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posite Mathematics (Mcb)-For Class Ii
(Paperback) by Agarwal R.S. Vikas Aggarwal
Language: English Available (Delivered in 2-4 working days.) See Details Stated Delivery time is for Major Metros
Other Locations might take more time depending on the courier coverage
Book Summary of Composite Mathematics (Mcb)-For Class Ii
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 and application skills |
Interactive Software Demos
for Learning Differential Equations
Since the time of Isaac Newton, differential equations have been useful
for modeling of a wide variety of dynamical physical systems. For example,
the motion of a mass acted upon by a force can be modeled by a second-order
differential equation using Newton's second law.
The objective of this project is to visualize solutions to
basic differential equations used in various undergraduate courses on
applied mathematics, physics, and engineering.
The visualization is provided by real-time web-enabled
software technologies. It is expected that the interactive software
demos smooth out the student's learning curve and help instructors
in lecturing the undergraduate courses.
Learning Goals:
Classify critical points of the dynamical system and local stability
of critical points. Match solutions of differential equations
and trajectories on a phase plane of the system. Understand
differences between finite and infinite trajectories
on a phase plane. Identify the separatrix curves on the phase plane.
Control behaviour of the system by changing initial values
of the system. Understand the role of damping for motion of
the pendulum.
Learning Goals:
Understand hypotheses and constraints of mathematical modeling.
Classify critical points of the dynamical system. Understand
differences between local and global stability of critical points.
Match population cycles of the predator-prey system
and periodic solutions of the dynamical system.
Learning Goals:
Identify limit cycles on a phase plane of the system.
Control the flow of trajectories that draws the global phase portrait
of the system. Understand global stability of critical points
and limit cycles. Utilize the Hopf bifurcation of the dynamical system.
Software Requirements:
The software demos work with Microsoft Internet Explorer.
They are read-only with other browsers such as Netscape.
Before starting the demos, maximize the browser window and
close other applications on your computer. |
Product Details
See What's Inside
Product Description
By Linda Sheffield, Susan Johnsen
Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K–12 schools. The book describes—and demonstrates with specific examples from the CCSS—what effective differentiated activities in mathematics look like for top learners. It shares how educators can provide rigor within the new standards to allow students to demonstrate higher level thinking, reasoning, problem solving, passion, and inventiveness in mathematics. By doing so, students will develop the skills, habits of mind, and attitudes toward learning needed to reach high levels of competency and creative production in mathematics fields.
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The Center for the Study of Mathematics Curriculum (CSMC) leaders developed this volume to further the goal of teachers having opportunities to interact across grades in ways that help both teachers and their students see connections in schooling as they progress through the grades. Each section of this volume contains three companion chapters appropriate to the three grade bands—K–5, 6–8, and 9–12—focusing on important curriculum issues related to understanding and implementing the CCSSM.
Connect the process of problem solving with the content of the Common Core. The first of a series, this book will help mathematics educators illuminate a crucial link between problem solving and the Common Core State Standards.
How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)?
This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for high school. Discover what students should learn and how they should learn it, including deep support for the Mathematical Modeling conceptual category of the CCSS. Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You'll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students. Extensive tools to implement a successful and coherent formative assessment and RTI response are included.
How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)?
This leader companion to the grade-level teacher guides illustrates how to sustain successful implementation of the CCSS for mathematics. School leaders will discover how to support and focus the work of their collaborative mathematics teams for significant student achievement and improvement. Readers will receive explicit guidance and resources on how to lead and exceed the assessment expectations of the common core.
How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)?
This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematicsHow do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)?
This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for grades 3–5. Discover what students should learn and how they should learn it at each grade level, including deep support for the unique work for Number & Operations—Fractions in grades 3–5 and learning progression models that capstone expectations for middle school mathematics readiness.
This highly practical, comprehensive guide combines NCTM's wealth of knowledge from experts in the fields of formative and summative assessment with research-based data and offers a library for understanding both formative and summative assessment.
Transform math instruction with effective CCSS leadershipThis professional development resource helps principals and math leaders grapple with the changes that must be addressed so that teachers can implement the practices required by the CCSS.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Classes are not aimed exclusively towards math competitions. Instead, IDEA Math is a program that can help students
develop logical thinking and problem solving skills in the long run. We have found that our program not only broadens and
deepens the students' knowledge and skills in mathematics, but also help them develop perseverance and creativity that
will benefit them in the long-run, regardless of their career paths.
I have taken IDEA MATH classes last year, will the classes be repeated for next year?
We have reorganized our series this year so that the majority of the material will be brand new. In future
years, students could choose to move up from one series to another. Moreover, if a student chooses to be in a series for two
years in a row, we will insert new problems and concepts into that series from year to year.
How am I (the student) evaluated? Are there any evaluation tests?
During each of the 6-week courses, there will be two 1 to 1.5 hour tests to check each student's progress. One test will be in
the middle of the course, and the other will be at the end. The tests are intended as check points. They
are not evaluations.
Since we focus on contest preparation, there will be various forms of mock contests. Scores/results will be
kept only for the purpose of practicing, not for evaluation. We try to use these activities to stimulate students' interest and
get them used to the contest atmosphere, instead of pressuring them through evaluation.
Who shall I meet at IDEA MATH?
Other capable students from the Massachusetts area who are passionate about mathematics. Many of our students have developed
lasting friendships with their IDEA MATH peers, and many have learned a great deal from their peers as well as their instructors.
What is the difference between IDEA MATH and what I am learning in school?
The depth. At IDEA MATH, we do not focus on introducing students to higher math concepts, say Calculus. However, we go into
much greater depth with topics covered in a middle/high school curriculum. For example, an eighth grade geometry math class may
cover the triangle are formula of base times height divided by two, but our Math Roots Series will introduce students to three
or four more important ways to calculate the same area. Students will see the connection between these different ways.
Can I sit in for a class?
Usually we do not allow sit-ins. However, we do encourage all prospective students to join us for the Open House.
Application
How do I apply?
You need do online registration first (creat your account), take the evaluation test, and then register course online.
Small Group and Private Lessons
Do you offer private lessons?
Yes. We offer lessons for all mathematical subjects, standardized tests and competitions for small groups and individuals.
How do I schedule a private or small group lesson?
Please call (603)686-1706 or email [email protected].
What is the rate of private and small group lesson?
The price varies by the subjects, levels and the group's size, with a range from $40 to $100 per hour per person.
Please contact us for specifics. |
... variable • numerical substitution • algebraic conventions such as the omission of the multiplication sign • developing algebraicformulas from number patterns BACKGROUND INFORMATION: Since the sixteenth century, variables and formulas have been the key concepts and instruments of algebra. Formulas ... |
Pedricktown Precalculus...Most topics and concepts of calculus come from practical problems and needs, wherever in physics, engineering, or economics, and often evoke very visual intuitive constructs and situations. The trick when teaching calculus is, therefore, to find that right balance between the necessary mathemati... |
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing... more...
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed... more...
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and... more...
Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization... more...
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This is a supplement to reinforce understanding of mathematical physics concepts. Contains problems that bring physics to life by relating it to daily experiences. The chapters are divided into two or more topic sections, each with its own Solved Examples and Practice Exercises. |
IS and LMInstitutional InvestorsCommercial Bank Risk Management These lecture Notes are from a Year 2 economics module on Money, Banking and Finance, delivered by Andros Gregoriou of the University of East Anglia. Author(s): Andros GregoriouEnvironmental engineering The KS3 pupils particularly in Year 9 (Y9) the themes of air/ soil/water pollution were chosen because of their links to the KS3 National Curriculum for Science ( e Author(s): Whitley David Dr.;Andresen Jon Dr.Montessori Activities: Maths Preliminary math activities to promote learning about numbers, size and colors. Indirect Preparation for numeracy which is an awareness of cardinal numbers, ordinal numbers, numerals, one to one correspondence, sequencing and tally counting. Also concepts of size, length, area and volume. These activities are suitable for beginning mathematicians as well as infants, toddlers and 3 - 6 year olds. Author(s): No creator set
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Get to the Core: High School Algebra and Functions Standards with Fathom (Beginner)
Description
This webinar will present a variety of activities that focus on content standards in the domains of algebra and functions. Specifically, we'll look at activities that support interpreting and building linear, quadratic, and exponential functions. We'll also discuss how Fathom use supports the Standards for Mathematical Practice by providing "a statistical package" that proficient students can use "to visualize the results of varying assumptions, explore consequences, and compare predictions with data" (Use appropriate tools strategically).
No prior experience with Fathom is necessary.
Presenter
I was a public high school math teacher in the Bay Area for 13 years, most of them at Arroyo High School, a comprehensive high school in San Lorenzo, but also a year at Leadership High School, a charter school in San Francisco. During that time I focused on supporting all students to take and pass Algebra 1, and also taught computer programming and a Sketchpad-based course on geometry in art. Since 2004, I've been a development editor and now product manager at Key Curriculum, where I have worked on textbooks, software, technology curriculum, and professional development courses. |
Math IIC covers a variety of mathematical
topics. ETS, the company that writes the SAT IIs, provides the following
breakdown of the topics covered on the test:
Topic
Percent of Test
Usual Number of Questions
Algebra
18%
9
Plane Geometry
—
—
Solid Geometry
8%
4
Coordinate Geometry
12%
6
Trigonometry
20%
10
Functions
24%
12
Statistics and Sets
6%
3
Miscellaneous
12%
6
While accurate, this breakdown is too broad to really
help you direct your studying toward the meaningful areas of the
test. We've created the following detailed breakdown based on careful
examination of the test:
Topic
Percent of Test
Usual Number of Questions
Algebra
18%
9
Arithmetic
2%
1
Equation solving
5%
2.5
Binomials, polynomials, quadratics
14%
7
Solid Geometry
8%
4
Solids (cubes, cylinders, cones, etc.)
4%
2
Inscribed solids, solids by rotation
1%
0.5
Coordinate Geometry
12%
6
Lines and distance
6%
3
Conic sections (parabolas, circles)
5%
2.5
Coordinate space
2%
1
Graphing
2%
1
Vectors
1%
0.5
Trigonometry
20%
10
Basic functions (sine, cosine, tangent)
12%
6
Trigonometric identities
4%
2
Inverse trigonometric functions
2%
1
Trigonometry in non-right triangles
1%
0.5
Graphing trigonometric functions
1%
0.5
Functions
24%
12
Basic, compound, inverse functions
8%
4
Graphing functions
6%
3
Domain and range of functions
8%
4
Statistics and Sets
6%
3
Mean, median, mode
2%
1
Probability
2%
1
Permutations and combinations
4%
2
Group questions, sets
1%
0.5
Miscellaneous
12%
6
Arithmetic and geometric series
4%
2
Logic
1%
0.5
Limits
1%
0.5
Imaginary numbers
1%
0.5
This book is organized according to the categories in
the above breakdown, allowing you to focus on each topic to the
degree you feel necessary. In addition, each question in the practice
tests at the back of this book has been categorized according to
these topics so that when you study your practice tests, you can
very precisely identify your weaknesses and then use this book to
address them. |
Few would argue that, through its development of science and technology, the human species has been more successful than any other in taking control of the environment and using the resources of the earth to its own advantage. It is probably equally clear that this dramatic development of science and technology is only possible because of our ability to think creatively, consistently and logically. Indeed, there seems to be a parallelism, a consistency, between the rules that govern logical thought and the rules that govern the functions of the physical universe. The physical universe is quite logical and consistent. It reveals its secrets to those who study it using creative, consistent and logical thought. And for the development of one's ability to exercise this very useful way of thinking there is probably no better approach than through the study of mathematics.
So welcome to the Department of Mathematics where you will have the opportunity to hone your thinking skills by taking some of our twenty four courses in algebra, statistics, trigonometry, calculus and differential equations. In addition to improving your ability to think clearly, you will also learn about many of the astounding mathematical discoveries that have been made throughout the centuries and how they can be used for practical applications in science, engineering, business and the health fields.
I encourage you to humbly and enthusiastically place yourself in the hands of our experienced and capable faculty who are fully devoted to teaching you mathematics. If you do this, you will be taken on an intellectual journey to fascinating places that you cannot easily imagine. You will come away not only well prepared with the technical knowledge you need for your chosen career or field of study, but with an enhanced ability to think more clearly, more deeply, more rigorously, more analytically and more precisely about yourself and everything you encounter. Welcome to the world of mathematics! |
1. ID # 1416-19
2. $10.50 FOR PRIORITY MAIL SHIPPING WITH TRACKING
$3.99 FOR STANDARD MEDIA MAIL WITH TRACKING.(8-14 days to deliver)
3. the book has no marks. pages like never used. corners has small wear, tape on.
4. the book can be used to normal student textbook and New Mexico Edition.
5. the sale is final.
6. The teacher's edition contains full answers for every problem in the student textbook, even and odd. it also contains answer key for the following workbooks:
Challenge
problem solving
reteach
practice B
the item is not for resale. the sale is final.
=================================
ON HOLD means the item was sold out. click to order another TEACHER'S EDITION |
A Look at Real-World Problem Solving 1.0 description
This paper (A LOOK AT REAL-WORLD PROBLEM SOLVING) presents an example of a real world problem that addresses several important points in the problem solving process. The example problem involves the trajectory of a projectile. The problem is to reach a desired point by selecting a launch angle. This problem has a wide variety of real applications: rocket and missile launching, targeting and intercepts, satellite orbit transfers and rendezvous, numerical optimization, polynomial root finding, and solving nonlinear equations. The mathematics needed to solve the problem are not too involved - only algebra and trigonometry. The process of solving the problem, however, is at times detailed and tedious. But, this is a concept that needs to be taught: real-world problems are not necessarily easy. Before looking at the solution, we will examine the real-world problem solving process. |
Synopsis
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering
Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences.
Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including:
Approximation and estimation
Isolating important variables
Generalization and special cases
Dimensional analysis and scaling
Pictorial methods and graphical solutions
Symmetry to simplify equations
Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension.
Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day |
Maths
Why Should I Study This Subject?
There are many reasons why people choose to study A Level Mathematics. It might be a requirement for what you want to study at university. Since maths is one of the most traditional subjects a good grade in maths can boost an application for almost every course! Studies have also shown that people with Maths A Level also tend to earn more on average than people without it. Though this itself may or may not be a good enough reason to study maths, the skills it allows you to develop include problem solving, logic and analysing situations. Add in the improvements to your basic numeracy skills and that bit of creativity needed to solve maths problems and you've got yourself a set of skills which would make you more desirable for almost any job! Finally, you might also really like maths - this is as good a reason as any to continue studying it. If you study something you enjoy you are likely to do better at it. With maths there is the excitement of new discoveries you will make. You will see more of the beauty of it and realise just how much everything in the universe is connected to mathematics.
The bottom line is, maths is an amazing subject to have at A Level and provided you have a solid understanding of the GCSE concepts before you start, alongside some perseverance and effort, you should be able to do well.
What Will I Study?
Year 1: Core 1, Core 2 & either Mechanics 1 or Statistics 1 or Decision 1
Year 2: Core 3, Core 4 & either Mechanics 1 or Statistics 1 or Decision 1 or Mechanics 2 or Statistics 2
How Will it be Assessed?
Each of the modules is assessed by an exam only.
Exam Board
Edexcel, for further details:
What Can I do Next?
Many university courses such as physics, psychology, economics, computing, engineering and business studies prefer students to have A Level maths if possible. Having A level maths is a great signal to any employer that you can think logically, work hard and have a great level of numerical skill.
What Grades Will I Need?
8 GCSE grades A*- C. Students are required to have at least an A grade at GCSE to study maths at A Level. |
Short Description for Cambridge Checkpoint Maths: Student's Book Bk. 3 These market leading resources are used in schools throughout the world and are matched to the Curriculum Framework to provide superb support for you and your students. Full description
Full description for Cambridge Checkpoint Maths: Student's Book Bk. 3
This widley-used and highly-respected Student's Book, for Cambridge Secondary 1 Maths, is fully matched to the Curriculum Framework, Cambridge Checkpoint Tests and the Cambridge Progression Tests. It includes sections on calculations and mental strategies that provide accessible guidance through these difficult topics. There are also chapters that focus on ICT, investigations and problem-solving, helping your students to apply Maths to real-life situations. |
Course Overview
About Self-Directed Courses
In a self-directed course, you can start and stop whenever you like, progressing entirely at your own pace and going back as many times as you want to review the material.
Explore more than half a dozen of the most important math tools that journalists encounter — and have fun doing it.
This course covers everything from reducing fractions and other math essentials to topics specifically for journalists, such as calculating costs of living and estimating crowd sizes. The goal is to make routine math routine.
Along the way, you'll find a range of resources to give you additional learning support. Quizzes, activities, interactive activities and games — complete with high-score boards — offer fun ways to learn the math basics that every journalist needs to know.
What Will I Learn:
Upon completing this course, you will be able to:
List the terms, syntax and rules for performing calculations necessary for math proficiency
Work with fractions
Perform arithmetic more accurately and efficiently
Find help – both on and off the Web
Calculate a percentage and recognize the subtle differences between percent change, percent of total and percentage points vs. percent
Calculate means, medians and modes, and know when it's best to use each as a measure of "average"
Compare numbers more meaningfully by creating ratios, ranks and rates
Understand the basic approaches to and pitfalls of calculating cost of living, weighted averages and crowd estimates
Who should take this course:
Anyone who wants to get better at the routine math every journalist needs when writing or editing a story, covering an event or creating infographics. If you don't know how to calculate a crowd estimate or don't know the difference between percentage points and percents, this course is for you. |
Mathematics Requirements by Major
This information is designed to help students who participate in the Early Mathematics Placement Tool (EMPT) program for high school juniors to interpret and assess their test scores in relation to requirements at University of Wisconsin System and Wisconsin Technical College System campuses.
The score report, which each student receives, indicates the level at which the student would likely start, if he or she were to take a mathematics course right now, at one of the University of Wisconsin System or Wisconsin Technical College System campuses. The descriprions of the levels are provided for each odd number scale point. Students placing at an even numbered scale point have skills that fall between those provided for the points immediately above and below it.
A broad description of the Early Mathematics Placement Tool levels appears below. How the levels are defined in terms of actual courses may vary from campus to campus and can be found in the beginning course sequence chart for each campus.
The campus specific information also outlines the minimum mathematics requirements for specific college majors. Students can find out what mathematics course they are prepared for at this time and how many more mathematics courses they would need to fulfill requirements of a particular institution or major program.
With this information, students will have a chance to improve their mathematics preparation in high school by taking an appropriate mathematics course in their senior year. A mathematics teacher or counselor can assist students in interpreting the EMPT results as related to students' college aspirations and suggest an appropriate mathematics course to bridge any gaps in their mathematics preparation. Even if students are right on track in their mathematics preparation, they should enroll in a mathematics class in their senior year, because mathematics skills tend to become rusty if not continuously practiced.
Adequate mathematics preparation prior to entering college saves a student both time and money. A student taking high school level courses at college must pay tuition, but does not receive credits which count towards a college degree. Such a student thereby extends the time it takes to finish college with a degree.
Please note that both mathematics curricula and majors requirements are continually reviewed by campuses and thus the information contained in this booklet is fluid. Students should always check with their intended campus prior to enrolling for the most up-to-date information.
The UW System Mathematics Placement Test is required of students entering a UW institution. It is similar to the EMPT but somewhat longer. Hopefully, for students taking a college preparatory mathematics course in their senior year, the UW Mathematics Placement Test scores will be higher than the EMPT scores. But they could turn out lower if students do not take such a mathematics course.
Description of Early Mathematics Placement Tool Levels
Level 1
Students at Level 1 have a weakness in basic mathematics skills and need to commit to a great deal of preparation in order to be ready for college-level mathematics. If preparation is not undertaken in high school, the student will start the college mathematics course sequence at the lowest level and will pay for mathematics courses which do not count toward his/her degree.
Level 2
Level 3
Students at Level 3 demonstrate skills in basic mathematics, but have weaknesses in algebra. Students at this level need to commit to further algebra preparation in order to be ready for college-level mathematics. If preparation is not undertaken in high school, the student will most likely start the college mathematics course sequence at a low level and will pay for mathematics courses which will not count toward his/her degree.
Level 4
Level 5
Students at Level 5 have basic algebra skills and are usually ready for a college algebra course. Further strengthening of these skills is usually required for most college and university programs.
Level 6
Level 7
Students at Level 7 have the algebra skills to take courses at the pre-calculus level, but need to develop better algebra and trigonometry skills to take calculus.
Level 8
Level 9
Students at Level 9 have the skills required for the calculus sequence. |
February 4, 2013
FREE MATH LESSON - "Geometry Terms: Student Reference Set"
The sources in this book contain terms, pictures and definitions of geometry concepts for the elementary classroom. Simply copy a set for each student in your class. Then place them in their math journals. Now they have a quick, ready reference for |
Course
4 Unit 7 - Functions and Symbolic Reasoning 1st Edition
In Course 4, the
mathematical strands in the Contemporary Mathematics in Context
program become increasingly blended within units. The content of this
unit is from both the algebra and functions strand and the geometry and
trigonometry strand. (See the descriptions of Course
4 Units.)
Unit Overview
Functions and
Symbolic Reasoning extends student ability to manipulate symbolic
representations of exponential, common and natural logarithmic, and trigonometric
functions and to solve exponential, logarithmic, and trigonometric equations.
Trigonometric identities are developed and proved or disproved. Geometric
representations of complex numbers are used to reason about and to find
roots of complex numbers.
Unit Objectives
To use properties of exponents to transform exponential expressions
into equivalent exponential expressions
To solve exponential equations
To use relationships between logarithms and exponentials to
write logarithmic equations in forms without logarithms
To know and be able to use the definitions of the six trigonometric
functions of angles in standard position
To know and be able to use the fundamental trigonometric identities
To prove a statement of equality is an identity
To solve trigonometric equations
To represent complex numbers geometrically
To interpret multiplication of complex numbers geometrically
To use DeMoivre's Theorem to find all the roots of a complex
number
Sample Overview
There are two different
samples from Functions and Symbolic Reasoning. The first sample
consists of Investigations 1 and 2 from Lesson 2, "Reasoning with Trigonometric
Functions." These investigations introduce the cosecant, secant, and
cotangent functions and begin work with trigonometric identities.
The second sample
is the "Looking Back" lesson for this unit. This lesson is intended to
provide students with tasks that will encourage them to look back at the
unit as a whole. Students review, synthesize, and apply the knowledge
gained during the study of the unit.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design.
Contact
Adobe with any technical questions
about their software or its installation.
How the Algebra
and Functions Strand Continues
Algebraic representations
of surfaces and conic sections are introduced in Unit 8, Space
Geometry.
A unit from the algebra and functions strand that develops understanding
and skill in the use of standard spreadsheet operations while reviewing
and extending many of the basic algebra topics from Courses 1-3 is recommended
for students intending to pursue college programs in social, management,
and some of the health sciences or humanities. |
A book on basic math that explains how math really works
A book on basic math that explains how math really works
Please, recommend me a book (or books) on basic math/pre-algebra that really explains how math works from the inside out. What I mean by that is a book that goes really deeply into exploring math giving you true understanding of what's going on behind the scenes so to speak. For example, why the long division method even works, why when dividing one fraction by another fraction is supposed to be carried out the way it is, why dividing by zero doesn't really make much sense, why a negative number multiplied by another negative number gives a positive number and stuff like that. So a book that gives the basis for basic math and arithmetics. Not like the books which only explain how to superficially perform math operations and algorithms. I looked into the for dummies series, but they are all like that, don't provide you with that kind of explanation.
I don't really think that such a book exists. Don't get me wrong, there are a lot of books that explain exactly what you want. A lot of books explain how the long division works, how multiplication of fractions works, why multiplication of negative numbers result in a positive number. The problem is that such a book is usually quite advanced. The subject that treats such questions is abstract algebra, and it's a college-level math course.
Furthermore, if you want everything to be explained, then you will need to deal with proofs. So before reading abstract algebra, you should read up on mathematical proofs.
If you wish to try out abstract algebra, then I can recommend the book "A first course in Algebra" by Fraleigh. Everybody who is familiar with proofs will be able to tackle this book. But it will still be a difficult read.
If you want to do proofs and sets first, then Velleman's "how to prove it" is a good read.
I realize that I have not been helpful at all. As I understood your questions, you wanted easy books that explain everything. I have given you hard books. The problem is that there are no easy books that explain it all (as far as I'm aware). I think your best bet is posting the questions you have on the forums here. That way you won't have to read an entire book.
Algebra by Gelfand is well motivated and fairly rigorous (at least for high school algebra standards). Lectures on Elementary Mathematics by Lagrange also seems to be like something you are looking for (you may find it online here).
Most arithmetic algorithmic (e.g. long/synthetic division, multiplication with multi-digit numbers, &c.), however, are things that you should easily be able to justify on your own if you know a bit of algebra.
If you want to find out how mathematics is done, I'd recommend watching Vi Hart's Youtube channel and reading Hilbert's Geometry and Imagination.
MacLane? Really? That may be too advanced, don't you think? The OP asks for a book on basic math/pre-algebra!
Well, I've read just the beginning, but it seems any person could understand a lot of this book. Look at wiki entry. I guess at least first part of the book is readable by anyone. It definitely is "behind the scenes" book. But yeah, this is perhaps too much philosophy, it seems the OP is looking for something more practical.
I think it to a large degree is a matter of psychological satisfaction, which can vary between individuals; some people ask the question "Why?" more often than others. Eventually, you'll hit a wall where you feel satisfied with the mathematical theory "behind" things. Personally, I'm using "Basic Mathematics" by Serge Lang as complementary studying in high school right now, and I think it's enough for me. However, it's probably not for you because it assumes some things without proof, like distributivity, associativity and commutativity. I, on the other hand, think it's OK to do so since I think I have a sufficient intuitive understanding why those properties must be true.
I would suggest that you look into the above mentioned books and see if something fits you. Good luck! |
Assignment 5: Chapter 2
Write up to hand in on F 9/13: Problems 1, 2 and 5.
Work on to present in class Problems 3 and 4.
Assignment 4: Section 1.4
Write up to turn in on Friday, 9/6: 1,2 and 6.
Work on to present in class: 3, 4 and 5.
Assignment 3: Study section 1.4 for Monday. We learn about one of the most important properties/axioms of
Real Numbers: The Least Upper Bound Axiom. This is what distinguishes R from Q.
Assignment 2: Write up 3,5,8 and 10 to turn in on Monday, 9/3. Work on the others to present
in class on Friday, 8/30.
Assignment 1: Get a copy of the textbook from the book store (if you haven't done so already). Read Chapter
0 and Sections 1.1 and 1.2 by Wednesday. Write up problems 2, 3 and 5 to turn in on Friday.
Be prepared to discuss the rest of the problems in 1.2 in class on Wednesday. |
More About
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Overview
This book gathers thousands of up-to-date equations, formulas, tables, illustrations, and explanations into one invaluable volume. It includes over a thousand pages of mathematical material as well as chapters on probability, mathematical statistics, fuzzy logic, and neural networks. It also contains computer language overviews of C, Fortran, and Pascal.
Mathematicians, students and researchers constantly refer to various sources for different formulas, equations, etc. The Handbook of Mathematical Formulas puts up-to-date equations, formulas, tables, illustrations, and explanations in one invaluable reference volume. Fully up to date, this handbook will quickly become the standard reference for every mathematician and student. 1025 |
Warner, Victoria
Middle School Math 8 is a yearlong course that builds upon the student's mathematics experiences. The course will engage students in the study of a variety of topics including number and operations, algebraic relationships, geometry, measurement, and data and probability. The course is designed to stimulate mathematical thinking and promote problem solving while allowing students to communicate and make conceptual connections.
Algebra I
This is a full-year course that introduces students to the terminology, symbolism and structure of algebra. Students are taught to solve practical problems using algebraic techniques. Students will use various problem-solving techniques coupled with estimation and computation skills to solve problems. Students will graph linear and nonlinear equations, solve linear and quadratic equations, solve systems of equations and inequalities, perform operations on rational numbers as well as polynomials, and continue patterns involving functions. Students will interpret data using graphs, charts, and tables; work with scale drawings using ratios and proportions; solve equations, use formulas to find area, perimeter, and volume, work with real numbers; and express numbers in different forms including powers, roots, scientific notation, decimal notation, fractional notation, and percent. Students who are planning to attend a four-year college should take four years of mathematics beginning with Algebra I. |
This course is designed to help students sharpen their skills or as a resource that teachers can employ to help struggling students stay up to speed. Energetic and enthusiastic Professor Terry Caliste helps students understand complex numbers, simplify radicals and combine radical expressions. At the conclusion of this course, students will understand and know how to use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.
Benefits • Learn how to use simple mathematic processes to solve problems.
• Students easily sharpen their skills and stay up to speed.
• Step—by—step instruction motivates students to succeed in math. |
Interactive DVD Lecture Series for Beginning & Intermediate Algebra
This comprehensive video resource offers an easy-to-use navigation menu that helps students quickly find and focus on the examples and exercises that they need. Students will find the following resources: *A complete lecture for each section of the text highlights key examples and exercises. New "pop-ups" reinforce key terms, definitions, and concepts while Martin-Gay presents the material. An easy-to-use navigation menu helps students quickly find and focus on the examples and exercises that they need. *Interactive Concept Check exercises measure students' understanding of key concepts and common trouble spots. After a student selects an answer from several multiple choice options, Martin-Gay explains why the answer was correct or incorrect. *Study Skill Builder videos reinforce the study skills-related skills and concepts found in Section 1.1, Tips for Success in Mathematics, and in the Study Skills Builder exercises found in the Student Resources section at the back of the text. * The Chapter Test Prep Videos help students during their most teachable moment-when they are preparing for a test.
This Martin-Gay innovation provides step-by-step solutions for the exercises found in each Chapter Test. *Complete solutions on video for all exercises from the Practice Final Exam (located in Student Resources) help students prepare for the real thing. Overview segments review key problem-solving strategies. |
The study of Mathematics has been a fundamental part of education since ancient times and has lost none of its relevance in modern times. In fact, much the contrary. Mathematics permeates our lives, enables us to communicate across vast distances, shrinks our technology to the palm of our hands, and opens up more and more of the nature of the world to our investigations.
We understand full well that many of our students come to use with little of this sense of wonder, rather with a sense of fear and apprehension.
We strive constantly to meet our students where they are, bring them into a new relationship with mathematics, and open up the possibilities of mathematics for them and for their careers.
Math
Curriculum
The Mathematics department curriculum has two components, one developmental, the other college-level.
The Developmental Mathematics Program
For those that are not ready to undertake college-level mathematics, either because they have been away from the subject for a while or because they have yet to fully grasp the fundamentals and put them into practice, the developmental mathematics program provides coursework for students demonstrating deficiencies in mathematical skills. MATH 049, Elementary Algebra, and MATH 149, Intermediate Algebra are consecutive 3-unit courses that prepare students for college-level work in mathematics. We also offer a self-paced version of Intermediate Algebra (MATH 1491) for those who fall somewhere in-between these two traditional courses. Placement in these classes is based on a proficiency examination score. A grade of "C" (2.0) or higher in MATH 049 is required to enroll in MATH 149. A grade of "C" (2.0) or higher in MATH 149 or 1491 is required to enroll in college level mathematics courses.
The College-Level Mathematics Program
All university students are required to complete at least one college-level mathematics course. Many departments ask for an additional mathematics course, so please check your major department's course requirements. College-level mathematics courses are designated with a number in the 200s, such as Business Math and Statistics, College Algebra and Trigonometry with Descriptive Geometry. In addition, the department may occasionally offer lower- or upper-division topics courses in mathematics.
For more information about the Mathematics department curriculum, contact Prof. Marty Tippens, Chair, at [email protected] |
Faculdade de Ciências e Tecnologia
Mathematics
Cycle
Degree
Coordinator
Opening date
September
Vacancies
30
Fees
1037.20 Euros
Schedule
Daytime
Education objectives
Mathematics is a science that underpins all scientific and technological areas, and also the Economics and Social Sciences.
The main objective of the course that now presents itself is to provide a sound basic training in mathematics, balanced in its various aspects, covering the areas of knowledge essential to the development in later cycles (2. And 3. Cycles) of advanced training. It is intended that this training provides the necessary basis for further studies in the area of Mathematics Education or in the area of Applied Mathematics.
As an example of areas in applied mathematics, to develop in later cycles, according to the specific skills of the faculty of the Mathematics Department of the FCT to mention: Actuarial; Algebra and Logic, Numerical Analysis and Differential Equations, Operational Research and Optimization, Probability and Statistics.
Statistics is the art of extracting information. It has applications, among others, market research, design and interpretation of experiences and Financial Mathematics. The Operational Research is aimed at creating models that allow the study of complex systems and optimal use of resources. The Actuarial Science aim to study the risk (life, accident risk, risk in the stock market). Differential Equations and its Numerical treatment are the foundation of modern physics and engineering, are still present in many biological processes and economic.
Algebra and Logic as core areas of mathematics are also largely responsible for the development of information and recent computational techniques. the |
books.google.co.uk elements of the differential calculus |
ACCELERATED PRE-CALCULUS SUMMER STUDY GUIDE
CHAPTER 12: SETS, RELATIONS AND FUNCTIONS
A "set" is a collection of "objects." Each object in the set is called an "element of the set." The elements usually have something in common.
For example, the following, {monkey, bear, lion, giraffe, zebra}, is called a set of elements. What do these elements have in common? One answer might be that they are animals in a local zoo.
Notice the symbols "{" and "}". We will call theses symbols "set enclosures.""{" is the "left set enclosure" and "}" is the "right set enclosure."
The following set {2, 4, 6, 8, 10, ...} is a collection of objects that are numbers. The elements are 2, 4, 6, 8 and 10, and what these elements have in common is that they are positive even numbers. Notice that the set {2, 4, 6, 8, 10, ...} has 3 periods after the number 10. These three periods, called "ellipsis," mean "and so forth" or suggest that the elements in a set continue on forever or as mathematicians say "continue on to infinity."
When we need to represent some "recognizable pattern" mathematicans often use ellipsis. Consider the following set: {3, 6, 9,..., 90, 93, 96}. I have left out many numbers from this set but the ellipses suggest I am incrementing each subsequent number by 3 and the set contains all the numbers incremented by 3, starting at 3, going to the number 96.
Can you see the pattern in the following? {...1, 2, 4, 8, 16, 32, 64, 128...} If you take any number in this set and multiply it by 2 you will get the next number in the set. Pattern recognition skills are very important in the world of mathematics!
SECTION 12.2: DOMAIN, RANGE, RELATION
Let's look at this set: { (1,3), (-2,4), (5,-2), (-1,-3) } This is a set of ordered pairs which can be used to represent points in the Cartesian Coordinate System. The points below can be represented by our set of ordered pairs { (1,3), (-2,4), (5,-2), (-1,-3) }.
The set of x-values of a set of ordered pairs { (1,3), (-2,4), (5,-2), (-1,-3) } is named the "domain." The domain in this instance is {-2, 1, -1, 5}.
The set of y-values of a set of ordered pairs is named the "range." The range in this instance is {4, 3, -2, -3}.
The set of ordered pairs is also named a "relation." So { (1,3), (-2,4), (5,-2), (-1,-3) } is a relation.
ans: The domain is {5, 4, 3, 6} and the range is {–3, 6, –1, 3} Comment: Notice that the x coordinate, 5, occurs twice in {(5, –3), (4, 6), (3, –1), (6, 6), (5, 3)}. Mathematicians have agreed to write an x value in the domain once even though it may occur more than once in the relation. The same goes for the range: notice the y coordinate 6 occurs twice in the relation but is written only once in the range.
There is a very special "relation" called a "function." Functions are very powerful in the world of applications as we will see in Chapter 16 of this manual.
WHAT IS A FUNCTION?
If each x-value of a relation has one unique y-value assigned to it, then the relation is named a "function."
ex. 1) { (1,3), (1, 5), (-2,4), (5,-2), (-1,-3) } is not a function! Look at the set of ordered pairs to your left. Note the ordered pairs in blue. The x-value 1 has two different y-values, 3 and 5.
Hence, we say { (1,3), (1, 5), (-2,4), (5,-2), (-1,-3) } is not a function.
ex. 2) { (1,3), (-2,4), (5,-2), (-1,-3) } is called a function.
Why? Because each x-value has only 1 y value.
ex. 3) { (7,5), (-7, 5), (-7,4), (-7,-2), (6,-3) } is not a function. Look at the set of ordered pairs to your left. The x-value -7 has three different y-values 5,4,and -2. Hence, we say { (7,5), (-7, 5), (-7,4), (-7,-2), (6,-3) } is not a function.
ex. 4) { (7,-2), (-2,-2), (4,-2), (-3,-2) } is a function.
Why? Because each unique x-value has only 1 y-value.
COMMENT: All functions are relations but not all relations are functions. Remember, a relation is nothing more than a set of ordered pairs.
12.4 GRAPHS OF FUNCTIONS VERSES NON-FUNCTIONS
A set of ordered pairs that is a function will have more than one point falling on a vertical line. Let's compare the graph of a function to a graph of a non function.
FUNCTION
NOT A FUNCTION
{ (1,3), (-2,4), (5,-2), (-1,-3) }
{ (1,3), (1, 5), (-2,4), (5,-2), (-1,-3) }
FUNCTION
NOT A FUNCTION
{ (7,-2), (-2,-2), (4,-2), (-3,-2) }
{ (7,5), (-7, 5), (-7,4), (-7,-2), (6,-3) }
We will be looking at functions in greater depth in chapter 16. This was a brief introduction. |
**NOTE*** THE NEW 2.0 VERSION OF THIS TITLE HAS BEEN SUBMITTED AND IS AWAITING APPROVAL. PLEASE BEAR WITH US DURING THIS PROCESS. THE CURRENT VERSION IS NOT COMPATIBLE WITH THE 3.0 OS We have added many new features to iScroll 2.0 which will enhance the user experience. Our New accusync technology enables a flawless word for word sync in addition to the following key features: Key iScroll Features: • Turn Audio on/off • View text in landscape/portrait • Fast-forward/rewind • Move through paragraphs/chapters • Search for words/phrases • Look up words on Google/Wikipedia (great for studying!) • Highlight or annotate text (great for studying!) • Adjust text size • Change font type, size and color • Adjust line spacing, backlight and background color • Adjust text justification • Change reading speed England and spent her early years in France. She married mathematician George Boole. She was the author of several works on teaching and teaching mathematics in particular. This short book, Philosophy and Fun of Algebra, is meant to be read by children and introduces algebra and logic. She uses the word "algebra" broadly, defining it as a "method of solving problems by honest confession of one's ignorance". Using this definition, Boole introduces, in a conversational manner, the concepts of logic and algebra, illustrating these concepts with stories and anecdotes, often from biblical sources. At times, her discussion seems somewhat mystical, speaking of the imagination and angels as messengers which guide one toward the next step in a logical investigation. Boole ends the book with a reminder that algebra's essential element is "the habitual registration of the exact limits of one's knowledge" and a call for the public to keep this principle in mind when encountering any situation. Table of Contents: 01 - From Arithmetic to Algebra - 00:08:37 02 - The Making of Algebras - 00:05:03 03 - Simultaneous Problems - 00:04:53 04 - Partial Solutions.. Elements of Complexity - 00:04:07 05 - Mathematical Certainty… - 00:03:41 06 - The First Hebrew Algebra - 00:10:38 07 - How to Choose Our Hypotheses - 00:12:04 08 - The Limits of the Teacher - 00:06:14 09 - The Use of Sewing Cards - 00:04:22 10 - The Story of a Working Hypothesis - 00:07:54 11 - Macbeth's Mistake - 00:07:05 12 - Jacob's Ladder - 00:02:35 13 - The Great x of the World - 00:04:18 14 - Go Out of My Class-Room - 00:04:20 15 - Square Root of Minus One - 00:03:04 16 - Infinity - 00:04:26 17 - From Bondage to Freedom - 00:05:46 18 - Appendix - 00:02:07 This great title is now available in its entirety on the iScroll®, a Text Synchronized Audiobook™ (TSA) reader that will completely change the way you experience your favorite book. Choose to read, listen or both. Numerous studies have shown that simultaneous reading and listening dramatically increases focus, concentration and retention, ultimately boosting your learning capacity. Key iScroll features: Scrolling text with narration Continuous playback of all chapters Option of listening, reading or both Font size adjustment Scroll speed adjustment Bookmark feature to start where you left off Read in Portrait or landscape mode We intend to produce quality products for your reading pleasure. We are constantly updating our software, thus we honor and appreciate any feedback from you to further enhance our products. All iClassix titles are in the public domain obtained from Librivox. We appreciate the work of all librivox volunteers and it is our intention to bring all their titles to the iPhone community. |
Fundamentals of Math - Teacher Edition (old)Employ problem solving and real-life uses of math to reinforce computation skills and to build a solid math foundation. Each chapter contains a biographical sketch of an innovator.
The Teacher Edition includes student pages with presentation notes, answers, and "Extra for Experts" activities. |
Discrete And Combinatorial Mathematics - 5th edition
Summary: This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-maki...show moreng this the ideal text for preparing students for advanced study.
Features
This text has an enhanced mathematical approach, with carefully thought out examples, including many examples with computer sciences applications.
Historical reviews and biographies bring a human element to their assignments.
The Rules of Sum and Product. Permutations. Combinations: The Binomial Theorem. Combinations with Repetition. The Catalan Numbers (Optional). Summary and Historical Review.
2. Fundamentals of Logic.
Basic Connectives and Truth Tables. Logical Equivalence: The Laws of Logic. Logical Implication: Rules of Inference. The Use of Quantifiers. Quantifiers, Definitions, and the Proofs of Theorems. Summary and Historical Review.
3. Set Theory.
Sets and Subsets. Set Operations and the Laws of Set Theory. Counting and Venn Diagrams. A First Word on Probability. The Axioms of Probability (Optional). Conditional Probability: Independence (Optional). Discrete Random Variables (Optional). Summary and Historical Review.
The Principle of Inclusion and Exclusion. Generalizations of the Principle. Derangements: Nothing Is in Its Right Place. Rook Polynomials. Arrangements with Forbidden Positions. Summary and Historical Review.
2003 Hardcover Fine Clean copy with no writing or highlighting on the pages. Pages, Spine, Boards are like new. Minor scratching on cover. Excellent condition inside and out. No damage to the book...show more. All items guaranteed, and a portion of each sale supports social programs in Los Angeles. Ships from CA. ...show less
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WOW! I had no idea how easy this really was going to be. I just plug in my math problems and learn how to solve them. Algebra Buster is worth every cent!02-01 :
Mathematics Concepts and skills Mcdougal Lttle California test prep
quadratic equations using square roots
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CPM teacher Manual
Power and Roots and Worksheet
maple solve gradient
What is the difference between evaluation and simplification of an expression? |
books.google.de - The... and Patterns
Tilings and Patterns
The for geometry courses and independent study. 1987 edition.
Review: Tilings and Patterns (A Series of books in the mathematical sciences)
Nutzerbericht - Andrew - Goodreads
A wonderful example of how a whole branch of study is constructed from the ground up. Who would think there was so much fruitful math from just the concept of fitting tiles together?Vollständige Rezension lesen |
Short Description for Complex Variables Contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. This work is aimed at both students and professionals alike. Full description
Full description for Complex Variables
Using the same innovative and proven approach that made the authors "Engineering Mathematics" a worldwide bestseller, this book can be used in the classroom or as an in-depth self-study guide. Its unique programmed approach patiently presents the mathematics in a step-by-step fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference. It uses a unique programmed approach that takes readers through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises. It contains many Quizzes, Learning Outcomes, and Can You? checklists; and is ideal as a classroom textbook or a self-learning manual. |
Wolfram Research The Mathematical Explorer
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Please Note: Pricing and availability are subject to change without notice.
The Mathematical Explorer allows one to explore some of the most fascinating topics in mathematics from ancient Greece up to the 21st century. Your customers will be able to walk in the computational footsteps of history's greatest mathematicians and discover the answers to many of their most perplexing questions as The Mathematical Explorer introduces them to some of the stories and faces behind the math.
Educational and entertaining, The Mathematical Explorer delves into the historical and cultural details behind the most important mathematical concepts. With The Mathematical Explorer, you can perform a wide range of numerical and symbolic calculations and create an unlimited array of graphics.
Take this interactive journey through intriguing problems that have challenged mathematicians since the ancient Greeks. Walk in their computational footsteps, and experience the wonder of discovery that has fascinated amateurs and professionals throughout the ages. Requirements
MacOS/Win 00/09/NT/ME |
CalcPlot3D, an Exploration Environment for Multivariable Calculus
Using CalcPlot3D to Visually Verify Homework in Multivariable Calculus
One way to use CalcPlot3D, a versatile Java applet, is to demonstrate new concepts during multivariable calculus lectures. I often develop a new concept on the chalk board first and then take a couple minutes to make the concept come to life using the applet. Students find these demonstrations helpful and fun, and they bring variety to my presentations, helping students process the new concepts in a new way.
An even more exciting way to use CalcPlot3D in class is to engage in a visual exploration of new concepts using "What if…" types of questions. An example of a topic for which I find this approach works especially well is exploring the variety of possible parameterizations of a plane/space curve, paying special attention to the behavior of the velocity and acceleration vectors. Using these sorts of visual demonstrations in class improves student learning, but to fully engage students in the exploration and discovery process and give them the best chance of learning the geometric nature of the calculus concepts, I feel it is vital to give students opportunities to "play" with the concepts visually themselves. This article focuses on one way this can be done: by requiring students to visually verify solutions to particular homework problems and turn these in for a grade. [Another way this project supports student engagement and "play" is with the guided explorations being developed for various concepts. See the main project website to explore these. At this writing, there are explorations for Dot Products, Cross Products, Velocity & Acceleration Vectors, and Lagrange Multiplier Optimization.]
Below is a list of example topics where I often assign this type of visual verification exercise to my students to get them to begin using the applet on their own. Once they start using the applet in this way (because they have to), students often report using the applet more often on their own to explore additional exercises they complete from the textbook and on other assignments. Before giving a visual verification assignment involving new skills with the applet, I always demonstrate using CalcPlot3D to visually verify a similar problem we worked on the board. Once students have seen one example using the applet, most have little trouble completing the exercise on their own.
Without further discussion, let's look at some examples of how this can be done! As you develop your own examples, please send them along to me! I would love to develop a library of useful ways to use this applet. |
Number Systems
Real Numbers
Euclid's division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. Proofs of results – irrationality of root 2, root 3, root 5 , decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.
Algebra
1. Polynomials
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.
2. Pair of Linear Equations in Two Variables
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions/inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be...
[continues] |
Course starts out easy and then suddenly gets difficult. The math isn't too tough but there are a LOT of formulas to memorize. We didn't need the book at all for the class as we used StatsPortal (a service you need to purchase) but that has an ebook on it. |
Numerical analysis is the study of algorithms for computing
numerical solutions to mathematical problems. The course provides an
introduction to the ideas of numerical analysis via simple problems in analysis
and algebra. We will study the efficiency of the algorithms as well as their implementation. .
Topics and reviews
Representation of floating point numbers, their implementation on the computer, loss of significance. |
MATH C103: Introduction to Mathematical Economics
Selected topics illustrating the application of mathematics to economic theory. This course is intended for upper-division students in Mathematics, Statistics, the Physical Sciences, and Engineering, and for economics majors with adequate mathematical preparation. No economic background is required. Also listed as Economics C103.
Units:4
Overall Rating:5 Stars
A
Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
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 of a formula can be parsed once, and calculated many times with different variable values.
MultiplexCalc is an indispensable calculator designed for math teachers, scientists, engineers, university and college faculty and students, financiers and other professionals.
MultiplexCalc features include the following:
* User-friendly interface
* You can build linear, polynomial and nonlinear equation set
* Unlimited customizable variables
* Scientific notation for numerical value
* Scientific calculations and unlimited expression length
* Parenthesis compatible and unlimited nesting for expression
* Upper case and lower case can be freely used in expression
* History of calculation sessions
* Comprehensive help
* Calculation range: (1.797E-308, 2.225E308)
* High precision calculation - features up to 38 digits after the decimal point
* Accurate result display - features up to 24 digits after the decimal point
* Your can do standard manipulation with "Expression" edit box such as cut, copy and paste operations
GraphiCal is a programmable graphics calculator which lets you visualize expressions and formulas as graphs in a chart. Creates animated video clips from a sequence of graphs. Built-in functions (>50) include integration, root finding ..Learning mathematics can be a challenge for anyone. Math Flight can help you master it with three fun activities to choose from! With lots of graphics and sound effects, your interest in learning math should never decline.
MaTris is a nice program for practicing the basic operations of arithmetic. The calculation method is preselectable. It includes simple counting exercises, addition with symbols, addition/subtraction, multiplication and divisionThis is an advanced expression and conversion calculator. Vast array of built-in functions, constants and confersion operations that can be extended with your own user-defined functions. Now with graphs. |
This semester, I am serving as the teaching assistant for the
Math 220 (Calculus) discussion sections AD1 and AD5 which correspond to the lecture section AL1 being taught by
Randy McCarthy. The course webpage is located
here; please note that this page is a supplement to, NOT a replacement of, the official
course webpage.
4. It has been my pleasure to lead our discussions this semester. I am proud of each one of you for working hard and learning not only the
required material, but improving your reasoning and problem solving abilities. Good luck on the final exam. (December 10, 2008)
3. When you are asked to compute a derivative on a quiz, you do not need to simplify your work unless it is stated otherwise.
2. I should have placed more emphasis on one particular point in my classes. Many of the limit laws I was using in class,
such as distributing a limit between the sum or difference of two functions, only works when the limit of both functions exist independently. See Section 1.3
in the textbook for more details. Also, I am including an example from the homework (also listed above) of when the limit of two functions that do not exist add
to make a functions where the limit of the function exists.
1. The definition of one-to-one on page 30 (section 0.3) given in the textbook is NOT the definition generally
accepted in mathematics literature. The accepted definition can be realized by replacing "exactly one" with "at most one" in the definition.
With respect to quiz papers, if the student uses either of these definitions correctly, no deductions will be taken with respect to
this particular concept. |
Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.
Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.
Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
This completely revised Fourth Edition of the book, appropriate for all engineering under-graduate students, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications. The book focuses clearly on teaching students numerical methods and in helping them to develop problem-solving skills.
A distinguishing feature of the present edition is that it provides references to MATLAB, IMSL and Numerical Recipes program libraries for implementing the numerical methods described in the book. Several exercises are included to illustrate the use of these libraries.
Additional worked examples and exercises have been added for better appreciation and understanding of the material. Answers to some selected exercises have been provided. |
Winder ACT MathI particularly enjoy studying set theory (including logic) and point-set topology. As an undergrad, discrete math was a course required by my curriculum. I have also taken courses on point-set topology, abstract algebra, and probability theory, as part of my graduate studiesDuring |
Exam1_StudyGuide
Course: MATH 260, Fall 2009 School: illinoisstate.edu Rating:
Word Count: 317
Document Preview problems could appear on the exam; therefore it is highly recommended that you make every effort to complete those problems. Exam 1 Topics: 1. Sets: showing two sets are equal, showing one set is a subset of another, set notation, setbuilder notation, finding the power set of a given set, the sets N, Z, Q, R. 2. Set operations: union, intersection, set difference, complement, symmetric difference, cartesian product. Given various sets, applying these operations. 3. De Morgan's Laws and Set Properties proving various set properties are true or finding a counter-example to show a statement is false. 4. Binary relations, reflexive, symmetric, transitive: showing that given a relation is reflexive, symmetric, or transitive or finding a counter-example to show that the relation does not satisfy any one of these properties. 5. Equivalence relations: determining whether a given relation is an equivalence relation, finding the equivalence classes. 6. The relationship between equivalence relations and partitions. 7. Definition of a function. 8. Surjections, injections, and bijections: showing that a function is one-to-one or onto. 9. Composition of functions: what is it, how is it defined. 10. The Division Algorithm, finding the "q" and the "r". 11. Definition of divides and properties of div. Jordon Math 260 Fall 2008Reading Assignment GuidelinesFor almost every class meeting this term, you will be given a reading assignment together with two or three questions to which you must respond. Below is a description of the requirements you will
Math 260, Fall 2008 H. JordonExtra Homework ProblemsInstructions: Answer each of the following questions on a separate piece or pieces of paper. Each question is worth 5 points. You may work with each other to solve the problems but the final write-up m
Systems Analysis and Design in a Changing World, Fourth Edition22Learning ObjectivesxExplain the purpose and various phases of the systems development life cycle (SDLC) Explain when to use an adaptive approach to the SDLC in place of a more predictiv
Math 105 Prelim #2 October 28, 2004This exam has a formula sheet, 7 problems and 7 numbered pages. You have 90 minutes to complete this exam. Please read all instructions carefully, and check your answers. Show all work neatly and in order, and clearly i
Math 105, Fall 2004 Solutions to Prelim 21.(a) Henri has to take 3 bottles from 5+7=12, and the order in which they are taken doesn't matter. Therefore, there are 12 3 possible choices. (b) Henri has to choose 1 bottle from the 5 bottles of red and 2 bo
Prelim 1 SolutionsProblem 1 (Total 10 points) Give the least square line that has the best fit to the following data points: (0, 2), (1, -2), (2, -2) and (3, 2). Hint: Recall that the slope and y-intercept of the best fit line are given by the formulasn
IT430 Lab 2 - Network Protocols and Scanning Name _, _ Directions: Work in groups of 2 to complete this lab. Goals: - Learn how to use VMWare - Understand the importance of using secure network protocols - Understand why hackers can transport a great quan
Scenario 1: Mobile Tactical Network for Special Operations Customer: J6, US Special Operations Command Support Staff: 1 Army officer and 20 brand-new enlisted troops with a mix of all services. You are tasked with designing a network for Special Operation
IT430 Lab 4 Gaining Network Access Names _, _ Directions: Work in groups of 2 to complete the following tasks and provide answers Goals: - Understand how hackers might use a listener program to gain access to a network - Understand how programs bypass ant
IT430 Network and Firewall Lab Name _, _ This lab is to be completed in teams of 2, no more than 3. Goals: Understand basic networking components Connect a simple network Understand Cisco Commands Understand the difference between a host firewall and a ne
IT430 Lab 8 Penetration Testing Demo Name(s) _, _ Goals: - Analyze vulnerabilities and determine possible attack vectors for many of the exploits learned in class Part I Metasploit Open the each image and go to the initial snapshot for each Open Green-XP
IT430 Lab 5 Linux and Unix Security Names _, _ Directions: Work in groups of 2 to complete the following tasks and provide answers Goals: - Understand the basic steps in improving the security on a Linux system Stopping unnecessary services/closing ports
Systems Analysis and Design in a Changing World, Fourth Edition1414Learning ObjectivesxDiscuss examples of system interfaces found in information systemsxDefine system inputs and outputs based on the requirements of the application programxDesign
Chapter 7Reporting and Interpreting Cost of Goods Sold and InventoryANSWERS TO QUESTIONS1. Inventory often is one of the largest amounts listed under assets on the balance sheet which means that it represents a significant amount of the resources avail
Lecture 25 Appendix B: Some sample problems from Boas Here are some solutions to the sample problems concerning solutions of 2 nd order differential equations, sometimes with time dependence as in Chapter 13.13.4: 2 Solutions: Here we consider the 1-D wa
Final Exam: Economics 101 June 12, 2002READ THE INSTRUCTIONS: You have three hours. Do all 5 questions; each has equal weight. Please be sure to number each problem by number and part, especially if you choose to do them out of order. You will get creditMidterm Exam: Economics 101You have one hour and fifteen minutes. Do all 3 questions; each have equal weight. Good luck.February 10, 1997 David K. Levine1. Short AnswersFor each of the normal form games below, find all of the Nash equilibria. Which arChapter 6 Circular Motion and GravitationCircular MotionConsider an object moving at constant speed in a circle. The direction of motion is changing, so the velocity is changing. Therefore, the object is accelerating. The direction of the acceleration i
A. 1. SamuelAbstract: Two machine-learning procedures have been investigatedin some detail using the game ofcheckers. Enough work has been done to verify the fact that a computer can be programmed so that it will1learn to play a better game of checke
COVER FEATUREThe Architecture of Virtual MachinesA virtual machine can support individual processes or a complete system depending on the abstraction level where virtualization occurs. Some VMs support flexible hardware usage and software isolation, whi
A Case for End System MulticastYang-hua Chu, Sanjay G. Rao, and Hui Zhangfyhchu,sanjay,[email protected] Mellon UniversityABSTRACTThe conventional wisdom has been that IP is the natural protocol layer for implementing multicast related funct
Network Working Group R. DanielRequest for Comments: 2168 Los Alamos National LaboratoryCategory: Experimental M. Mealling Network Solutions, Inc. June 1997 Resolution of Uniform Resource Identifiers using the Domain Name SystemStatus of this Memo
Congestion Avoidance and ControlVan JacobsonLawrence Berkeley LaboratoryMichael J. KarelsUniversity of California at BerkeleyNovember, 1988IntroductionComputer networks have experienced an explosive growth over the past few years and with that growNotes on Using gdb, the GNU Debugger Benjamin ZornUsing a symbolic debugger will make writing and debugging the programs you will write in this course much easier. The best debugger to use with the version of C+ we are using in this class is gdb, the GNU
The Chubby lock service for loosely-coupled distributed systemsMike Burrows, Google Inc.AbstractWe describe our experiences with the Chubby lock service, which is intended to provide coarse-grained locking as well as reliable (though low-volume) storag
I. refinement A. definition- REFINEMENT GIVES A STRONGER SPECIFICATIONA specification S1 is refined by S2 (S1 <= S2)if and only if every correct implementation of S2is a correct implementation of S1.A refinement is "plug compatible"; this includes |
Abstract
A not-insignificant number of undergraduate engineers have problems with mathematics. School mathematics often has to be reinforced during undergraduate studies, where a lack of
understanding at the lower level often impedes learning at the higher level. Here, visualisations can help - either by contextualising the mathematics, or by using graphical
visualisations. In this latter case, "A picture is worth a thousand words" is most appropriate. However, even students who have problems rearranging equations are almost invariably able to "read", understand and draw graphs - basically visualisations of mathematical equations, be
they as simple as the straight-line equation or as complicated as the solution of a second-order
partial differential equation. Consequently, displaying graphs (i.e. visualising) can help deepen insight into mathematical processes. This, in turn, can raise a student's mathematical proficiency, predilection, awareness and eventual achievement. This paper deals with, amongst others, the following questions. Does using MathinSite improve mathematical achievement and if so, how? How does using MathinSite score over other computer-based learning techniques? |
Summary of Content: The success of applied mathematics in describing the world around us arises from the use of mathematical models, often using ordinary and partial differential equations. This module continues the development of such models, building on the modules G11CAL and G11APP. It introduces techniques for studying linear and nonlinear systems of ordinary differential equations, using linearisation and phase planes. Partial differential equation models are introduced and analysed. These are used to describe the flow of heat, the motion of waves and traffic flow. Continuum models are introduced to describe the flow of fluids (liquids and gases, such as the oceans or the Earth's atmosphere).
Method and Frequency of Class:
Activity
Number Of Weeks
Number of sessions
Duration of a session
Lecture
22 weeks
1 per week
2 hours
Lecture
22 weeks
1 per week
1 hour
Activities may take place every teaching week of the Semester or only in specified weeks. It is usually specified above if an activity only takes place in some weeks of a Semester
Further Activity Details: One two-hour class and one one-hour class per week timetabled centrally, some of which may be used for examples classes and/or problem classes.
Method of Assessment:
Assessment Type
Weight
Requirements
Exam 1
80
2 hour 30 min written examination
Coursework 1
5
Exercise 1
Coursework 2
5
Exercise 2
Coursework 3
5
Exercise 3
Coursework 4
5
Exercise 4
Convenor:
Dr P Matthews Dr G Adesso
Education Aims:
This module aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations. This module leads to further study of mathematical models in medicine and biology and fluid mechanics. It also provides a foundation for further study of differential equations.
Skills
reason logically, work analytically and justify conclusions using mathematical arguments with appropriate rigour;
work with abstract concepts and in a context of generality;
transfer expertise between different topics in mathematics ;
develop appropriate mathematical models and relate them to applications;
communicate results with clarity using appropriate styles, conventions and terminology;
use high level of numeracy and accuracy to solve complex problems;
select and apply complex concepts, appropriate methods and techniques to familiar and novel situations;
work effectively, independently and under direction;
adopt effective strategies for study. |
Students will develop reasoning and problem solving skills as they study topics such as congruence and similarity, and apply properties of lines, triangles, quadrilaterals, and circles. Students will also develop problem solving skills by using length, perimeter, area circumference, surface area, and volume to solve real-world problems.
ALGEBRA 1
RGL: 9
PRE: Completion of Algebra A & B with a grade of C- or better
In this course the student will learn some of the basic operations needed to transform and solve equations involving one or more unknown quantities. The study of geometry is included with a focus on the concepts of area and volume.
ALGEBRA II
RGL: 9
PRE: Completion of Algebra 1 with a grade of a C- or better
A study of more advanced algebraic concepts with an introduction to the fundamental trigonometric ratios. Geometric figures and their properties are introduced as are deductive reasoning and proof.
ALGEBRAA
PRE: successful completion of 8th grade math
RGL: 9-12
Algebra ½ is the first class of a two year Algebra 1 program. Students will explore the following topics: algebraic equations, expressions, and functions, rational numbers, linear equations, proportions, graphing relations, analyzing linear equations, and inequalities. A scientific calculator is recommended.
ALGEBRA B
RGL:
PRE: Completion of Algebra A
This is the second part of the two year Algebra 1 program. Students will begin with a review of concepts from the previous class. New explorations include: statistics, probability, systems of linear equations, graphic solutions, multiplication, division, and factoring of polynomial expressions, Pythagorean Thermos, and operations with rational expressions and equations.
PRE CALCULUS-INDEPENDENT STUDY (Honors Class)
RGL: 12
PRE: consent with Instructor
Students who wish to pursue degrees in the sciences or engineering may want to consider completing Algebra II and Geometry in their junior year so they would be able to take calculus in their senior year. Taking calculus will provide students with an advantage on the ACT and SAT tests and on college mathematics placement exams. |
APPLIED MATHEMATICS-WORKBOOK
by PHAGAN
No options of this product are available.
Description
Applied Mathematics is a comprehensive text designed to benefit students in various fields of study. Text content emphasizes the application of mathematics to a variety of vocational and technical areas. The text uses realistic applications to develop problem-solving skills and provide an understanding of the importance of math in the real world.
The |
Recommended Titles
Adopts an informal, user-friendly approach, describing mathematical processes in everyday language. Mathematical ideas are then developed by example rather than by formal proof. Covers the first-year... |
Courses
Course Details
MATH 046 Elementary Algebra and Geometry
5
hours lecture,
5
units
Letter Grade or Pass/No Pass Option
Description: Elementary algebra and geometry serves as the foundation for the other math courses and is the first of a two-course integrated sequence in algebra and geometry intended to prepare students for transfer level mathematics. This course covers the real number system; writing, simplifying, solving and graphing of linear equations in one variable; solving linear inequalities in one variable; solving systems of linear equations in two variables; algebraic operations with polynomial expressions and factoring; functions; operations involving rational expressions and related equations; and geometric properties of lines, angles, and triangles. This course is intended for students preparing for higher-level geometry and algebra courses. (Formerly MATH 95). |
Introductory And Intermediate Algebra - 07 edition
ISBN13:978-0073298146 ISBN10: 007329814X This edition has also been released as: ISBN13: 978-0073298078 ISBN10: 0073298077
Summary: Miller/O'Neill/Hyde's Introductory and Intermediate Algebra is an insightful and engaging textbook written for teachers by teachers. Through strong pedagogical features, conceptual learning methodologies, student friendly writing, and a wide-variety of exercise sets, Introductory and Intermediate Algebra is a book committed to student success in mathematics.
1.1 Sets of Numbers and the Real Number Line 1.2 Order of Operations 1.3 Addition of Real Numbers 1.4 Subtraction of Real Numbers 1.5 Multiplication and Division of Real Numbers 1.6 Properties of Real Numbers and Simplifying Expressions
7.1 Solving Systems of Linear Equations by Graphing 7.2 Solving Systems of Equations by Using the Substitution Method 7.3 Solving Systems of Equations by Using the Addition Method 7.4 Applications of Systems of Linear Equations in Two Variables 7.5 Systems of Linear Equations in Three Variables and Applications 7.6 Solving Systems of Linear Equations by Using Matrices |
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience. contents
Preface
Diagnostic Pretest
0. Prealgebra Review
0.1 Simplifying Fractions
0.2 Adding and Subtracting Fractions
0.3 Multiplying and Dividing Fractions
0.4 Using Decimals
How Am I Doing? Sections 0.1–0.4
0.5 Percents, Rounding, and Estimating
0.6 Using the Mathematics Blueprint for Problem Solving
Use Math to Save Money
Chapter 0 Organizer
Chapter 0 Review Problems
How Am I Doing? Chapter 0 Test
Math Coach
1. Real Numbers and Variables
1.1 Adding Real Numbers
1.2 Subtracting Real Numbers
1.3 Multiplying and Dividing Real Numbers
1.4 Exponents
1.5 The Order of Operations
How Am I Doing? Sections 1.1–1.5
1.6 Using the Distributive Property to Simplify Algebraic Expressions
1.7 Combining Like Terms
1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas
1.9 Grouping Symbols
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Chapter 1 Organizer
Chapter 1 Review Problems
How Am I Doing? Chapter 1 Test
Math Coach
2. Equations, Inequalities, and Applications
2.1 The Addition Principle of Equality
2.2 The Multiplication Principle of Equality
2.3 Using the Addition and Multiplication Principles Together
2.4 Solving Equations with Fractions
How Am I Doing? Sections 2.1–2.4
2.5 Translating English Phrases into Algebraic Expressions
2.6 Using Equations to Solve Word Problems
2.7 Solving Word Problems: The Value of Money and Percents
2.8 Solving Inequalities in One Variable
Use Math to Save Money
Chapter 2 Organizer
Chapter 2 Review Problems
How Am I Doing? Chapter 2 Test
Math Coach
3. Graphing and Functions
3.1 The Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 The Slope of a Line
How Am I Doing? Sections 3.1–3.3
3.4 Writing the Equation of a Line
3.5 Graphing Linear Inequalities
3.6 Functions
Use Math to Save Money
Chapter 3 Organizer
Chapter 3 Review Problems
How Am I Doing? Chapter 3 Test
Math Coach
Cumulative Test for Chapters 0–3
4. Systems of Linear Equations and Inequalities
4.1 Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations in Three Variables
How Am I Doing? Sections 4.1-4.2
4.3 Applications of Systems of Linear Equations
4.4 Systems of Linear Inequalities
Use Math to Save Money
Chapter 4 Organizer
Chapter 4 Review Problems
How Am I Doing? Chapter 4 Test
Math Coach
5. Exponents and Polynomials
5.1 The Rules of Exponents
5.2 Negative Exponents and Scientific Notation
5.3 Fundamental Polynomial Operations
How Am I Doing? Sections 5.1–5.3
5.4 Multiplying Polynomials
5.5 Multiplication: Special Cases
5.6 Dividing Polynomials
Use Math to Save Money
Chapter 5 Organizer
Chapter 5 Review Problems
How Am I Doing? Chapter 5 Test
Math Coach
6. Factoring
6.1 Removing a Common Factor
6.2 Factoring by Grouping
6.3 Factoring Trinomials of the Form x2 + bx + c
6.4 Factoring Trinomials of the Form ax2 + bx + c
How Am I Doing? Sections 6.1–6.4
6.5 Special Cases of Factoring
6.6 A Brief Review of Factoring
6.7 Solving Quadratic Equations by Factoring
Use Math to Save Money
Chapter 6 Organizer
Chapter 6 Review Problems
How Am I Doing? Chapter 6 Test
Math Coach
Cumulative Test for Chapters 0–6
7. Rational Expressions and Equations
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions
How Am I Doing? Sections 7.1–7.3
7.4 Simplifying Complex Rational Expressions
7.5 Solving Equations Involving Rational Expressions
7.6 Ratio, Proportion, and Other Applied Problems
Use Math to Save Money
Chapter 7 Organizer
Chapter 7 Review Problems
How Am I Doing? Chapter 7 Test
Math Coach
8. Rational Exponents and Radicals
8.1 Rational Exponents
8.2 Radical Expressions and Functions
8.3 Simplifying, Adding, and Subtracting Radicals
8.4 Multiplying and Dividing Radicals
How Am I Doing? Sections 8.1—8.4
8.5 Radical Equations
8.6 Complex Numbers
8.7 Variation
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Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach
9. Quadratic Equations and Inequalities
9.1 Quadratic Equations
9.2 The Quadratic Formula and Solutions to Quadratic Equations
9.3 Equations That Can Be Transformed into Quadratic Form
How Am I Doing? Sections 9.1—9.3
9.4 Formulas and Applications
9.5 Quadratic Functions
9.6 Compound and Quadratic Inequalities in One Variable
9.7 Absolute Value Equations and Inequalities
Use Math to Save Money
Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
Cumulative Test for Chapters 0-9
10. The Conic Sections
10.1 The Distance Formula and the Circle
10.2 The Parabola
10.3 The Ellipse
How Am I Doing? Sections 10.1—10.3
10.4 The Hyperbola
10.5 Nonlinear Systems of Equations
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Chapter 10 Organizer
Chapter 10 Review Problems
How Am I Doing? Chapter 10 Test
Math Coach
11. Additional Properties of Functions
11.1 Function Notation
11.2 General Graphing Procedures for Functions
How Am I Doing? Sections 11.1—11.2
11.3 Algebraic Operations on Functions
11.4 Inverse of a Function
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Chapter 11 Organizer
Chapter 11 Review Problems
How Am I Doing? Chapter 11 Test
Math Coach
12. Logarithmic and Exponential Functions
12.1 The Exponential Function
12.2 The Logarithmic Function
12.3 Properties of Logarithms
How Am I Doing? Sections 12.1—12.3
12.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms
12.5 Exponential and Logarithmic Equations
Use Math to Save Money
Chapter 12 Organizer
Chapter 12 Review Problems
How Am I Doing? Chapter 12 Test
Math Coach
Practice Final Examination
Appendix A: Foundations for Intermediate Algebra: A Transition from Beginning to Intermediate
Appendix B: Practice with Operations of Whole Numbers
Appendix C: Tables
Appendix D: Determinants and Cramer's Rule
Appendix E: Solving Systems of Linear Equations Using Matrices
Appendix F: Sets
Solutions to Practice Problems
Answers to Selected Exercises
Glossary
Applications Index (Available in MyMathLab)
Index
Photo Credits
New to this edition
New and Updated Features
The end-of-chapter material has been further enhanced to provide more alsoUse Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. The topics discussed in Use Math to Save Money have been updated based on a student survey of more than 1,000 developmental math college students.
Steps to Success (formerly called "Develop Your Study Skills") has been updated and expanded to provide students with more guided techniques for improving their study skills and succeeding in math.
New Instructor and Student Resources
Worksheets with the Math Coach tie the complete learning package together, providing extra vocabulary and practice exercises for every section of the text. Every chapter also includes the Math Coach Problems from the book and videos so students can follow along, and have plenty of space to show their work.
The Lectures Series on DVDfeaturing Math Coach and Chapter Test Prep Videos has been completely revised to provide students with extra help for each section of the textbook. The videos include:
A new interface allows easy navigation to objectives and key examples and exercises.
The new Math Coach Videos give students an office hour with the authors! In these videos, the authors expand upon the end-of-chapter Math Coach materials that are in the text and coach students on how to avoid commonly made mistakes.
Chapter Test Prep Videos provide step-by-step video solutions to every problem in each "How Am I Doing?" Chapter Test in the textbook.
Chapter Test Prep Videos and Math Coach Videos are available in MyMathLab and on YouTube™.
New to MyMathLabPre-made (and pre-assigned in the Ready to Go course) "How Am I Doing?" mid-chapter review homework that lets students pause at critical junctures to make sure they are "getting it."
Pre-made chapter review quizzes that are pre-assigned in the Ready to Go course and generate personalized homework assignments based on students' quiz results.
A Pre-made (and pre-assigned in the Ready to Go Course) pre- and post- test for every chapter.
A new Stepped-OutConcept Check Questions exercise style that guides students through solutions, helping them understand not only the steps involved, but the reasoning behind them.
Pre-made (and pre-assigned in the Ready to Go course) Math Coach Homework for every chapter that uses the stepped-out concept check approach to coach students before the test to the areas where mistakes are most commonly made and show them how to avoid these pitfalls.
Use Math to Save Money Animations are assignable and offer an interactive way for students to use the math they are learning to cut costs and spend less.
All videos from the Lecture Series on DVD with Math Coach and Chapter Test Prep Videos.
Content Updates
Section 0.6: Using the Mathematics Blueprint for Problem Solving has been added to Chapter 0.
The presentation of topics in Chapter 2 has been refined, including the addition of Section 2.7: Solving Word Problems: The Value of Money and Percents
Updates to Chapter 3 include the introduction of a new Graphing Organizer. This organizer summarizes the graphing methods presented in the chapter and notes the advantages and disadvantages of each. The objective of finding the slopes of parallel and perpendicular lines has been relocated to Section 3.4.
Features & benefits
Students will find many opportunities to check and reinforce their understanding of concepts throughout each chapter:
Student Practice problems are paired with every example in the text. The full solutions to each practice problem are located in the back of the text, allowing students to check their work as they go.
The "How Am I Doing?" mid-chapter review exercises let students pause at a critical juncture to make sure they are "getting it."
End-of-Section Exercises progress from basic to challenging, and each exercise set includes Verbal and Writing Skills, and Mixed Practice exercises.
A Quick Quiz at the end of each exercise set contains three problems that cover the essential content of that section. This simple assessment tool measures whether students know when they are ready for new material, and when they need further review.
A Concept Check question at the end of each Quick Quiz asks students to explain how and why a method works in their own words, forcing students to analyze problems and reflect on the mathematical concepts.
Classroom Quizzes in the Annotated Instructor's Edition parallel every Quick Quiz, which allows instructors to quickly assess the understanding of the class at any point in the chapter.
The End-of-Chapter Material provides severalThe Chapter Test Prep and Math Coach Videos are available in MyMathLab and on YouTube.
Use Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. Topics have been updated based on a student survey of more than 1,000 developmental math colleges.
Author biography
John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Massachusetts with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.
Jennifer Crawford received her BS in mathematics from the University of Minnesota – Duluth in 1995 and her MS in mathematics from the University of Minnesota – Twin Cities in 1998. She taught a wide range of courses at North Shore Community College in Danvers, Massachusetts for five years. She currently teaches at Normandale Community College in Bloomington, Minnesota where her focus is working with developmental math students. She lives in Minneapolis, Minnesota with her husband, two young children, and black lab. |
MAA Review
[Reviewed by Mark Hunacek, on 09/06/2012]
A student learning special relativity for the first time must contend not only with counter-intuitive concepts such as time dilation and length contraction but also with fairly cumbersome equations such as the Lorentz equations
x' = γ (x – vt)
t' = γ (t – (v/c2)x)
(where γ = 1/√(1-v2/c2) and c is the speed of light), which relate the position and time of an observer O at rest and a moving observer O'. The novel idea of this slim, succinct book is to seek to replace reliance on these equations with geometric reasoning. Of course the "geometry" here is not the ordinary Euclidean geometry we all learned in high school, and which is based on circles in the sense that the set of all points at distance 1 from the origin is a circle. Here, instead, the geometry is based on hyperbolas: the squared distance of a point (x, y) from the origin is defined to be x2 – y2, so the "unit circle" in this geometry is really a hyperbola. The ordinary trigonometric functions are then replaced by the hyperbolic functions sinh, cosh, and tanh, applied to angles that show up in spacetime diagrams. (Such a diagram plots the position x and time t of an object, with t running up the vertical axis and x moving along the horizontal one; thus, for example, a vertical line depicts an object that stays motionless as time passes.)
The book starts with two introductory chapters, the first of which (very) rapidly contrasts Newton's and Einstein's physics and the second of which functions as a quick overview of the physics of special relativity, including the derivation of the Lorentz equations from the two basic postulates of special relativity (that the laws of physics apply in all inertial reference frames and that the speed of light is the same for all inertial observers). This is followed by two chapters on Euclidean "circle geometry" and the non-Euclidean "hyperbola geometry" that will be used throughout the book, introducing the hyperbolic trigonometric functions from several different (but equivalent) points of view.
The geometry of special relativity begins in earnest with the next chapter, which introduces spacetime diagrams and a particular angle in them called the rapidity, which turns out to be the angle between a worldline and the vertical (ct) axis (ct, rather than t, because we want to measure time and space in the same units). The ideas developed here are exploited in two subsequent chapters ("Applications" and "Paradoxes") which discuss the geometric ideas behind such topics as length contraction, time dilation, the twins paradox, and others.
There are then three (non-consecutive) chapters that struck me as the most demanding in the book: chapter 9, on relativistic mechanics, addresses the relationship between mass and energy and gives insight into the famous equation E = mc2; chapter 11, on relativistic electromagnetism (which, thanks to my dismal background in physics, I only dimly understood) unifies electricity and magnetism; chapter 13 provides a warp-speed look at general relativity.
The book concludes with two chapters that are really just straight mathematics, no physics: one chapter ("Hyperbolic Geometry") discusses various models for hyperbolic geometry, and the other ("Calculus") offers a geometric derivation of the trigonometric and exponential functions.
There are thirteen substantial worked-out examples in the book, all of which struck me as both interesting and illuminating; instead of scattering them throughout the text the author puts them all in three chapters (7, 10 and 12) devoted entirely to them. There are no exercises, but the author does occasionally explicitly leave something to the reader to ponder, such as the resolution of the "manhole cover" paradox in chapter 8.
Despite the fact that there are at least two other books (one quite recent) with titles that are very similar to this book's, Dray's approach really does appear to be novel. Dragon's new book The Geometry of Special Relativity: A Concise Course, for example, seems (based on an admittedly cursory glance) to be addressed to a considerably more sophisticated audience than is this text, and while geometric ideas are certainly mentioned the ones that are discussed in Dray do not appear to take center stage in Dragon. There is also a book by Callahan with the similar-sounding title The Geometry of Spacetime, but that book is considerably different than this one; unlike this text, it covers both general and special relativity (so "geometry" as used in the title of that book really refers to differential geometry, which finds extensive use) and the discussion of special relativity in the first half of the book emphasizes linear algebra notation; matrix computations appear throughout. This is consistent with a primary idea in Dray's book (that the Lorentz transformation is really just a hyperbolic rotation) but the manner of presentation is different. (Anybody planning to look at both books should also note that Callahan, in contravention of what I believe is now standard practice, uses the horizontal, rather than vertical, axis for time.) Finally, I should perhaps mention Taylor and Wheeler's Spacetime Physics, endorsed by the author but unseen by me, which apparently contained a lot of this material in its first edition but left much out of it out of the second.
The question then arises, of course, whether "novel" necessarily means "better". I found that the geometric discussions did shed some light on the underlying ideas, but I also thought at times that the calculations used in them were just disguised versions of the calculations used from a more traditional approach (which, I think, any serious student of special relativity should be familiar with, since these ideas appear so frequently in the literature). So, while I enjoyed reading this book and certainly learned from it, I tend to think that it would serve best as a supplemental text for a course in special relativity rather than as a main text. (The very succinct writing style, and the total lack of homework exercises, also influenced this opinion.) The author himself may think this, because he writes in the preface that the book "is not intended as a replacement for any of the excellent textbooks on special relativity" but is intended as an introduction "to a particularly beautiful way of looking at special relativity… encouraging students to see beyond the formulas to the deeper structure." This goal, I think, has been met: on more than one occasion as I read this book I found myself looking at other texts to compare discussions, and I generally found that the process seemed to have a synergistic effect: I got more out of both books by doing this. This is unquestionably a book that anybody who teaches special relativity will want to look at. |
Graphs And Digraphs - 5th edition
Summary: Written for advanced undergraduate and beginning graduate students, the fifth edition of this best-selling book provides a wide range of new examples along with historical discussions of mathematicians, problems, and conjectures. It features new and expanded coverage of such topics as toughness, graph minors, perfect graphs, list colorings, nowhere zero flows, list edge colorings, the road coloring problem, and the rainbow number of a graph. Additional applications, exercises, and ex...show moreamples illustrate the concepts and theorems. A solutions manual is available for qualifying instructors |
New Signpost Maths for Victoria by Alan McSeveny
The title of this book is New Signpost Maths for Victoria and is written by author Alan McSeveny. The book New Signpost Maths for Victoria is published by Pearson Education Australia. The ISBN of this book is 9780733983443 and the format is Paperback. The publisher has not provided a book description for New Signpost Maths for Victoria by Alan McSeveny.
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Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
Contains three interconnected content strands are incorporated into 10-11 units of work that can be completed in the school year.
Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
Books By Author Alan McSeveny, as well as references to the Scope and Sequence charts.A graded series for seven student books from years 1 to 7. The full colour student books have been written to meet all the requirements of the Queensland Essential Learnings with particular references to 'ways of working' through inquiry-based activities at each year level, as well as references to the Scope and Sequence charts.
New Signpost Maths for Queensland is a |
Hi. I am right now doing the Arithmetic book and I am can tell that I am really having a hard time. Can anyone make a recommendation? I just don't get the problems and feel like I need alot of practice on just basics.
Have you worked through the Math Essentials book ("Book Zero") yet? You'll find that a lot of the more fundamental math concepts are covered in detail in that book. To a certain extent, the other quant books assume that you're comfortable with those basics and then add on complexity to make the topics more like what you'll see on the actual GMAT |
In answer to your other questions
>>Anyways, must I learn the analytic geometry if I just want to make simple programs that resemble something of 3d, but maybe not 100% accurate?
No, you can write very simple programs without understanding the maths. But that's all you'll be able to do. If you learn a little more, you'll be able to go much further. And you'll be able to make more sense of the maths on Wikipedia.
>>They don't teach any useful math at school and they aren't any time soon so I don't know where to start learning
Don't forget that it's more important to a teacher that the dull students aren't left behind, than the bright students get ahead. Maybe you can find a teacher who is willing to explain something to you outside of class. Or maybe a parent or relative of yours could help.
At my school there was a maths society where we explored topics outside of the curriculum...
Having a good teacher is probably the best way to learn this sort of stuff, but failing that a good book might be helpful. Check your library for something that's at the right level for you.
>>And I don't what this type of stuff means:
>>sin^2 (x) <<????
Basically, computer programmers need to make sure the computer understands them. Mathematicians need to make sure that other mathematicians understand them. So while programming languages tend to be fairly simple and consistent, mathematical notation is much less so.
Also remember that mathematics until recently was nearly always written by hand, and even today much is written by hand. A notation that's easier to read in slightly messy writing is a winner.
There are many areas of mathematics where there are a few different notations in popular usage. Often say Europe will use one notation and the US will use another.
Anyway, this is one case where "everybody knows" that sin^2(x) means sin(x)*sin(x). Just learn it.
>>$variable = new variabletype();
This is to do with object oriented programming, a big topic that I don't think you should worry about just yet. PHP does not require you to use it. |
The Grading System: Instructor Notes
The grading scheme from the student guide is reproduced below.
There are three components to the student's grade.
As the instructor, you are responsible for the determining the
section component and how you will
use it to adjust the student's final course grade.
Evaluating the section component. Since we consider cooperative
learning to be an essential feature of the introductory program, we
require that team homework count for at least 40% of the section component.
Aside from that, it is up to you how to determine the section component
of the grade. For example, you may choose to give weekly individual or
group quizzes and/or
daily reading quizzes; you may choose to collect individual homework;
you may choose to give credit for in-class work, presentations, extra
credit, good team evaluations, etc. It helps to choose a system
that encourages study habits that you believe will contribute to
student learning.
Informing the students.
It is important that you explain your system for evaluating the section component clearly
and carefully in your first day handout
so that your students know how they will be evaluated.
It is also important to ensure that the feedback you give students on their
section work accurately reflects the impact it will have on their
grade. There are many simple ways to achieve this. One is to
grade section work with a median of approximately 70%. If that does
not suit your class, or your grading, an alternative is
to announce the median score each time you return graded work.
The Grading System: Reproduced from the Student Guide
Grades in this math course.
All sections of this course use the same grading guidelines
to standardize the evaluation process.
Your final letter grade in the course will be based on three components:
The uniform component.
The section component.
The gateway component.
Your uniform component will determine your baseline letter
grade for the course. Your baseline grade will be adjusted by the
section and gateway components as described below to determine your
course letter grade.
1. The uniform component.
There are two uniform midterm exams and a uniform final exam.
Each of these exams will be taken by all students
in all sections at the same time, and are graded by all the instructors
working together.
Your uniform component score will be determined from your scores on each exam as follows:
Midterm Exam 1
25% of uniform component score
Midterm Exam 2
35% of uniform component score
Final Exam
40% of uniform component score
After each exam, a letter grade will be assigned to your uniform component score using
a scale determined
by the course director specifically for that exam.
We do not use the "10-point scale" often seen in high school
courses in which scores in the 90's get an A,
in the 80's get a B, and so forth;
the level of difficulty of the exams will be considered.
The scale for the uniform component score will apply to all students in all sections.
2. The section component. To help you learn the material,
you will be given a variety of reading assignments, team homework,
individual homework, quizzes and other in-class activities. Your instructor will decide how the section component is determined for your particular section and grade the section work to determine your section score.
The section component has the potential to increase your final grade above the baseline grade by one third of a letter grade (e.g., from a B+ to an A-, etc.); and, assuming that the assigned work is completed, this component cannot lower your final grade below the baseline grade by more than one third of a letter grade. So, if you are keeping up with the course and doing well
in your section work,
it will not only help you to do well in the uniform exams, but may also
add to your baseline grade. Similarly, if you
fall behind in your section work, it may reduce your baseline grade.
3. The gateway component. There will be one or two (depending
on the course you are taking)
online basic skills gateway test(s) which you need to pass by the
deadline announced in the course schedule. These routine tests are repeatable,
and in general do not pose a problem for students who are keeping up with the course work.
You may practice each test online
as many times as you like, and you may take
a test for a score as often as twice per day
until the deadline. The gateway tests do not have the potential to raise your baseline
grade, but if they are not passed by the deadline, the gateway component will
automatically reduce your final grade in the course. Deadlines and grade penalties
will be announced in your class. All sections of your course have the same deadlines
and penalties assigned to the gateway component.
Section averages.
Course policy is that a section's average final letter grade cannot differ
too much from that section's average baseline letter grades.
This means that the better your entire section does on the uniform exams,
the higher average letter grade your instructor can assign in your section.
It is therefore in your best interest to help your fellow students in
your section do well in this course.
In other words, cooperation counts!
Grades at the university.
Many students who come to the University of Michigan have to adjust
themselves to college grading standards.
The mean high school grade point average
(recalculated using only strictly academic classes)
of our entering students is around 3.6,
so many of you were accustomed to getting "straight A's"
in high school.
Students' first reaction to college grades is often,
"I've never gotten grades like these."
However, a grade of 15/20 on a team homework assignment
(which you might previously have converted to 75% - a high school C)
may well be a good score in a college math course.
Your own instructor is your best source of information on
your progress in the class.
Describing the grading system to students. You should state
explicitly how you plan to arrive at semester grades - what exams will be
given, approximately what weight they will have in the overall assessment of
the student's work, how team homework is counted, how much quizzes will
count, etc. The in-class component of the grade can be based on quiz
scores, individual homework, class participation, or whatever you find
appropriate. It is important to not to assign letter grades to the
in-class component of the grade because the grades you award at the end of
the term will have to be in alignment with the performance of your class on
the uniform exams.
Assigning final semester grades. The procedure for
calculating semester grades will be discussed in course meetings as the term
progresses.
Grade books and records. Keep a good, clear record of your
grades in a secure place. Don't lose it. Record all scores which
will count towards students' grades. Many grades complaints can be
prevented by keeping accurate records. It's easy to forget to record
grades before returning papers, so record everything, including all grade
changes, immediately. Students are very serious about their grades and
expect them to be treated as a strictly private matter. You do not
need to keep a record of students' attendance unless you choose to, however,
you may want to note any extended absences.
Complaints about your grading. From the point of view of
University of Michigan students, a great deal hinges on getting the high
grades they are accustomed to getting in high school. Many first term
freshman have never had a grade lower than an A! They will often
argue persistently over one or two points. This is not a sign that they
don't respect you. Of course, you should treat all student
complaints about grading mistakes or unfairness in a serious manner. |
Algebra 1, Algebra 2, Geometry and Basic Math lessons, that work great as lesson plans and for the students to learn in a step by step mode solution of problems and ... mrperezonlinemathtutor.com/../mrperezonlinemathtutor.com
Grade 9 Algebra by Elaine Ernst Schneider A Beginning Look at Basic Algebra - Lesson 1 Outline: Algebra provides the basics for all higher math. You will work with ...
Name Date Class 12-2 LESSON In a geometric sequence, the ratio between terms is constant This is a geometric sequence This is not a geometric sequence with a common ... psdweb.parklandsd.org/../7.12.L.2reteach.pdf |
This lucid and insightful exploration reviews complex analysis and introduces the Riemann manifold. It also shows how to define real functions on manifolds analogously with algebraic and analytic points of view. Richly endowed with more than 340 exercises, this book is perfect for classroom use or independent study. 1967 edition. |
TI-34 MultiView is ideal for middle school math, pre-Algebra, Algebra I and II, trigonometry, general science, geometry, and biology. MultiView display shows fractions as they are written on paper. View multiple calculations on a four line display and easily scroll through entries. Enter multiple calculations to compare results and explore patterns on the same screen. Simplify and convert fractions to decimals and back again. Integer division key expresses results as quotient and remainders. Toggle Key lets you quickly view fractions, decimals and terms including Pi in alternate forms. Functions include previous entry, power, roots, reciprocals, variable statistics and seven memories. Scientific calculator also features user friendly menus, automatic shutoff, hard plastic color coded keys, nonskid rubber feet, impact resistant cover with a quick reference card, and dual power with solar and battery operation. |
Extension Mathematics 1
10 Units 1000 Level Course
Available in 2012
This course prepares students for the commencement of undergraduate study in those courses that require a sound knowledge of mathematical principles. The depth and content of the course is similar to HSC 2 unit Mathematics. The course covers number systems, basic algebra, simultaneous and quadratic equations, functions and graphs, sequences and series. The course aims to develop the algebraic and graphical skills necessary for calculus.
Objectives
The course will develop: 1. an understanding of different number systems and how they are used within various scientific disciplines. 2. the ability to apply algebraic skills for the solution of real world problems. 3. the ability to apply graphical skills for the solution of real world problems. 4. the ability to communicate mathematics, orally and in writing. 5. an understanding and correct use of mathematical notation. 6. the formulation of real-world problems in the language of mathematics, and the ability to solve them. |
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Lecture Description
Linear Transformations , Example 1, Part 1 of 2. In this video, I introduce the idea of a linear transformation of vectors from one space to another. I then proceed to show an example of whether or not a particular transformation is linear or not.
Course Index |
overview
overview
This entry level calculator is perfect for middle school or high school students, and anyone who wants to solve math and science problems. The 9s is handy for anything, use it to add up bills, or solve metric conversions, or calculate currency exchange. It comes with 6 common metric conversions. And can edit statistics, calculate permutations, combinations and factorials. Solves trigometry and inverse functions.
simple to use scientific calculator with protective cover
6 common metric conversions
decimal point selection
quick and easy metric conversions for various measurement and number system conversions |
Modern Methods in Combinatorics
Objectives :
For a long time, Combinatorics was considered mainly as recreational mathematics. But in the past few decades, it has emerged as a mainstream area, with rich connections with more classical ones such as algebra, topology, geometry and probability theory. Moreover, because of its close links with computer science, Combinatorics has become a crucial scientific endeavor.
Besides classical tools, like the pigeonhole principle, the inclusion-exclusion principle, the double counting argument, induction, Ramsey argument, etc., some recent tools (the probabilistic, the algebraic, the linear algebra, the analytical and the topological methods) have shown their surprising power in solving a lot of combinatorial problems (classical and new ones). For example, with a mere knowledge of the concepts of linear independence and discrete probability, beautiful connections can be made between algebra, probability, and combinatorics. These new techniques have also found striking applications in other areas of discrete mathematics and the theory of computing.
Despite the beauty, the breadth and depth of results and applications of Combinatorics, research and teaching in this field are underrepresented in Argentina and South America. One of the main purposes of this school is to change this situation, by bringing a "guided tour" covering its most important branches, and by demonstrating its methods and power. Another related objective is the creation of research and academic networks and to build a frame for the interchange of ideas in this field.
Administrative and scientific coordinators
Daniel A Jaume, Universidad Nacional de San Luis, Argentine [email protected]
Date and location :
July 22-August 2, 2013, San Luis, Argentina
Scientific program :
A. 11 basic courses for undergraduate students
B. 7 advanced courses for graduate students
C. 4 lectures on the state-of-the-art
D. Tutorial Activities : Problem solving sessions, Group work sessions, Discussion sessions, and Open Problems Market (we will encourage the specialists to present and discuss one or two open problems for the students and the audience in general). |
Resources
Welcome to the world of Maple! With the right tools, you too can do amazing things. Maple will help you reduce the time to do any math problems. Graphing, calculus, equation solving, matrices … anything you'll likely encounter in a math course can be made easier.
The Maple Student Help Center is made specifically for you, with the right information to help get you up to speed and fully command the power of Maple. Remember, Maple is a professional product, and with a little help, you can get all of that power working for you.
The Math Oracles are a great way to get quick answers to standard math problems, including Plotting, Integration and Differentiation, Limits, Matrices, and Linear System Solving. Perhaps you're at the library and you don't have a computer with Maple on it ... and your homework involves a question where the answer is not in the back of the book. The solution? Simply visit the Maplesoft Online Math Oracles, enter your problem, and the answer will be given to you courtesy of an amazing technology called MapleNET.
Don't like reading manuals or help pages? Relax … these videos will be the ideal way for you to learn how to solve the most common types of math problems. They're short and easy to understand. So go get that bowl of popcorn and a nice cold drink and get a head start in Maple. |
Preface -- Vector analysis, which had its beginnings in the middle of the 19th century, has in recent years, become an essential part of the mathematical background required of engineers, physicists, mathematicians and other scientists. This requirement is far from accidental, for not only does vector analysis provide a concise notation for presenting equations arising from mathematical formulations of physical and geometrical problems, but it is also a natural aid in forming mental pictures of physical and geometrical ideas. In short, it might very well be considered a most rewarding language and mode of thought for the physical sciences. .
This Schaum's Outline gives you
. . Practice problems with full explanations that reinforce knowledge. Coverage of the most up-to-date developments in your course field. In-depth review of practices and applications. .
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! |
SNAP - British Columbia Pre Calculus 11
Quick Overview* Linear and Non-Linear Systems
* Quadratic Functions and Equations
* Polynomials and other Non-Linear Equations and Functions
* Inductive Reasoning
* Coordinate Geometry
* Finance
Each unit of the workbook includes the following features:
* A unit opener page that summarizes the curriculum outcomes to be addressed, identifies the lesson titles, and lists the prerequisite knowledge and skills students should have prior to beginning the unit
* Lessons that provide essential teaching pieces, explanations of the concepts, example problems, and detailed solutions
* Notes bars that contain key definitions, formulas, reminders, and important steps or procedures
* Practice exercises with questions related to the curriculum outcomes that allow students an opportunity to apply the concepts
* A review summary that provides a succinct review of the key concepts in the unit
* One or more practice tests that students can use to assess their understanding of the unit concepts |
Algebra I is a comprehensive course that provides an in-depth exploration of key algebraic concepts. Through a "Discovery-Confirmation-Practice" based exploration of algebraic concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include an Introductory Algebra review; measurement; an introduction to functions; problem solving with functions; graphing; linear equations and systems of linear equations; polynomials and factoring; and data analysis and probability.
Within each Algebra I lesson, students are supplied with a post-study "Checkup" activity, providing them the opportunity to hone their computational skills in a low-stakes, 10-question problem set before moving on to a formal assessment. Additionally, many Algebra I lessons include interactive-tool-based exercises and/or math explorations to further connect lesson concepts to a variety of real-world contexts.
To further assist students for whom language presents a barrier to learning, this course includes audio resources in both Spanish and English |
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include... More: lessons, discussions, ratings, reviews,...
An algebra practice program for anyone working on simplifying expressions and solving equations. Create your own sets of problems to work through in the equation editor, and have them appear on all of... More: lessons, discussions, ratings, reviews,...
The relations between stress and strain in linear viscoelastic theory are discussed from the viewpoint of application to problems of stress analysis. This consideration includes some important diff... More: lessons, discussions, ratings, reviews,...
Students will explore the richness of conic sections by building their own physical models and then constructing more flexible models with Sketchpad. Students retain a solid connection with th... More: lessons, discussions, ratings, reviews,...
Fifty Fathoms is a collection of fifty demonstrations that try to get at some of the tough ideas in an introductory statistics course. The book comes with a CD-ROM of Fathom Dynamic Statistics ... More: lessons, discussions, ratings, reviews,...
The worksheet presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with respect to using the direct met... More: lessons, discussions, ratings, reviews,...
This game offers a way to practice recognizing multiples of a number and applying divisibility tests. Players are presented with a target divisor and number globes in the playing area. They click the ... More: lessons, discussions, ratings, reviews,...
Commercial site with one free access per day. This is a graphing applet that uses sliders for a, b, h, and k. It is easy to see the effects of all. There is also a way to show the Pythagorean relatiAlterable worksheet in which students estimate the positions of points on unmarked number lines, on the intervals [0, 100], [0,1000], [-10, 0], [-100, 0]. Fee required for printing: see this page |
Find a Crossings, FL MathMath explains everything and it makes sense. My goal is to make it easy for students to understand math and who knows, they might even end up liking it! C and C++ are building blocks of all software there is. |
Hartshorne's Geometry: Euclid and Beyond (Springer Undergraduate Texts in Mathematics). I think it's a very instructive book and seems to be suitable for your purposes. He presents various geometrical constructions, Hilbert's Axioms (incidence, betweenness, congruence etc. ), geometry over fields, rigid motions, and so forth. |
Maths Plus is organised according to the three content strands of the Australian Curriculum: Mathematics
Number and Algebra
Measurement and Geometry
Statistics and Probability
Relevant Australian Curriculum: Mathematics content descriptions and proficiency strand references are included on every Student Book activity page and colour-coded Australian Curriculum: Mathematics cross-reference chart provided for each year level across all components. Maths Plus teaching components also align with student component by unit and page number. CLICK HERE to view the Maths Plus Australian Curriculum Edition resources online. |
Some of the content on this website requires JavaScript to be enabled in your web browser to function as intended. While the website is still usable without JavaScript, it should be enabled to enjoy the full interactive experience.
Mathematics, along with English, is a core content area that transcends disciplines. Math is used in biology, chemistry, engineering, statistics, and many other subject areas. It is also an area in which students tend to struggle. Educators on all levels and in many disciplines have come together in the math transitions meetings to discuss how to better align lessons, learning expectations, and scores between the K-12 and post-secondary levels. These events are coordinated by the Wyoming School-University Partnership and funded by support from the Qwest Foundation.
Mathematics Transitions Events
2013 Mathematics Lost in Transition Institute
April 4-5 Gillette, Wyoming
Number of participants: 35 7 K-12 educators 17 Community college educators 9 University of Wyoming educators 2 other |
The Definitive Guide to How Computers Do Math: Featuring the Virtual DIY Calculator
The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning
"The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer functions, you can easily extrapolate to more complex machines." -Fred Hudson, retired engineer/scientist
"This book-along with the virtual DIY Calculator-is an incredibly useful teaching and learning tool. The interesting trivia nuggets keep you turning the pages to see what's next. Students will have so much fun reading the text and performing the labs that they won't even realize they are learning." -Michael Haghighi, Chairperson of the Business and Computer Information Systems Division, Calhoun Community College, Alabama
"At last, a book that presents an innovative approach to the teaching of computer architecture. Written with authority and verve, witty, superbly illustrated, and enhanced with many laboratory exercises, this book is a must for students and teachers alike." -Dr. Albert Koelmans, Lecturer in Computer Engineering, University of Newcastle upon Tyne, UK, and the 2003 recipient of the EASIT-Eng. Gold Award for Innovative Teaching in Computer Engineering
Packed with nuggets of information and tidbits of trivia, How Computers Do Math provides an incredibly fun and interesting introduction to the way in which computers perform their magic in general and math in particular. The accompanying CD-ROM contains a virtual computer/calculator called the DIY Calculator, and the book's step-by-step interactive laboratories guide you in the creation of a simple program to run on your DIY Calculator.
How Computers Do Math can be enjoyed by non-technical individuals; students of computer science, electronics engineering, and mathematics; and even practicing engineers. All of the illustrations and interactive laboratories featured in the book are provided on the CD-ROM for use by high school, college, and university educators as lecture notes and handouts.
Biography
CLIVE "MAX" MAXFIELD is a bestselling author and engineer with a large following in the electronic design automation (EDA) and embedded systems industries. He is also one of the founders and President of the high-technology marketing consultancy TechBites (
ALVIN BROWN has spent over thirty years working in the electronics and computing industries. He currently acts as an engineering manager supervising remote development groups around the world |
Subcategories of Maths Skills
A LEVEL PURE MATHEMATICS
Level: AS & A2
This A level Pure Mathematics course is designed for students working at home. The topics are presented in small "chunks" with worked examples followed by activities for the student. Revision test...
A Distance Learning Course of 1 Lesson.
Course Description:
This course deals with a number of basic mathematical concepts that will be used during your study and/or work life. When you have worked through this unit you will be able to:...
This course deals with a number of basic mathematical concepts that will be used during your study and/or work life. When you have worked through this unit you will be able to:
Understand the number system and relationships between s...
This series is designed for users who want to improve their basic math skills. It covers basic mathematical calculations commonly used in business settings. Courses cover computing fractions and decimals, the order of operations for combine...
This course is about descriptive statistics, where numbers are used to summarise information about the world. Look in any newspaper, magazine or journal and you'll see charts, graphs, tables and diagrams being used in an attempt to reduce t...
A distance learning course is the ideal way to gain an A Level in Mathematics. Whether you're looking to go on to further education, improve your job prospects or expand your knowledge, distance learning A Level Mathematics is a flexible an... |
MATHEMATICS: Key Stage 3: Statistics and Probability is appropriate for study at Key Stage 3 (years 8 to 10) onwards. It contains good, well-explained teaching text, worked examples and exercises... More > accompanied by worked answers.< Less
MATHEMATICS: Number_Weights and Measures (157 pages) is appropriate for study at Key Stage 3 (years 8 to 10) and upwards. It contains good, clearly explained teaching text, worked examples and ... More > exercises accompanied by worked answers.< Less
MATHEMATICS: Key Stage 2: Statistics and Probability is appropriate for study at Key Stage 2 (years 5 to 7) and upwards. It contains well-explained teaching text, worked examples and exercises... More > accompanied by worked answers.< Less
Mathematics: Key Stage 2: Number (141 pages) is a text book designed for study from Key Stage 2 (year 5) and upwards. It contains well-explained teaching text, worked examples in graduated order of... More > difficulty and exercises (with worked answers).< Less
This book (44 pages) contains the level of mechanics required for GCSE Additional Mathematics (years 11/12) and GCE Advanced Subsidiary Mechanics 1 (year 13). It contains a wealth of worked examples,... More > including CCEA's past paper questions.< Less |
Odyssey Algebra
04/01/05
CompassLearning ( has expanded its entire suite of Odyssey products, including Odyssey Algebra for middle schools and secondary education. The browser-based curriculum will help teachers offer a comprehensive approach to math education, while providing a platform that supports a variety of instructional strategies and learning styles. Odyssey Algebra has 13 chapters and 131 objectives to cover in an entire school year. The curriculum's online features include interactive tutorials that are woven throughout the program and aids such as online calculators, graph paper, number lines, protractors, spreadsheets and rulers. The program also provides additional offline materials for students that are designed to extend learning beyond the classroom |
Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number …
Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with …Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, …
Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. …
For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more …
Mathematics for the Environment shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. These tools can then be used to understand and effectively deal with economic, environmental, and …
What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean's method. How the US tried to use game theory to win the Cold War, and why it didn't work. When students realize that …
Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Third Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually … |
Description
This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in otherPlane and Solid Geometry (Universitext |
It always shocks me to see high school students struggling to solve simple arithmetic problems. I happened to casually glance at the algebra homework of a ninth grader one day and saw "3×7 =" written next to a graphing question. Evidently, he did not immediately know the answer and was probably looking for a calculator. I later learned that this student was almost failing the algebra course, but I also could not help but wonder how much trouble the actually failing students were having. It simply seemed inefficient to me that these students were trying tolearn high school math, which is best learned with a solid foundation of fundamental concepts,when they couldn't remember the math they were supposed to have mastered six years ago.
The United States is one of the world's most technologically advanced countries, yet our mathematics program, especially at the secondary level, lags behind those of other industrialized countries [1][2]. Without a solid math background from grade school, the majority of adults in the US lack basic number sense skills – according to a poll conducted by the Center for Economic and Entrepreneurial Literacy almost 80% of adults interviewed did not understand the magnitude of a trillion [3]. These people may not completely understand the true size of the US's national debt or deficit, since for them, the figures may just seem like any big number.
Given American students' poor performance in math compared to other countries, it is unsurprising to find that the US tried a series math reforms throughout the latter half of the 20th century. Until 1960's, the predominant way of teaching math, often known as the "traditional" approach, emphasized memorization of basic facts and standard algorithms at the elementary level, followed by an endless array of exercises to reinforce the information. The rote memorization mindset continued through high school, and even into college; it was not uncommon to see a college calculus class that mainly focused on integration formulas and differentiation rules rather than on the fundamental meaning and purpose of derivatives and integrals [4]. Textbooks presented few problems that went beyond substituting into given algorithms, and teachers rarely explained or even mentioned the reasons and principles behind these algorithms. Consequently, math often appeared as a random collection of formulas to students. Critics have called this traditional method "parrot math" to stress that while students
eventually could reproduce most of the basic skills they were taught, they lacked any in-depth understanding of what they were learning [5].
In the 1960's, a radical change in the curriculum occurred in the US as a response to the Sputnik crisis, which spawned the Space Race against the Soviet Union. There was a general fear that the "traditional" math curriculum was not adequate to produce engineers that were well- grounded in advanced math. The National Science Foundation thus proposed "new math", which required students to learn abstract math concepts as early as elementary school, often before mastering basic computational skills. Set theory and abstract algebra, which were typically topics studied by advanced math undergraduates, made appearances in elementary school textbooks. Educators justified these new curriculum additions by claiming that students would grasp abstract math more easily in higher education if they were exposed to it earlier, although they did not make any explicit provisions for students who did not intend to further study science or engineering after high school [6].
Unfortunately, it was extremely difficult for students to process the abstract concepts, especially since they had very little concrete math background to build upon. For example, without a clear understanding of basic addition facts, ideas such as the Commutative Property of Addition seemed strange and unnecessary to students. According to Piaget's theory from developmental psychology, children generally do not develop the ability to perform abstract reasoning until adolescence, so the "new math" essentially tried to teach concepts that most children were not cognitively ready to learn [7].
As in the traditional approach, students had weak math foundations because they did not completely understand the ideas of the "new math". However, the new approach was even less effective in the long-run because abstract mathematical concepts had no common applications in the real world, whereas traditional arithmetic operations were at least used in day-to-day tasks. Furthermore, the teachers themselves often did not completely grasp what they taught since they were generally not exposed to abstract mathematics in secondary school, so explaining the concepts to elementary school children was nearly impossible. Students often came out of elementary school having a vague idea about technical advanced math terminology but without the ability to compute basic multiplication facts. Ultimately, the experiment was a failure, and most schools almost immediately switched back to the traditional approach in the 1970's [6].
The traditional approach continued to be the method of choice in schools across the US for another twenty years, and before long, arguments about students' shallow understanding of math formulas again emerged. A new movement came into focus in the late 1980's when the National Council of Teachers of Mathematics (NCTM) introduced a different set of standards that emphasized mathematical inquiry over routine calculations. Memorization of algorithms was nearly eliminated, calculators were encouraged, and students were asked to "discover" their own methods of doing basic operations. This "constructivist" proposal gave rise to many new textbooks in the 1990's, and it became popular as several large school districts adopted these new curriculum reforms [8].
Unfortunately, students and teachers were shortly faced with a new problem. To make the curriculum seem more modern, many programs encouraged heavy calculator use and did not require students to memorize basic facts. However, without adequate practice in these essential
computational skills, students began to have trouble with even basic arithmetic, and were rarely able to do even slightly complicated problems without technology. Also, without a methodical way to add fractions, multiply two-digit numbers together, convert between percents and decimals, or carry out other similar operations, students usually ended elementary school mathematics unable to perform these essential operations. Visualizing two fractions being added, for example, was preferred over more algorithmic approaches but only works practically for simple cases; with a problem like 2/13 + 5/16, intuition quickly breaks down and one must use more general methods [9]. While calculators have made tedious arithmetic unnecessary, basic computations show up frequently in numerous subjects that students may pursue later on, and in any case, it would be highly inconvenient for people to rely on a calculator for calculations that could be quickly done mentally with adequate practice.
Furthermore, perhaps as an attempt to avoid traditional methods, books commonly used variants of the standard algorithms for operations such as multiplication, division, and fraction addition. Besides being usually longer and more time-consuming, these "new" algorithms also misunderstood the NCTM reform's main objective: the goal was to help students understand math by finding alternatives to the traditional approach, not to replace existing algorithms. Incorporating an antiquated, inefficient "lattice" system for multiplying instead of the standard algorithm, for example, neither sped up the computation nor helped the student understand multiplication [10].
With all these unsuccessful changes in math programs over the past 50 years, it is not surprising that American students are behind their international counterparts in mathematics. But we rarely think about why students from other countries can learn math more thoroughly. A
lengthy study done by Ginsberg and colleagues followed the math education system in Singapore, which uses a system that would be undoubtedly classified as "traditional", yet is consistently ranked at the top among other countries by several international tests [11]. An internationally recognized program, "Singapore Math", is based on the Singapore curriculum and has also found much success by the schools that have tried it [12]. By investigating the principles behind the Singapore math curriculum, the authors found numerous flaws in our own math education system that makes our methods weaker, even though they are based on the same "traditional" approach as those of Singapore's system [11].
The first problem in our math curriculum is its lack of specific and unified standards. Each state is free to make its own curricula, and the NCTM guidelines are vague at best; they define objectives for a range of grade levels, and therefore different states vary greatly in suggesting when basic concepts are introduced. The inconsistent structure hinders textbook companies' efforts of developing effective programs. It also becomes harder to determine the quality of new programs because the states have distinct assessment methods that influence the results of pilot- program studies. Singapore's curriculum, on the other hand, is easy to describe because it is nationalized and unified. It is therefore much easier to produce learning materials that work for all schools and to evaluate the effectiveness of the overall curriculum [11]. While a completely standardized system is less feasible in the US because of its large size and diversity, there should be more specific national standards that prevent states from producing greatly differing curricula.
The second issue with American math education lies with the textbooks' contents. Most basic math textbooks have exercises that require little thought from the student, such as one-step formula plug-ins. Students thus cannot readily apply the principles they learn to more
complicated multi-step problems because they are not usually exposed to anything beyond their textbooks' rather simple exercises [4]. Singapore's textbooks, on the other hand, have basic drills as well, but move on to more challenging problems that apply the newly-learned concepts. By thinking through more involved questions, students master the basic procedure while developing their problem solving skills [11].
A related problem is that American curricula try to cover too many concepts in a single year. Partially, this is the result of the textbook publishers' attempts to satisfy as many standards and teacher demands as possible, which ultimately stems from the lack of curriculum centralization. While Singapore's standards only require about 15 topics per grade level, some state curricula contain over 50 topics to be covered in a school year [12]. Chapters and lessons therefore tend to be shorter and less in-depth. Although exposure to a diverse range of topics can arguably be beneficial, such a wide array of topics prevents deep comprehension of any specific topic. Therefore there is no time to develop the problem solving skills needed to tackle more complicated problems [11]. Middle and high school curricula tend to be similar in terms of their lack of depth. For example, Lockhart describes precalculus as a "senseless bouillabaisse of disconnected topics", many of which are glossed over because they are not introduced in a meaningful context [4].
Another serious weakness is the lack of qualified teachers who teach grade school math. Singapore's teachers must be certified through stringent exams before they even enter an education program, where they are paid a salary that is comparable to that of actual teachers. In contrast, prospective US teachers have the lowest math SAT scores on average out of all college majors. It is difficult to expect that the very individuals who did not thoroughly master math in
school would be able to produce competent math students. Singapore teachers also undergo a rigorous professional development program in addition to extensive annual training in new skills. Meanwhile, US teachers only attend short workshops, despite the fact that these workshops are "widely admitted to be ineffective for changing practice", and teachers are not required to pass very stringent exams. In fact, the exam for certifying 6th grade teachers is easier than the exams given to Singapore sixth graders [11].
Tailoring the curriculum to students of different abilities, commonly called "tracking", is also important to ensure that all students master the material, not just the most able ones. A study showed that programs that offered more comprehensive tracking systems scored higher on math achievement tests, even after adjusting for student backgrounds [13]. Singapore addresses this problem by providing a complete alternative program for struggling students that focuses more on repetition and is taught by well-qualified teachers. By contrast, while the US provides resources for less able students, most special programs for slower math students in the US follow no real framework; students who fall behind are generally put into unofficial "extra-help" classes that are taught by aides who often have not earned a college degree. If all citizens are to have good basic math skills, then the needs of all students must be addressed and equal attention should be given to those who require more time or a different approach to grasp the material [11].
The solution to the problematic American curriculum is not as simple as just converting to the Singaporean model. Students that have already used American textbooks for a long time may not have all the skills necessary to progress to the next level in the Singapore curriculum, since the order and depth of topics are likely to differ. Also, since each level of the Singapore
curriculum assumes knowledge of concepts taught in previous levels, any conceptual holes in American students' knowledge would prevent thorough understanding of the new topics introduced [11]. Finally, a sudden transition to more complicated and problem-solving based questions could initially be extremely difficult to students who are more accustomed to the American textbook exercises. A gradual change would be more appropriate, but then choosing the ideal resources to facilitate this change becomes a difficult task.
Newly implementing the program for first-grade students is not much more straightforward. Although students may yet not be accustomed to the "American way" like older students are, there are still other differences that prevent a smooth transition. As similar as the resources may be, the quality teachers will still differ between the two countries. The Singapore program presumes training in important methods used throughout the program, which in turn presumes a level of mathematical competence that may be higher than that of many US teachers. A lengthy professional program to train teachers in the US is conceivable but would be extremely expensive and require a large commitment that teachers' unions may resist [11]. Furthermore, the amount of time spent on math and science in school is vastly different between the two countries. Not only is the average school day in Asian countries longer, but also the proportion of time spent on math in school is also much greater in Asian schools. Unless more drastic reforms like lengthening the school day are considered, schools that plan to adopt a Singaporean math program must find ways to accommodate the greater required time commitment without significantly affecting the normal structure of the school day [14].
American schools may not be able to effectively adopt a close duplicate of the Singapore program, but they can certainly implement elements that make the Singapore curriculum
successful. Greater unification of standards across states would allow national textbook companies to provide more focus in their textbooks, as well as make reforms much simpler to carry out and assess. A more comprehensive track can be produced for students with greater trouble, and ideally, such classes are taught by qualified teachers. While the abilities of American teachers will not suddenly change, more substantial professional development programs rather than short, occasional workshops can improve how well they teach the new material. Furthermore, standards for future teachers should increase to ensure that the new generation of teachers are mathematically confident themselves before they try to present their knowledge of math to their students. While we do not need a population of scientists and mathematicians, all people should be able to know enough mathematics to understand how numbers are used in everyday life, such as for basic tax accounting or recipes. With these reforms in mind, we can envision a society in which statistics mean more to everyone than just vague numbers to spice up an article. Perhaps then, young students will master their multiplication tables sooner, so that rather than being stuck on basic facts, they can begin to build the critical thinking skills necessary to become mathematically literate citizens.
Discussion
4 comments for "Multiplication Tables? Dismal State of U.S. Mathematics Education"
Sidney Rosenbloom
The problem is cultural. Yes, cultural.
Over the past 30 or so years I have been following calls for educational (K-12) reform, math and science educational reform, saw oh so many task forces, blue ribbon commissions, expensive consultant-produced studies, thousands comments of hopeful or confused and off-target members of the public, all the way from Adm. Rickover commission to Bush's No Child Left behind etc.
This country, i.e. the middle class and its hopes for maintaining standard of living or at least preventing its further erosion, needs to have its education-industrial complex, it (in essence non-existing, globally really competitive) workforce training, some of its corporate priorities, globally proven governmental economic policies and somehow revised social contract aligned toward EXPORT-oriented business and societal mindset.
Along these lines we (again, the middle class hopes for reasonable standard of living) also radically change our value system and instead having so many students majoring in business, marketing, communication, creative writing, etc. etc. down to law believe in, appreciate, build export based job and career future for graduates of engineering, math, hard science fields.
Is this going to happen?
Unfortunately not, as cultural habits and preferences we share and keep so dear, along with our model of individualistic-at-any cost of capitalism (compared to say a continental/German/Scandinavian/Japanese version of capitalism) are – along with legislative bodies being bought by the top 1% will prevent any REAL, bona fide chance of such fundamental reform.
Obama's daughters will not also study engineering or science but might do law or something "soft" as the middle class will not start sending their kids to study science, math, engineering.
Popular culture (TV etc.) will continue to glamorize physicians, sleek lawyers, financiers, not "nerds" in IT, engineering, or science.
Neither party has any plan along these lines as well. One shouts about even less in taxes the other one demands traditional benefits of giving out fish instead teaching how to catch or farm one.
Our pride, inertia, ideology will continue to prevent us from adopting system such as in Germany, demonstrating, year after year, that yes, it is i possible to "spoil" workers with high wages, give them 6 weeks of annual paid vacation, universal health care, strong labor and environmental regulations, even strong euro (yes) and have the economy make so many HIGH-VALUE-added TANGIBLE products that the rest of the world is willing to buy to have export surpluses so large that only in 2009 another export-oriented giant, 15-times larger Peoples Republic of China took over as #1 exporter.
To close: math education at K-12 levels is outrage as I know, as MS in engineering, parent of six children (with top SAT scores and successful professional careers) and someone who have kept my hopes that it will get better. Sorry to say, also feminization of our K-12 system doesn't help either while it seems to "help" obsessive emphasis on writing, creative/persuasive writing as we have been increasingly trying to sell each other services with increasingly "sophisticated" spiel, while export-oriented countries flood our market with their tangible products.
As our huge post-WW2 free ride via monopoly on printing (increasingly worthless) reserve currency will gradually come to end, chicken will come to roost in earnest. As a billionaire Sam Zell estimates, American standard of living will then drop another 25 – 30%.
Again: I do not see any force changing this cultural predisposition. We even refuse, at Reagan's "advice" to adopt the metric system to start with.
jumper
First, thanks for the history lesson above in this article! But did you ever stop to think as we are getting closer to how the brain really works and the technology of brain scans we can do are showing the different areas of how and what the brain can do and can not do. So, my question for all of you who think it is because, " Oh they need to try harder" and "they are just lazy" or " they just do not have the right tutor" How sadly wrong you are and how many students fall through the cracks of the educational system that makes students fit a certain system that needed up grading years ago!
Secondly, it is simple logical answer, students may have a severe math disorder that will not allow them to go as far as their school program requires them too. What I mean by math disorder it is one that neurologically can not be helped by a tutor or taking a pill either! So, you say that student shouldn't go into that program! I know a student who is in a PhD program but yet can only do 9th grade level math! This student is exceptional in all areas of the program but the math. The math isn't really needed in the program since in the "real world" they use computers to compute the math problems.
Thirdly, all of those who have gone through the educational system of the universities and jumped through their hoops will good for you and I mean it! You are the few lucky ones that can actually do it. But that is ONLY because your genetic make-up doesn't have any faulty neurological problems that will interfere with your educational endeavors. However, I bet those that have been through the educational system may have Diabetes, Cancer, Arthritis later in their late years of life and other elements that we can all see. I needed to bring this up in my post here is these individuals who have passed their educational programs feel they are "privileged" and that everyone else should go through the same thing they went through especially attorneys when they have to take the seditious bar exam as one example. These same individuals really have a problem with others who can not do what they just accomplished. All I can say to those who do not and have not had to deal with neurological set backs in the educational system you are very fortunate and very lucky too I might add! You are not any more special than the rest of us and all of us humans have some sort of element that we have to deal with in our life we are ALL fallibly creatures!
And lastly, here is a list of famous people who were/are very successful without math! They all had something in common too they had some kind of math/educational disability. Here is the list: Nelson Rockefeller, Thomas Edison, Walt Disney, George Washington, Leonardo da Vinci. Of course this list can go on and on but yet it has been talked about over and over the gifted really do not fit the molds these universities so make it to be the only way to succeed. I'm not surprised that Yale University originally wrote this article they are one of many universities that perpetuate this way of thinking. May the creative and the intelligence people rise above oppression ..like the late Steve Jobs!
Education advocate
Your point is well taken. However, many children's struggle in math is the result of poor instruction and not neurological problem and if teachers cannot effectively teach math because of inadequate training and programming to children without neurological challenges that is a problem that needs to be addressed, don't you agree?
Jessica Ramer
Understanding mathematics requires both abstract reasoning and a solid knowledge base–which is developed largely through memorization.
As I have struggled to help kids learn, I am struck by *how many* kids seem unable to memorize multiplication facts–even after repeated coaching and drills. I have tried having the kids write out the tables, quizzing them orally, having them listen to CDS and even after months of work, they still fail. It is not a lack of effort on their part or mine, it is something else. Keep in mind that these kids do not have diagnosed learning disabilities, are not struggling to learn in a second language, and are not from America's most impoverished regions.
I can't shake the gut feeling that something is seriously wrong with many of America's children, although I don't have a clue what it is. Bad diet? Too much electronic entertainment that has destroyed their ability to focus? Has cell phone radiation impaired their memory? (Don't laugh. It seems to impair learning in lab rats.)
Maybe I was clueless as a kid, but it seems to me that 40 years ago, nearly all kids knew their multiplication tables by the end of third grade. Of course, teachers reviewed it every year to be sure, but most of us knew.
I would appreciate comments from other teachers on this phenomenon. |
This course introduces some basic notions of Algebra, and provides examples of how these methods apply to real-life problems. We examine linear equations and their graphs, systems of linear equations and linear inequalities in two variables, with application to linear programming. Next, we introduce matrices and their inverses, with applications to cryptography. Finally, we study some basic set theory, techniques of counting, permutations, and combinations, with applications to elementary probability.
Attendance
It is essential that you attend class regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. Students are responsible for finding out what material has been covered or what announcements have been made on days that they miss class.
Additional Contacts
If you have concerns/problems in the course, and are not comfortable discussing them with your instructor, please contact either of the following: |
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.
With an emphasis always on clarity and practical applications, this edition continues to provide real-world, technical applications that promote intuitive student learning. It includes all the mathematical topics needed by students in vo-tech programs. Computer projects are given when appropriate, and the graphing calculator fully integrated and calculator screens are given to introduce computations. |
UNIT 1 : SETS, RELATIONS AND FUNCTIONS : Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one – one, into and onto functions, composition of functions.
UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS : Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions.
Relation between roots and co – efficients, nature of roots, formation of quadratic equations with given roots.
UNIT 3 : MATRICES AND DETERMINANTS :UNIT 10: Differential Equations : Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations
UNIT 11 : CO – ORDINATE GEOMETRY : Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Straight lines : : : THREE DIMENSIONAL GEOMETRY : : VECTOR ALGEBRA : Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.
UNIT 12 : GENERAL PRINCIPLES AND PROCESSES OF ISOLATION OF METALS : Modes of occurrence of elements in nature, minerals, ores; steps involved in the extraction of metals – concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.
UNIT 13 : HYDROGEN :UNIT 14 : S – BLOCK ELEMENTS (ALKALI AND ALKALINE EARTH METALS) : Group – 1 and 2 Elements General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.
UNIT 3 : LAWS OF MOTION :UNIT 4 : WORK, ENERGY AND POWER : Work done by a constant force and a variable force; kinetic and potential energies, work – energy theorem, power. Potential energy of a spring, conservation of mechanical energy, conservative and non – conservative forces; Elastic and inelastic collisions in one and two dimensions.
UNIT 5 : ROTATIONAL MOTION : Centre of mass of a two – particle 8 : THERMODYNAMICS : Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics : reversible and irreversible processes. Carnot engine and its efficiency.
UNIT 9 : KINETIC THEORY OF GASES : Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases – assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applicationsUNIT 11 : ELECTROSTATICS : Electric Charges : Conservation of charge, Coulomb's law – forces di electric medium between the plates, Energy stored in a capacitor.
Three dimensional – perception : Understanding and appreciation of scale and proportion of objects, building forms and elements, colour texture, harmony and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil.
Transformation of forms both 2 D and 3 D union, substraction, rotation, development of surfaces and volumes, Generation of Plan, elevations and 3 D views of objects. Creating two dimensional and three dimensional compositions using given shapes and forms part in any form or medium without express written permission of EDUWEB SOLUTION AND SYSTEMS prohibited,
WARNING:Copying information from This website without permission of EDUWEB SOLUTION AND SYSTEMS is Illegal. |
Pre-Algebra
March 3, 2012
This course is designed to help students who have previously
shown a weakness in the fundamentals of mathematics as well as to
give all students a solid foundation in the fundamental concepts
of Algebra. Pre-Algebra is very helpful to incoming freshmen by
giving them a head start in their first year of high school
mathematics. |
This collection is included inLens:Community College Open Textbook Collaborative By: CC Open Textbook Collaborative Algebra: VectorsFor our purposes, a vector is a collection of real numbers in a one-
dimensional array.1 We usually think of the array as being arranged in a
column and write
x=x1x2x3|xnx=x1x2x3|xn .
Notice that we indicate a vector with boldface and the constituent elements
with subscripts. A real number by itself is called a scalar, in distinction from
a vector or a matrix. We say that xx is an n-vector, meaning that xx has nn
elements. To indicate that x1x1 is a real number, we write
x1∈R,x1∈R,
(1)
meaning that x1x1 is contained in RR, the set of real numbers. To indicate that
xx is a vector of nn real numbers, we write
x∈Rn,x∈Rn,
(2)
meaning that xx is contained in RnRn, the set of real n-tuples. Geometrically,
RnRnis n-dimensional space, and the notation x∈Rnx∈Rn means that xx is a
point in that space, specified by the nn coordinates x1,x2,...,xnx1,x2,...,xn. Figure 1
shows a vector in R3R3, drawn as an arrow from the origin to the point xx.
Our geometric intuition begins to fail above three dimensions, but the linear
algebra is completely general.
Figure 1: A Vector in R3
We sometimes find it useful to sketch vectors with more than three
dimensions in the same way as the three-dimensional vector of Figure 1. We
then consider each axis to represent more than one dimension, a hyperplane, in
our n-dimensional space. We cannot show all the details of what is happening
in n-space on a three-dimensional figure, but we can often show important
features and gain geometrical insight.
Vector Addition. Vectors with the same number of elements can be
added and subtracted in a very natural way:
Example 1
The difference between the vector x=111x=111 and the
vector y=001y=001 is the vector z=x-y=110z=x-y=110. These vectors are illustrated in Figure 2. You can see that this result is consistent with the definition of
vector subtraction in Equation 3. You can also picture the subtraction in
Figure 2 by mentally reversing the direction of vector yy to get -y-y and then
adding it to xx by sliding it to the position where its tail coincides with the
head of vector xx. (The head is the end with the arrow.) When you slide a
vector to a new position for adding to another vector, you must not change
its length or direction.
Figure 2: Subtraction of Vectors
Exercise 1
Compute and plot x+yx+y and x-yx-y for each of the following
cases:
x=132,y=123x=132,y=123 ;
x=-13-2,y=123x=-13-2,y=123 ;
x=1-32,y=132x=1-32,y=132.
Scalar Product. Several different kinds of vector multiplication are
defined.2 We begin with the scalar product. Scalar multiplication is defined
for scalar aa and vector xx as
ax=ax1ax2ax3|axn.ax=ax1ax2ax3|axn.
(4)
If |a|<1|a|<1, then the vector axax is "shorter" than the vector x; if |a|>1|a|>1, then the
vector axax is '"longer" than x. This is illustrated for a 2-vector in Figure 3.
Figure 3: The Scalar Product axax
Exercise 2
Compute and plot the scalar product axax when x=11/2l/4x=11/2l/4 for
each of the following scalars:
a=1;a=1;
a=-1;a=-1;
a=-1/4;a=-1/4;
a=2.a=2.
Exercise 3
Given vectors x,y,z∈Rnx,y,z∈Rn and the scalar a∈Ra∈R, prove the
following identities:
Footnotes
In a formal development of linear algebra, the abstract concept of a
vector space plays a fundamental role. We will leave such concepts to a
complete course in linear algebra and introduce only the functional techniques
necessary to solve the problems at hand.
The division of two vectors is undefined, although three different "divisions" are defined |
Study Guides
Introduction to Matrix Arithmetic
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Introduction to Parabolas
A conic section is a shape obtained when a cone is sliced. The study of conic sections began over two thousand years ago and we use their properties today. Planets in our solar system move around the sun in elliptical orbits. The ...
Introduction to Conversion from Degrees to Radians
Trigonometry has been used for over two thousand years to solve many real-world problems, among them surveying, navigating, and problems in engineering. Another important use is analytic—the trigonometric ...
Introduction to Sequences and Series Formulas
A sequence is an ordered list of numbers. Although they list the same numbers, the sequence 1, 2, 3, 4, 5, 6, ... is different from the sequence 2, 1, 4, 3, 6, 5, .... Usually a sequence is ...
Introduction to Number Systems
Calculus is one of the most important parts of mathematics. It is fundamental to all of modern science. How could one part of mathematics be of such central importance? It is because calculus gives us the tools to study rates of ...
Introduction to Coordinates in One Dimension
We envision the real numbers as laid out on a line, and we locate real numbers from left to right on this line. If a < b are real numbers then a will lie to the left of b on this line. See ... |
MATH 329: Rings & Fields
This is one of two courses introducing algebraic structures and techniques fundamental to mathematics and useful in many areas of science and engineering. Topics include: rings, subrings, ideals, fields, integral domains, polynomial rings, extension fields, finite fields, famous impossible constructions and Galois theory.
Credits:3
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MathTV will help you study and improve your math skills via user-friendly videos that take you step by step until the solution is revealed and explained. Among the different topics available are exercises in basic mathematics, algebra (linear equations, factoring, rational expressions, logarithms, and more), trigonometry (complex numbers and polar coordinates, graphing, and inverse functions) and finally calculus (integration, derivatives, and the applications of both). |
Introduction of the GMAT, the CAT methodology, GMAT strategic preparation plan, and use of the GMATWorkshop mistake log, GMAT Math I – GMATWorkshop Data sufficiency best practice; timing/pacing best practice and guessing strategies for time-pressure situations. Number properties; divisibility rules. GMATWorkshop Data sufficiency best practice.
Session 2:
Roots and powers, percentage and fractions, etc. All building-block concepts such as odds and evens, prime number, fractions, factorials and functions discussed with most representative examples.
Session 3:
Concepts and examples about Ratio, proportion and variation, statistics, mixture and alligations, speed, time and distance, races, etc.
Session 4:
An overview of critical concepts including necessary conditions, sufficient conditions and others. Different types of arguments and major/minor types of CR questions are discussed, such as typical methods to strengthen, weaken an argument, or find out the assumptions. Common logical fallacies and CR strategies are explained so that you can apply them in the Critical reasoning section and the analytical writing part. |
Math 1C
Text: JAMES STEWART: Calculus Early Transcendentals SIXTH edition (Note that we are NOT using 7th edition)
Graphing calculator required: TI- 83+, 84+ are the recommended models.
I will generally be demonstrating with a TI-83 or 84 in class.
TI-89 or any other calculator that can do symbolic mathematics, has a computer
algebra systems or can graph in 3D will NOT be allowed on any exams or quizzes in this class.
If you have a TI-89 or similar calculator, it will be wonderful for homework and learning but
out of fairness to all students, you can not use it for exams or quizzes.
TI-83, 84, 86 calculators are available on loan from the library for several hours or several
days at a time. There is a limited supply.
This course will use a website in CATALYST at
Catalyst is De Anza College's course management system.
Enrolled students will be able to log in to the course website as of the beginning of spring quarter:
For graphing on a TI-83 or TI-89
The TI-83 and TI-89 support a sequence graphing mode that is not available on the TI-86.
You can use the sequence graphing mode to graph a sequence or partial sums of a series.
You can also adapt the methods posted above for the TI-86; the TI-83 and TI-89 have all
the same functionalities of the TI-86 that is used in those two sets of instructions.
Your keystrokes will be different in order to find those settings or functions;
if you can't locate a function or setting, look in the Catalog.
Note that the TI-83 and TI-89 do not support custom menus that can be set up in the TI-86.
Optional:
Proof by contradiction that e is irrational This is an indirect proof that relies on the series expansion of e.
If you have taken Math 22 (Discrete Math), you have proved that the square root of 2 is irrational,
using a proof by contradiction. You now have the tools to prove that e is irrational. |
Algebra And Trigonometry - 01 edition
ISBN13:978-0534434120 ISBN10: 0534434126 This edition has also been released as: ISBN13: 978-0534380298 ISBN10: 0534380298
Summary: James Stewart, the author of the worldwide best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. Algebra and Trigonometry was designed specifically to help readers learn to think mathematically an...show mored to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, College Algebra, Third Edition, and Precalculus, Third EditionGoodwill Savannah Savannah, GA
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Calculus
Calculus is a branch of mathematics that expands upon the principles used in algebra and geometry to include the idea of limits. There are two main sub-categories of calculus—differential calculus and integral calculus. Each has a different focus.
Integral calculus deals with the idea of accumulation, while differential calculus examines the rate of change. Common calculus terminology includes words such as integrals, functions and derivatives.
The following academic lectures are designed to give you insight into this branch of mathematics and help you understand the concepts involved in calculus. |
Description
In more and more schools, students are now being assessed not only on traditional (algorithmic and computational) math skills, but also on how-and how well-they handle reasoning and problem solving. However, until now, these additional skills have been difficult to assess in an objective, accurate... Expand and efficient way. But not any more. "Comprehensive assessment" includes the traditional paper-and-pencil tests plus relatively new ways (e.g., portfolios, journals, observations, interviews, projects, performance tasks, rubrics) to assess what students know about math, and how they reason, solve problems and communicate about it, This unique new handbook provides everything you need-background information, problems for various grade levels, detailed answers, forms, teaching suggestions-to assess students throughout the semester or at any time...easily, accurately and effectively!
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Measure and Integration. A Concise Introduction to Real Analysis
John Wiley and Sons Ltd, July 2009, Pages: 238
A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis
Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis.
The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes:
Measure spaces, outer measures, and extension theorems
- Lebesgue measure on the line and in Euclidean space
- Measurable functions, Egoroff's theorem, and Lusin's theorem
- Convergence theorems for integrals
- Product measures and Fubini's theorem
- Differentiation theorems for functions of real variables
- Decomposition theorems for signed measures
- Absolute continuity and the Radon-Nikodym theorem
- Lp spaces, continuous-function spaces, and duality theorems
- Translation-invariant subspaces of L2 and applications
The book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign.
Providing an efficient and readable treatment of this classical subject, Measure and Integration: A Concise Introduction to Real Analysis is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.
Preface.
Acknowledgments.
Introduction.
1 History of the Subject.
1.1 History of the Idea.
1.2 Deficiencies of the Riemann Integral.
1.3 Motivation for the Lebesgue Integral.
2 Fields, Borel Fields and Measures.
2.1 Fields, Monotone Classes, and Borel Fields.
2.2 Additive Measures.
2.3 Carathéodory Outer Measure.
2.4 E. Hopf's Extension Theorem.
3 Lebesgue Measure.
3.1 The Finite Interval [-N,N).
3.2 Measurable Sets, Borel Sets, and the Real Line.
3.3 Measure Spaces and Completions.
3.4 Semimetric Space of Measurable Sets.
3.5 Lebesgue Measure in Rn.
3.6 Jordan Measure in Rn.
4 Measurable Functions.
4.1 Measurable Functions.
4.2 Limits of Measurable Functions.
4.3 Simple Functions and Egoroff's Theorem.
4.4 Lusin's Theorem.
5 The Integral.
5.1 Special Simple Functions.
5.2 Extending the Domain of the Integral.
5.3 Lebesgue Dominated Convergence Theorem.
5.4 Monotone Convergence and Fatou's Theorem.
5.5 Completeness of L1 and the Pointwise Convergence Lemma.
5.6 Complex Valued Functions.
6 Product Measures and Fubini's Theorem.
6.1 Product Measures.
6.2 Fubini's Theorem.
6.3 Comparison of Lebesgue and Riemann Integrals.
7 Functions of a Real Variable.
7.1 Functions of Bounded Variation.
7.2 A Fundamental Theorem for the Lebesgue Integral.
7.3 Lebesgue's Theorem and Vitali's Covering Theorem.
7.4 Absolutely Continuous and Singular Functions.
8 General Countably Additive Set Functions.
8.1 Hahn Decomposition Theorem.
8.2 Radon-Nikodym Theorem.
8.3 Lebesgue Decomposition Theorem.
9. Examples of Dual Spaces from Measure Theory.
9.1 The Banach Space Lp.
9.2 The Dual of a Banach Space.
9.3 The Dual Space of Lp.
9.4 Hilbert Space, Its Dual, and L2.
9.5 Riesz-Markov-Saks-Kakutani Theorem.
10 Translation Invariance in Real Analysis.
10.1 An Orthonormal Basis for L2(T).
10.2 Closed Invariant Subspaces of L2(T).
10.3 Schwartz Functions: Fourier Transform and Inversion.
10.4 Closed, Invariant Subspaces of L2(R).
10.5 Irreducibility of L2(R) Under Translations and Rotations.
Appendix A: The Banach-Tarski Theorem.
A.1 The Limits to Countable Additivity.
References.
Index.
"The book is well thought out, organized and written. It has all the results in measure theory that are necessary for both pure and applied mathematics research." (Mathematical Reviews, 2011) |
Make algebra more approachable for struggling students with these practice problems, definitions, clear examples, tips, and references! Instructions designed to simplify difficult concepts cover number systems, exponential expressions, square roots and radical expressions, graphing, as well as linear and quadratic functions. An assessment section with answer keys allows students to see how much they have learned. |
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