and recent reprints in postscript format; a comprehensive bibliography on combinatorial games; and links to information on conferences and
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Avoiding Weapons of Math Destruction
"Reflections from a student teacher." Blog posts, which date back to September, 2012, have included "First Week Excitement," "The Flipped Classroom," and "The Challenge of Open-Ended Questions."
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The Awari Oracle - John Romein
Play the ancient African "count and capture" strategy board game, related to mancala, and also known as wari, awale, oware, or ayo. Dutch computer scientists from Amsterdam's Vrije Universiteit developed a program that computes the best move and eventual
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Shiro Chemistry algebra extensively and understand what we need to do to master it. Calculus introduces abstract mathematical concepts that often require significant explanation in to understand its fundamental concepts. Calculus becomes even more complex in the second half of the basic course |
Search Loci: Convergence:In J. R. Newman
(ed.), The World of
Mathematics, New
York: Simon and
Schuster, 1956.
The Unique Effects of Including History in College Algebra
The Modules (2)
Introduction to Polynomials: Looks at the efforts put forth in finding zeros of polynomials and includes a brief introduction to the lives of Niels Henrik Abel and Evariste Galois. This historical module excerpt illustrates the difficulties Abel and Galois had in breaking into the mathematical circles of their time. "Niels Henrik Abel, at the age of sixteen, proved that a general formula for solving a quintic (fifth degree) polynomial did not exist…. However, since he was largely self taught, leading mathematicians in Paris, such as Cauchy, largely ignored him… Evariste Galois had equally important discoveries. At sixteen, Galois had the desire to enter the most prestigious engineering school of the day, the École Polytechnique… [W]hen Galois submitted a paper to the school as part of the admission process, Cauchy lost the paper. He attended another school for the purpose of training to become a teacher. However, he kept his mathematical studies up and submitted a second paper to the École Polytechnique. This paper also appears to have been lost." (Hagerty and Smith, 2006).
Polynomials: Looks at theoretical methods to help find zeros of polynomials. The module looks at Horner's method and how information traveled in eras prior to modern-day technology. It includes a discussion of the difficulty of crediting the correct civilization with the development of a topic as it is believed that Horner did not develop the method credited to him; in fact, the Ancient Chinese knew of this method (Eves, 1992).
Technology: Looks at methods to use technology to find zeros of polynomials, and discusses the rapid changes in technology. The goal is to have the students take a look at when the Internet was developed and realize that instant messages were not always possible. The students need to realize that their parents enjoyed "Pong" and "Pacman" and their grandparents had the radio. Thus, the students need to revaluate the question "My parents didn't need math, why do I?" |
Mathematics Department
General description of expectations for math courses:
Students taking an online math class should expect to have work assigned on a daily basis (Monday through Friday). Students receive a pacing guide at the beginning of each term that shows them exactly what to complete each day of the semester. All work must be completed by midnight on the date it is listed on the pacing guide.
While taking a minimester math class with our campus, you should plan on spending a minimum of 15 hours per week. Students taking a semester-long math class should plan on spending about 10 hours per week on the class. If you are taking a summer semester course, please plan on spending 20 hours per week.
Frequency of Math Chats:
All instructors will hold at least one chat a week according to the schedule posted in each course. These chats are designed to enhance student mastery of the AKS and to provide an opportunity for remediation, reinforcement, and extension. Students are required to attend these chats or listen to the chat recording within 48 hours.
***Face to Face Requirements:
The only face-to-face requirement for mathematics is the Final Exam and/or End of Course Test at the end of the semester. Select courses also require students to come take a county Interim exam at the midpoint of the term.
We also do reserve the right to have a student come take an assessment in a proctored setting at any point during the semester if the need arises.
Materials Pickup Information:
The following math classes require a textbook, which must be checked out from our campus on our scheduled Materials Pickup time:
If at all possible, students should have regular access to a calculator while taking our online math classes. Graphing calculators are the ideal choice for most of our courses. Unfortunately, our campus does not have calculators that we can provide to our students, but we do have a graphing calculator you can download for free onto your computer.
Please click here to see a sample online math course syllabus and associated due dates calendar. |
gebra, the Easy Way
For use in schools and libraries only. Covers the fundamentals of algebra, including explanations of equations, negative numbers, exponents, roots, ...Show synopsisFor use in schools and libraries only. Covers the fundamentals of algebra, including explanations of equations, negative numbers, exponents, roots, functions, graphs, and logarithms |
2 Algebra
These lessons will help students understand how classroom lessons about lines of best fit, slope, quadratic equations, percent of change, polynomials, and the Pythagorean theorem are applicable to future careers.
The lessons address the following questions:
Lesson 1: How are best-fit lines important in many careers?
Lesson 2: How might a personal trainer use slope to analyze a workout and plan for future training sessions?
Lesson 3: How can finding the vertex of a parabola be a useful career skill?
Lesson 4: How are formulas containing radicals — such as those for sight distance — useful to the military and in other careers?
Lesson 5: How can the ability to calculate percent of change be important in retail careers?
Lesson 6: How might a postal worker use polynomials to determine whether boxes of different sizes meet the post office's shipping requirements?
Lesson 7: How is the Pythagorean theorem useful to utility workers?
Lesson 8: How can matrices be used to display and interpret data in various careers?
Lesson 9: How is the concept of exponential growth important in banking careers?
Lesson 10: How can using elimination or substitution in a system of equations determine important statistics in sports |
TI-Nspire™ CAS with Touchpad
CAS Comparison Chart
CAS stands for Computer Algebra System. Using a CAS system on a calculator means that the calculator will be able to perform symbolic manipulation of variables without a value being assigned to those variables. The comparison chart below gives some examples of how answers might look different on TI-Nspire CAS as opposed to TI-Nspire and also some of the additional functionality of TI-Nspire CAS. Here are some of examples of the types.
Mathematical constants and variables are recognized and simplified symbolically
Simplify trigonometric identities
Will give exact values for special angles on the unit circle
Algebraic calculations
TI-Nspire handheld
TI-Nspire CAS handheld
Find approximate values for solution of an equation
Exact and approximate values for solutions of an equation
Polymonials are factored and expanded
Complex solutions and zeros can be found
Calculus calculations
TI-Nspire handheld
TI-Nspire CAS handheld
Find numerical approximations of the derivative at a point
Find numerical approximations of the integral value for a given interval
Calculate limits of an expression (including right-hand and left-hand limits)
Find derivatives of function as well as find a derivative at a point
Find values for definite and indefinite integrals
Uses correct notion for derivatives and integrals as students would see in a textbook or write on paper
CAS can help students develop algebraic patterns. In these examples, CAS is used as a learning tool and can help students discover the algebra themselves. This allows for a solid conceptual understanding and can provide a basis for learning of by-hand symbolic manipulation. |
Everyone needs a little help with middle
school and high school math. We have developed a series of programs
that help a student with pre-algebra, algebra, pre-calculus and calculus
skills. Topics include equation solving, plotting functions and
studying probability. Kids and teens often ask us what is the
purpose of learning hard subjects like math. Our answer is simple!
You must understand math in order to develop anything of interest using
your personal computer. Really good computer games use complex math.
We use many of these math concepts in our Computer Programming tutorials.
We hope you will become interested in
learning how to develop your own math programs and games using our
Computer Science For Kids
& Teens
Programming Tutorials. If you are a High- School Math
Teacher you may want to look at our Real World
Math Tutorial For High School Students.
Probability
A study of probability using one
to five dice as an example. Compare theory to practice.
Right Triangle See relations betweens angles and
side lengths in a right triangle. |
Info for Students
Algebra Nation was created especially to help YOU succeed on the Algebra End-of-Course (EOC) exam.
Algebra Nation is meant for you to use on your own time. You're a busy student with lots of other activities and responsibilities. Forgot how to solve literal equations when you're starting homework at 9PM? Hop onto Algebra Nation and watch Zach and other Study Experts break it down for you. Want to ask a question while you're waiting for the bus? Grab your smartphone, snap a picture of your homework question, and post it to the wall. Want to get some extra practice before a test or quiz? Try out the "Test Yourself!" practice tool, which tells you exactly what you answered correctly or incorrectly, offers a video that teaches you exactly how to solve the problem, and directs you to the videos that will help you brush up on your skills.
What are you waiting for? Work smarter, not harder and try Algebra Nation out.
All you have to do is click the "Enter Algebra Nation" button on AlgebraNation.com Follow the on-screen directions and get started today. Watch the Introduction to Algebra Nation video above for more information! |
Washington, NJ PrecalculusWe study elementary set theory and use Venn diagrams. We also spend time studying combinatorics, since this is very beneficial for brain development and also because combinatorics is linked to probability theory. How do we study probability? |
The elementary school curriculum in recent years has begun
to include a significant amount of geometry, including reasoning about
important and fundamental ideas.This course is designed to provide students intending to become
elementary school teachers with the beginnings of a strong background to teach
this geometry.
While the geometry topics will be basic, the course will go
into them deeply.There is much to
think about in considering basic geometry ideas. Since the course will
emphasize understanding, reasoning, and communication, class discussion and
writing will be key components of the course.
Because this course is for future elementary teachers, few
of whom are math majors, the course will be designed to be friendly and
accessible to students who have not been in a math course recently.The subject matter lends itself to
visual and hands-on approaches, and these will be utilized fully.
As suggested above, there will regular writing, projects and
some assigned readings beyond the textbook.Because of the importance of reasoning and communication,
in-class work will be essential. In particular, attendance at all of every (or
almost every) class is required. If you will miss all or part of class on a
regular basis, you should not take this course.
Since this is a Credit/No Credit course on topics in
elementary mathematics, one might assume that this would be an easy course,
especially if one has a strong math background.On the contrary, to get Credit in the course, a student must
achieve a satisfactory level in all components of the course, including writing
and classroom participation.So
the course will demand a significant and consistent amount of work from
everyone, whatever her/his math background.On the positive side, consistent serious work should suffice
for a Credit grade, even if a student brings a weaker math background.
There will be some tests and also a final exam at the
regularly scheduled time, but it will not be the conventional sort of exam.
Note that this is a content course, not a methods course.
While we will aim to model good teaching techniques, we will be addressing
mainly questions of mathematical content, not methods for teaching elementary
school students. If you enter the Teacher Education Program in the UW College
of Education, you will take a methods course on teaching elementary mathematics. |
Cover
Title Page
Copyright
PREFACE
Linear algebra is now included in the undergraduate curriculum of
most universities. It is generally recognized that this branch of
algebra, being less abstract and directly motivated by geometry, is
easier to understand than some other branches and that because of the
wide applications it should be taught as early as possible. The ...
CONTENTS
CHAPTER I. LINEAR SPACE
In the euclidean plane E, we choose a fixed point 0 as the origin,
and consider the set X of arrows or vectors in E with the common
initial point 0 . A vector a in E with initial point 0 and endpoint A is
by definition the ordered pair (O, A ) of points. The vector a = ( 0 , A)
can be regarded as a graphical representation of a force acting at the ...
CHAPTER II. LINEAR TRANSFORMATIONS
At the beginning of the last chapter, we gave a brief description of
abstract algebra as the mathematical theory of algebraic systems and,
in particular, linear algebra as the mathematical theory of linear
spaces. These descriptions are incomplete, for we naturally want to
find relations among the algebraic systems in question. In other ...
CHAPTER III. AFFINE GEOMETRY
To define the basic notions of geometry, we can follow the so
called synthetic approach by postulating geometric objects (e.g.
points, lines and planes) and geometric relations (e.g. incidence and
betweenness) as primitive undefined concepts and proceed to build
up the geometry from a number of axioms which are postulated to ...
CHAPTER IV. PROJECTIVE GEOMETRY
In order to have a concise theory without all these awkward exceptions,
we can - and this is a crucial step towards projective
geometry - extend the plane A (and similarly the plane A') by the
adjunction of a set of new points called points at infinity. More
precisely, we understand by a point at infinity of A the direction ...
CHAPTER V. MATRICES
This therefore suggests the notion of a matrix as a doubly indexed
family of scalars. Matrices are one of the most important tools in the
study of linear transformations on finite-dimensional linear spaces.
However, we need not overestimate their importance in the theory of
linear algebra since the matrices play for the linear transformations ...
CHAPTER VI. MULTILINEAR FORMS
Linear transformations studied in Chapter II are, by definition,
vector-valued functions of one vector variable satisfying a certain
algebraic requirement called linearity. When we try to impose similar
conditions on vector-valued functions of two (or more) vector
variables, two different points of view are open to us. To be ...
CHAPTER VII. EIGENVALUES
Given a single endomorphism o of a finite-dimensional linear
space X, it is desirable to have a base of X relative to which the
matrix of o takes up a form as simple as possible. We shall see in this
chapter that some endomorphisms can be represented (relative to
certain bases) by matrices of diagonal form; while for every ...
CHAPTER VIII. INNER PRODUCT SPACES
We began in Chapter I by considering certain properties of vectors
in the ordinary plane. Then we used the set V2 of all such vectors
together with the usual addition and multiplication as a prototype
linear space to define general linear spaces. So far we have entirely
neglected the metric aspect of the linear space V2 ; this means that |
You, too, can understand geometry---- just ask Dr. Math ? ! Are things starting to get tougher in geometry class? Don't panic. Dr. Math--the popular online math resource--is here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems,... more...
Learn geometry at your own pace What are congruent circles? How do you find the hypotenuse of a triangle? What is the sum of the angles in a decagon? How can you apply geometric equations to your daily life? With the unbeatable study companion Geometry: A Self-Teaching Guide, you'll discover the answers to these questions and many more. This thorough... more...
There's no such thing as too much practice. This reproducible program builds skills incrementally. By inviting students to "show what they know" in a variety of new formats, these stimulating lessons will enable struggling students to actually enjoy the learing process. As in all of the binder programs, the dual emphasis is on (1) mastery of the basics... more...
Meyer's Geometry and Its Applications, Second Edition , combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text... more...
Part of the ''Demystified'' series, this title teaches complex subjects in an easy-to-absorb manner and is designed for users without formal training, unlimited time, or genius IQs. It helps users understand circle and triangle models; inverses of circular functions; graphs of functions; coordinate conversions; angles and distances; and more. more...
Tough Test Questions? Missed Lectures? Not Enough Time? Lucky for you there is Schaum's.... more...
Deformable objects are ubiquitous in the world, on various levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. This book provides an overview of the state of science in analysis and synthesis of non-rigid shapes. more...
Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more...
The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... |
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