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Companion Encyclopedia of the History and Philosophy if the Mathematical Sciences, Vol. 2 (Vol 2) (Routledge reference)
Companion Encyclopedia of the History and Philosophy if the Mathematical Sciences, Vol. 2 (Vol 2) (Routledge reference) GRATTAN - GUINNESS I is available to download at BookMoving Mathematics is one of the most basic and most ancient types of knowledge.This eBook is available to download at bookmoving.com and it has been shared by user as GRATTAN - GUINNESS I's eBooks, Yet the details of its historical development remain obscure to all but a few specialists.Companion Encyclopedia of the ... Textbook The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century.
In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics.
Contents of Volume 1: -Ancient and Non-Western Traditions -The Western Middle Ages and the Renaissance -Calculus and Mathematical Analysis -Functions, Series, and Methods in Analysis -Logic, Set Theories, and the Foundations of Mathematics -Algebras and Number Theory
Contents of Volume 2: -Geometries and Topology -Mechanics and Mechanical Engineering -Physics, Mathematical Physics, and Electrical Engineering -Probability, Statistics, and the Social Sciences -Higher Education andInstitutions -Mathematics and Culture -Select Bibliography, Chronology, Biographical Notes, and Index
Companion Encyclopedia of the History and Philosophy if the Mathematical Sciences, Vol. 2 (Vol 2) (Routledge reference)
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The Nature of Mathematics and the Mathematics of Nature
Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences. Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity. Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in ...
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, ...
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Successful application of mathematical principles to solve a range of challenging problems. Clear integration of knowledge, understanding and skills from different areas. Comprehensive responses containing all necessary detail.
B
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Successful application of mathematical principles to solve a variety of problems. Some integration of knowledge, understanding and skills from different areas. Some responses lacked necessary detail or contained minor errors.
C
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory application of mathematical principles to solve some problems. Satisfactory integration of knowledge, understanding and skills from different areas, when given some direction.
D
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Limited application of mathematical principles to solve problems.
E
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Limited application of mathematical principles to solve even the most basic problems.
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Monthly Archives: January 2011
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John Page describes his 'Math Open Reference' project as a free interactive textbook on the web, initially covering Geometry.
The tools include various function explorers. Younger students could explore linear functions for example, whilst older students could use the general Graphical Function Explorer to explore any functions, trigonometric for example.
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This course teaches students
The CPLEX mathematical programming engine delivers the power to solve large-scale, real-world optimization problems, the reliability necessary for mission-critical decision making, and the speed required in today's interactive applications. It also comes with fast and,reliable implementations of the fundamental algorithms used for solving demanding mathematical optimization problems.
The course is split between core and optional units that allow for a more customized classroom experience by letting students request additional material on areas of specific relevance to their work. A combination of instructor-led presentations and lab exercises enables students to learn the concepts, architecture, components, processes, and procedures necessary to model and solve a variety of problem types using CPLEX. This course begins with an overview of linear programming (LP), and subsequent units teach students how to create and solve LP models using ILOG Concert Technology. Students also learn about mixed-integer programming (MIP), quadratic programming (QP), and debugging. The optional units that are available for students cover topics such as CPLEX performance tuning, working with LP callbacks, preprocessing, columnwise modeling, and parallel CPLEX.
Hinweise
The unit and exercise durations listed below are estimates, and may not reflect every class experience. If the course is customized or abbreviated, the duration of unchanged units will probably increase.
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Technical Calculus with Analytic Geometry - 4th edition
Summary: This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus a...show morere introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs. ...show less
The Cartesian Coordinate System. The Slope. The Straight Line. Curve Sketching. Discussion of Curves with Graphing Utilities. The Conics. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes; Standard Equations of the Conics. Review Exercises.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition. Basic Integration Formulas. Area Between Curves. Improper Integrals. The Constant of Integration. Numerical Integration. Review Exercises.
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gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a course. To that end, a lot of examples and supporting exercises are inserted throughout the text, which will help students to become acquainted with the subject. less
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I'm in year12 and I'll be finishing further maths a-level this June. I hope to do maths at uni and I want to learn something new from next September. So I was wondering if it's possible to self teach some 1st year university maths?
I don't know how to go on about it; where should I start? Which branch of mathematics do people learn first when they go to uni?
Could you recommend me some introductory textbooks?
Please don't recommend doing BMO/STEP instead. 1 year is a long time and I want to start learning something new. (I'll probably do some BMO problems anyway for fun! )
textbooks, I would reccomend Excursions into Mathematics, which studies topics that you probably won't encounter at university in depth and from the ground up, and in a rigorous style. However, it is quite expensive. If you want textbooks specific to the main areas of Maths, you can look on which usually has a lot of cheap textbooks on it. Search Amazon for the reputable textbooks, and then search for the cheap versions on this website. Older textbooks tend to be cheaper, so look for classic textbooks.
(Original post by Bobifier)I have always found to be very helpful. They cover at least as far as my second year analysis stuff (I know this because my searches are still occasionally redirected to them) and I have always found them to be helpful when I have ended up at them. I think they mostly cover Analysis, but he has other topics there as well. Look at the 'class notes' section at the top. A warning: they claim that using the notes is not a substitute for attending lectures. As you progress to university you will find that most published lecture notes claim this, but it is all lies
(Original post by nuodai)This, definitely.
I'd start with Spivak and Beardon. Spivak basically covers the material in a first year Analysis course - broadly speaking, it aims to put calculus on a firm, rigorous footing. If I remember correctly (I left my copy at home...) it starts off with formalising the ideas of limits and infinite sequences/series before (after some work) defining differentiation, proving various results like the product/chain rules and moving on to integration, getting to the Fundamental Theorem of Calculus and beyond.
Beardon is an introduction to linear algebra and groups - it's a very good foundation book. It covers groups, particularly permutations, as well as group actions, applications to symmetry of regular solids and Möbius transformations. The other major topic area is vector spaces and linear transformations (matrix algebra, eigenvalues and eigenvectors, etc)
Amongst some of the results proved are:
- The fundamental theorem of algebra
- The Cayley-Hamilton theorem (relating polynomial operations of linear transformations)
- Lagrange's theorem (the first fundamental theorem in group theory)
all of which (and much more) you'll cover in a first-year uni course.
They're definitely worth forking out a bit for rather than trying to use university lecture notes, which whilst often good at covering the pure definitions/theorems, are rarely good at actually explaining what's going on.
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Picture yourself doing your homework. Sitting. Staring at the equation. Outwardly silent, but inwardly screaming, "Why?! Why doesn't this make any sense? I studied! What is the problem? Am I just dumb or something?" combines learning the math and doing the homework. After you plug in your equation, it will go through it step by step with you. Your homework gets done and you learn how to work the math problems at the same time errors prentice hall math software
I'm not understanding errors prentice hall math software and I'm falling way behind in class. Is there anyway to get help at home using my computer? I have a computer in my room and I know how to use it
Yes, there is help with errors prentice hall math software
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Discrete Mathematical Structures - 6th edition
Summary: Key Message: Discrete Mathematical Structures Sixth Edition offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers and assumes a college algebra course as the only prerequisite. Key Topics: Fu...show morendamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics
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Reform Elements:
Emphasis on
mathematical concepts through the extensive use of conceptual exercises
and pedagogical techniques such as the Rule of Four (numerical,
geometric, algebraic, and communication-oriented approaches to
concepts).
Through our Internet site, we now add a Fifth element:
interactive discourse. The student can now go on-line and take a
quiz, interact with on-line tutorials, play a zero-sum game with the computer, or watch a visual simulation of a Markov process or a limit. The possibilities are
endless, and the site continues to grow and evolve.
Traditional Elements:
Inclusion of almost all the topics found in more traditional texts.
While the books are technology-oriented, the organization of the matertial has been planned to ensure that students equipped with
nothing more than a scientific calculator will not find themselves at a
significant disadvantage.
The texts are carefully structured and tightly organized for easy navigation and reference, and we have taken pains to be mathematically precise in all our definitions and statements of results.
Abundance of practice and drill exercises
Large numbers of application exercises to choose from
Options in Technology
The use of graphing calculators and computer software has been thoroughly integrated throughout the discussion, examples, and exercise sets, beginning with the first example of the graph of an equation in Chapter 1.
Flexibility in Choice of Technology We incorporate, in parallel, all of the following technologies: graphing calculator (based on the TI-83), computer spreadhseet (based on Excel), and on-line utilities offered at this web site. As a result, the text can be used in a classroom devoted to a single technology mode (for instance, graphing calculators only) or in a setting where instructors and students can choose different technologies for different topics.
Influence of Technology on Material
The focus on technology plays an important conceptual and pedagogical role in our presentation of many topics. For example, our discussion of the operations of arithmetic in Appendix A includes a careful discussion of formula syntax for technology. Our discussion of mathematics of finance includes descriptions of using technology to solve problems normally requiring techniques not norally covered in finite mathematics courses. Our treatment of curve sketching was written with the graphing calculator in mind, and we have used an approach that is well-suited to the increasingly popular approach of using graphing calculators to draw the graphs and then using calculus to explain the results. Some of the real power of technology is seen in the chapter on applications of the integral, where we guide the student in the use of technology to analyze mathematical models based on real data, make projections, and calculate and graph moving averages.
Exercise Sets
We regard the strength of our exercise sets as one of the best features of the First Edition. Our comprehensive collection of exercises provides a wealth of material that can be used to challenge students at almost every level of preparation, and includes everything from straightforward drill exercises to interesting and rather challenging applications. We have therefore included, in virtually every section of every chapter:
Applications Based on Real Data A most striking distinguishing feature of these texts is the diversity, breadth and sheer abundance of examples and exercises based on real, referenced data from business, economics, the life sciences and the social sciences.. This focus on real data has contributed to the creation of a book that students in diverse fields can relate to, and that instructors can use to demonstrate the importance and relevance of calculus in the real world.
Communication and Reasoning Exercises These are exercises designed to broaden the student's grasp of the mathematical concepts, and include exercises in which the student is asked to provide his or her own examples to illustrate a point, design an application with a given solution, "fill in the blank" type exercises, and exercises that invite discussion and debate. These are often exercises with no single correct answer.
Technology Exercises Our technology exercises have been designed for all three types of technology discussed in the books: graphing calculator, Excel, and web site technology tools, often in relation to real, referenced data where by-hand computation would be difficyult.
Revisited Themes Many of the scenarios used in application examples and exercises will be revisited several times throughout the book. Thus, for instance, students will find themselves using a variety of techniques, from graphing through the use of derivatives to elasticity of demand, to maximize revenue in the same application.
Up-To-Date Pedagogy
We would like students to read this book. We would like students to enjoy reading this book. Thus, we have written the book in a conversational and student-oriented style to encourage the development of the student's mathematical curiosity and intuition. Some unique features of our pedagogy include:
Question-and-Answer Dialogue We frequently use informal question-and-answer dialogues that anticipate the kind of questions that may occur to the student and also guide the student through the development of new concepts.
Quick Examples Most definition boxes include one or more straightforward examples that a student can use to solidify each new concept as soon as it is encountered.
Guideline Boxes (New to this edition) These are collections of "frequently asked questions" and answers at the end of many sections whose purpose it is to answer common student questions and reinforce new concepts (Click on picture opposite to see a sample.)
Before We Go On Most examples are followed by supplementary interpretive discussions under the heading "Before we go on." These discussions may include a check on the answer, a discussion of the feasibility and significance of a solution, or an in-depth look at what the solution means.
Communication and Reasoning Exercises These are exercises designed to broaden the student's grasp of the mathematical concepts. They include exercises in which the student is asked to provide his or her own examples to illustrate a point or design an application with a given solution. They also include "fill in the blank" type exercises and exercises that invite discussion and debate. These exercises often have no single correct answer.
Combining the Text and Website
Our powerful student website can be used in several ways:
As a Computer Classroom Instruction Medium Our on-line section-by-section tutorials cover a large and expanding number of topics in the books, and provide a convenient medium for in-class instruction. Through the numerous interactive features built in to the tutorials, along with the on-line utilities, students can participate actively in the classroom rather than passively as note-takers. The tutorials are designed to outline the main features within each section, preparing the student for a more in-depth reading of the textbook.
As a home study and review medium In addition to the tutorials, the student can use our detailed chapter summaries which serve as a supplementary "mini-text" complete with links to related pages, additional examples, on-line utilities, and interactive elements. Alternatively, the student can use the chapter true-false quizzes to test conceptual understanding of the material.
As a Collection of Technological Tools
To support the use of technology, we offer a comprehensive array of on-line utilities: graphing and function evaulation utilities, regression and finance tools, matrix algebra and matrix pivoting tools, statistics utilities and graphers, and specialized utilities for linear programming, Markov processes, and game theory. As indicated in the text, these utilities can be used in place of, or along with, graphing calculators and spreadsheets.
Application Projects
Every chapter begins with the statement of an interesting problem scenario that is returned to at the end of that chapter in a section titled "You're the Expert." This extended application uses and illustrates the central ideas of the chapter, and can be used as a reading project, group project, or take-home test. The themes of these applications are varied, and they are designed to be as non-intimidating as possible. Thus, for example, the authors avoid pulling complicated formulas out of thin air, but focus instead on the development of mathematical models appropriate to the topics.
Among the more notable of these applications are an example of modeling Internet spending based on actual data, an example using marginal analysis to design a strategy for regulating sulfur emissions, and an example on using Benford's Law to spot fraudulent tax returns. These applications are ideal for assignment as individual or group projects, and it is to this end that we have included groups of exercises at the end of each.
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Further Mathematics builds on the foundations created through following the A-Level Mathematics course. The study of a second A Level in mathematics provides the opportunity to significantly enhance the skills of analysis and mathematical reasoning. This leads not only to the acquisition of a body of knowledge that forms a bridge to any mathematically related degree course, but also establishes the rigour of logical argument that is essential for success in many other disciplines at university level.
Background needed
It is essential that students studying this course have a considerable interest and appreciation for mathematics, together with a proven aptitude for the subject. They should be conversant with all aspects of the Higher Tier GCSE course, which needs to be reflected by a grade A or A*.
AS Course content
During the first year of study there is a strong interdependence with the A Level Mathematics course. Students cover the second applications module of the Mathematics course together with modules in Further Mathematics and Decision Mathematics. The module in Decision Mathematics considers strategies for the most efficient solution of real life problems, such as the shortest route between two points in a network. This requires the application of standard algorithms, which are ideally suited to use with computers.
A2 Course content
The second year of the course largely focuses on Pure Mathematics and Mechanics. The Pure Mathematics Modules FP1 and FP2 lead to a significant expansion in the applications of Calculus, including the methods of solution for a variety of differential equations. Students are also introduced to a range of topics not encountered in the A Level Mathematics course. Prominent amongst these are Complex Numbers and Linear Transformations, the latter of which requires the development of Matrix Algebra.
The study of Mechanics is extended to include modules M2 and M3. Major developments covered will include motion in horizontal and vertical circles and Simple Harmonic Motion.
Assessment
Assessment is based entirely on terminal module examinations
Opportunities for enrichment Students are invited to participate in the UK Senior Maths Challenge, which is held in November each year. An exceptional performance provides access to further rounds of the competition, culminating in the International Olympiad.
What the students say
"Further Maths gave me the confidence and inspiration to take on Maths at university."
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I don't know dutch, but maybe someone out there who knows some will do something. Open Source isn't something that other people do, we all can contribute if we find something we can help with! by matthewkrehFeb 2
Open-Source Textbooks Instead I am concentrating recommendations and examples within the undergraduate mathematics curriculum, so please visit the Open Math Curriculum page. If you are linking to this site, please use that page for a broad list, or link to linear.pugetsound.edu specifically for the Linear Algebra text.
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The Mathematics Department at Mission College is one of the largest departments in the college, offering about seventy sections and serving about 1500 students each semester.
The department offers courses ranging from basic arithmetic to calculus, linear algebra, and differential equations. Courses are taught by fourteen full-time faculty members and about twenty-five associate faculty members.
MAPS: Math Achievement Pathway to Success
Are you lost in math? Find your way with the MAPS program!
MAPS is a comprehensive approach to teaching and learning that will give you the opportunity to finally succeed in mathematics. Find out more on the MAPS page.
Associate in Science for Transfer degree in Mathematics (AS-T)
AS-T degree in Mathematics allows students to complete an Associate degree and satisfy lower division general education and major requirements for transfer at the same time.
Course Sequences and Prerequisites
Here you will find a Math Map to get an overview of mathematics course sequences and prerequisites.
Department Student Learning Outcomes
The Mathematics Department at Mission College offers courses at three
levels: basic skills, associate's degree, and transfer.
Students completing mathematics courses at Mission College will be able to:
solve problems using mathematical terminology, symbols, operations,
and techniques according to the course content and level of study;
apply technology including calculators and computers to mathematical
problems;
improve computational and problem-solving skills;
construct mathematical models of "real life" problems and draw conclusions from these models;
formulate and test mathematical conjectures;
adapt general mathematical techniques to course-specific problems;
display logical thought processes;
and value mathematical ways of thinking.
Students will be assessed through written homework, quizzes, tests, and/or oral and written projects.
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Linear Transformation
In this lesson our instructor talks about linear transformation. First he does introduction to linear transformations. Then he does examples on projection mapping, images, range, and linear transformation.
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Linear Transformation
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Linear algebra is one of the reasons I fled engineering school and became a writer many years ago. Mathematical abstractions and my mind just do not seem to know how to mix.
I would like to say that reading The Manga Guide to Linear Algebra has caused a complete breakthrough in my stubborn resistance to any math beyond simple equations. But that would be a complete lie. Linear transformations, inverse matrices, and eigenvectors still do not compute well inside my head. Of course, the good news – for me – is that they really don't have to. I'm an old guy now and not worried about becoming a scientist or mathematician. I'll never have to know a diagonalizable matrix from a determinant to cash a Social Security check.
But many young peopledo need to know linear algebra. And The Manga Guide to Linear Algebra can be helpful for any serious student, from middle-school age through college, who is wrestling with linear algebra concepts. It's a fun book that mixes karate and romance with real math in a now well-proven comic book style that facilitates learning.
You do have to get past the fact that even this book has trouble presenting an easily grasped definition of linear algebra. "That's a tough question to answer properly," young math whiz Reiji Yurino confesses to his new love interest, Misa Ichinose. But once you do slide past his mind-numbing response ("Broadly speaking, linear algebra is about translating something residing in an m-dimensional space into a corresponding shape in an n-dimensional space"), each key concept is presented and illustrated in clever and helpful ways amid an unfolding story of young love and having to learn self-defense.
Thanks to this book, I now know more about linear algebra than I learned in my doomed attempt to become an electrical engineer. And who knows? If I had had the book many decades ago, I might now be lecturing in a university classroom, stealing quotes from Reiji Yurino, and telling you with a chuckle: "You can generally never find more than n different eigenvalues and eigenvectors for any nxn matrix."
Seriously, if you know someone who is facing linear algebra with dread (maybe it's you) or struggling with it and now expressing frustration and resistance, this book likely can help.
life
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Secondary Mathematics I [2011]
Interpret functions that arise in applications in terms of a context. For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and intervals for exponential functions whose domain is a subset of the integers. Mathematics II and III will address other function types. N.RN.1 and N.RN.2 will need to be referenced here before discussing exponential models with continuous domains.
F.IF.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Distance-Time Graphs
This tutorial is designed to help students understand the concept of slope and how distance-time graphs represent the relationship of collected data.
Function Flyer
The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
Growth Rate
In this lesson from Illuminations, students are given growth charts for the heights of girls and boys in order to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
Interpreting Functions Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Understand the concept of a function and use function notation." / Standards F.IF.1, F.IF.2, F.IF.3 and Cluster "Interpret functions that arise in applications in terms of a context" / Standards F.IF.4, F.IF.5 and F.IF.6 and Cluster "Analyze functions using different representations" / Standards F.IF.7 and F.IF.9.
Multi-Function Data Flyer
The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
Rate of Change and Slope
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review
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Finiteinite Mathematics, Tenth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, incorporating new applications and features to make the math real and accessible. Current applications for business And The social/life sciences, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, readers will find new ways to get involved with the material, such as "Your Turn" exercises and "Apply It" vignettes that encourage active part... MOREicipation. Revised artwork and many optional opportunities for technology use allow for increased visualization and a better understanding of difficult concepts. MyMathLab brings everything together by providing a complete online course solution with multimedia resources such as a comprehensive series of video lectures, graphing calculator help, and increased exercise coverage. Finite Mathematics, Tenth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as "Your Turn" exercises and "Apply It" vignettes that encourage active participation.
Extended Application: Using Integer Programming in the Stock-Cutting Problem
5. Mathematics of Finance
5.1 Simple and Compound Interest
5.2 Future Value of an Annuity
5.3 Present Value of an Annuity; Amortization
Chapter 5 Review
Extended Application: Time, Money, and Polynomials
6. Logic
6.1 Statements
6.2 Truth Tables and Equivalent Statements
6.3 The Conditional and Circuits
6.4 More on the Conditional
6.5 Analyzing Arguments and Proofs
6.6 Analyzing Arguments with Quantifiers
Chapter 6 Review
Extended Application: Logic Puzzles
7. Sets and Probability
7.1 Sets
7.2 Applications of Venn Diagrams
7.3 Introduction to Probability
7.4 Basic Concepts of Probability
7.5 Conditional Probability; Independent Events
7.6 Bayes' Theorem
Chapter 7 Review
Extended Application: Medical Diagnosis
8. Counting Principles; Further Probability Topics
8.1 The Multiplication Principle; Permutations
8.2 Combinations
8.3 Probability Applications of Counting Principles
8.4 Binomial Probability
8.5 Probability Distributions; Expected Value
Chapter 8 Review
Extended Application: Optimal Inventory for a Service Truck
9. Statistics
9.1 Frequency Distributions; Measures of Central Tendency
9.2 Measures of Variation
9.3 The Normal Distribution
9.4 Normal Approximation to the Binomial Distribution
Chapter 9 Review
Extended Application: Statistics in the Law—The Castaneda Decision
10. Markov Chains
10.1 Basic Properties of Markov Chains
10.2 Regular Markov Chains
10.3 Absorbing Markov Chains
Chapter 10 Review
Extended Application: A Markov Chain Model for Teacher Retention
11. Game Theory
11.1 Strictly Determined Games
11.2 Mixed Strategies
11.3 Game Theory and Linear Programming
Chapter 11 Review
Extended Application: The Prisoner's Dilemma—Non-Zero-Sum Games in Economics
Marge Lial was always, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in1983, where he currently is Professor of Mathematics.
Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He is currently (2002-2005) governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club's Inner City Outings program.
Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is currently a Professor of Mathematics and Chair of the Department of Mathematics and Statistics at Youngstown State University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations.
In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program.
A father of four children, Nate enthusiastically coaches soccer and softball. He also loves music, playing several instruments, and is a tenor in the Shenango Valley Chorale. More information about Nate Ritchey can be found at:
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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.
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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
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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.
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Guys and Gals! Ok, we're tackling algebra for first grade and I was absent in my last algebra class so I have no notes and my professor discusses stuff way bad that's why I didn't get to understand it very well when I attended our math class a while ago. To make matters worse, our class will have our examination on our next meeting so I can't afford not to study algebra for first grade. Can someone please help me attempt to learn how to answer couple of questions about algebra for first grade so that I am ready for the examination. I'm hoping that someone would assist me ASAP.
Greetings Dude What's up. Well I've been reading your post and believe me : I know what it feels like. Some time ago I was in the same problem, but before you get a teacher, I will like to recommend you one program that's really cool: Algebrator. I really tried a lot of other programs but that one it's definitely the the one! The best luck with that! Tell me what you think!.
I used Algebrator as well, especially in Remedial Algebra. It helped me a lot, and you won't believe how simple it is to use! It solves the exercise and it also explains everything step by step. Better than a teacher!
Algebrator is a simple product and is definitely worth a try. You will also find many exciting stuff there. I use it as reference software for my math problems and can say that it has made learning math much more enjoyable.
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Guiding Principles for Development
The authors were guided by the following principles in the development of the Connected Mathematics materials. These statements reflect both research and policy stances in mathematics education about what works to support students' learning of important mathematics.
The "big" or key mathematical ideas around which the curriculum is built are identified.
The underlying concepts, skills, or procedures supporting the development of a key idea are identified and included in an appropriate development sequence.
An effective curriculum has coherence-it builds and connects from investigation to investigation, unit-to-unit, and grade-to-grade.
Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the problems in an investigation.
Ideas are explored through these tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.
The curriculum reflects the information- processing capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks.
Connected Mathematics is different from many more familiar curricula in that it is problem centered. The following section elaborates what we mean by this and what the value added is for students of such a curriculum.
Student Learning: Rationale for a Problem-Centered Curriculum
Students' perceptions about a discipline come from the tasks or problems with which they are asked to engage. For example, if students in a geometry course are asked to memorize definitions, they think geometry is about memorizing definitions. If students spend a majority of their mathematics time practicing paper-and-pencil computations, they come to believe that mathematics is about calculating answers to arithmetic problems as quickly as possible. They may become faster at performing specific types of computations, but they may not be able to apply these skills to other situations or to recognize problems that call for these skills. Formal mathematics begins with undefined terms, axioms, and definitions and deduces important conclusions logically from those starting points. However, mathematics is produced and used in a much more complex combination of exploration, experience-based intuition, and reflection. If the purpose of studying mathematics is to be able to solve a variety of problems, then students need to spend significant portions of their mathematics time solving problems that require thinking, planning, reasoning, computing, and evaluating.
A growing body of evidence from the cognitive sciences supports the theory that students can make sense of mathematics if the concepts and skills are embedded within a context or problem. If time is spent exploring interesting mathematics situations, reflecting on solution methods, examining why the methods work, comparing methods, and relating methods to those used in previous situations, then students are likely to build more robust understanding of mathematical concepts and related procedures. This method is quite different from the assumption that students learn by observing a teacher as he or she demonstrates how to solve a problem and then practices that method on similar problems.
A problem-centered curriculum not only helps students to make sense of the mathematics, it also helps them to process the mathematics in a retrievable way.
Teachers of CMP report that students in succeeding grades remember and refer to a concept, technique, or problem-solving strategy by the name of the problem in which they encountered the ideas. For example, the Basketball Problem from What Do You Expect? in Grade Seven becomes a trigger for remembering the processes of finding compound probabilities and expected values.
Results from the cognitive sciences also suggest that learning is enhanced if it is connected to prior knowledge and is more likely to be retained and applied to future learning. Critically examining, refining, and extending conjectures and strategies are also important aspects of becoming reflective learners.
In CMP, important mathematical ideas are embedded in the context of interesting problems. As students explore a series of connected problems, they develop understanding of the embedded ideas and, with the aid of the teacher, abstract powerful mathematical ideas, problem- solving strategies, and ways of thinking. They learn mathematics and learn how to learn mathematics.
Characteristics of Good Problems
To be effective, problems must embody critical concepts and skills and have the potential to engage students in making sense of mathematics. And, since students build understanding by reflecting, connecting, and communicating, the problems need to encourage them to use these processes.
Each problem in Connected Mathematics satisfies the following criteria:
The problem must have important, useful mathematics embedded in it.
Investigation of the problem should contribute to students' conceptual development of important mathematical ideas.
Work on the problem should promote skillful use of mathematics and opportunities to practice important skills.
The problem should create opportunities for teachers to assess what students are learning
In addition each problem satisfies some or all of the following criteria:
The problem should engage students and encourage classroom discourse.
The problem should allow various solution strategies or lead to alternative decisions that can be taken and defended.
Solution of the problem should require higher-level thinking and problem solving.
The mathematical content of the problem should connect to other important mathematical ideas.
Practice With Concepts, Related Skills, and Algorithms
Students need to practice mathematical concepts, ideas, and procedures to reach a level of fluency that allows them to "think" with the ideas in new situations. To accomplish this we were guided by the following principles related to skills practice.
Immediate practice should be related to the situations in which the ideas have been developed and learned.
Continued practice should use skills and procedures in situations that connect to ideas that students have already encountered.
Students need opportunities to use the ideas and skills in situations that extend beyond familiar situations. These opportunities allow students to use skills and concepts in new combinations to solve new kinds of problems.
Students need practice distributed over time to allow ideas, concepts and procedures to reach a high level of fluency of use in familiar and unfamiliar situations and to connect to other concepts and procedures.
Students need guidance in reflecting on what they are learning, how the ideas fit together, and how to make judgments about what is helpful in which kinds of situations.
Throughout the Number and Algebra Strands development, students need to learn how to make judgments about what operation or combination of operations or representations is useful in a given
situation, as well as, how to become skilful at carrying out the needed computation(s). Knowing how to, but not when to, is insufficient. Skills
in CMP under Mathematics Content and Algebra in CMP under Mathematics Content.
Rationale for Depth versus Spiraling
The concept of a "spiraling" curriculum is philosophically appealing; but, too often, not enough time is spent initially with a new concept to build on it at the next stage of the spiral. This leads to teachers spending a great deal of time re-teaching the same ideas over and over again. Without a deeper understanding of concepts and how they are connected, students come to view mathematics as a collection of different techniques and algorithms to be memorized.
Problem solving based on such learning becomes a search for the correct algorithm rather than seeking to make sense of the situation, considering the nature and size of a solution, putting together a solution path that makes sense, and examining the solution in light of the original question. Taking time to allow the ideas studied to be more carefully developed means that when these ideas are met in future units, students have a solid foundation on which to build. Rather than being caught in a cycle of relearning the same ideas at a superficial level, which are quickly forgotten, students are able to connect new ideas to previously learned ideas and make substantive advances in knowledge.
With any important mathematical concept, there are many related ideas, procedures, and skills. At each grade level, a small, select set of important mathematical concepts, ideas, and related procedures are studied in depth rather than skimming through a larger set of ideas in a shallow manner. This means that time is allocated to develop understanding of key ideas in contrast to "covering" a book. The Teacher's Guides accompanying CMP materials were developed to support teachers in planning for and teaching a problem-centered curriculum. Practice on related skills and algorithms are provided in a distributed fashion so that students not only practice these skills and algorithms to reach facility in carrying out computations, but they also learn to put their growing body of skills together to solve new problems.
Field Testing
Developing Depth of Understanding and Use
Through the field trials process we were able to develop units that result in student understanding of key ideas in depth. An example is illustrated in the way that Connected Mathematics treats proportional reasoning-a fundamentally important topic for middle school mathematics and beyond. Conventional treatments of this central topic are often limited to a brief expository presentation of the ideas of ratio and proportion, followed by training in techniques for solving proportions. In contrast, the CMP curriculum materials develop core elements of proportional reasoning in a seventh grade unit, Comparing and Scaling, with the groundwork for this unit having been developed in four prior units. Five succeeding units build on and connect to students' understanding of proportional reasoning. These units and their connections are summarized as follows:
Grade 6Bits and Pieces I and II introduce students to fractions and their various meanings and uses. Models for making sense of fraction meanings and of operating with fractions are introduced and used. These early experiences include fractions as ratios. The extensive work with equivalent forms of fractions builds the skills needed to work with ratio and proportion problems. These ideas are developed further in the probability unit How Likely Is It? in which ratio comparisons are informally used to compare probabilities. For example, is the probability of drawing a green block from a bag the same if we have 10 green and 15 red or 20 green and 30 red?
Grade 7Stretching and Shrinking introduces proportionality concepts in the context of geometric problems involving similarity. Students connect visual ideas of enlarging and reducing figures, numerical ideas of scale factors and ratios, and applications of similarity through work with problems focused around the question: "What would it mean to say two figures are similar?"
The next unit in grade seven is the core proportional reasoning unit, Comparing and Scaling, which connects fractions, percents, and ratios through investigation of various situations in which the central question is: "What strategies make sense in describing how much greater one quantity is than another?" Through a series of problem-based investigations, students explore the meaning of ratio comparison and develop, in a progression from intuition to articulate procedures, a variety of techniques for dealing with such questions.
A seventh grade unit that follows, Moving Straight Ahead, is a unit on linear relationships and equations. Proportional thinking is connected and extended to the core ideas of linearity- constant rate of change and slope. Then in the probability unit What Do You Expect?, students again use ratios to make comparisons of probabilities.
Grade 8Thinking With Mathematical Models; Looking For Pythagoras; Growing, Growing, Growing, and Frogs, Fleas, and Painted Cubes extend the understanding of proportional relationships by investigating the contrast between linear relationships and inverse, exponential, and quadratic relationships. Also in Grade Eight, Samples and Populations uses proportional reasoning in comparing data situations and in choosing samples from populations.
These unit descriptions show two things about Connected Mathematics-the in-depth development of fundamental ideas and the connected use of these important ideas throughout the rest of the units.
CMP Instructional Model
Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. The Connected Mathematics teacher materials are organized around an instructional model that supports this kind of teaching. This model is very different from the "transmission" model in which teachers tell students facts and demonstrate procedures and then students memorize the facts and practice the procedures. The CMP model looks at instruction in three phases: launching, exploring, and summarizing. The following text describes the three instructional phases and provides the general kinds of questions that are asked. Specific notes and questions for each problem are provided in the Teacher's Guides.
Launch
In the first phase, the teacher launches the problem with the whole class. This involves helping students understand the problem setting, the mathematical context, and the challenge. The following questions can help the teacher prepare for the launch:
What are students expected to do?
What do the students need to know to understand the context of the story and the challenge of the problem?
What difficulties can I foresee for students?
How can I keep from giving away too much of the problem solution?
The launch phase is also the time when the teacher introduces new ideas, clarifies definitions, reviews old concepts, and connects the problem to past experiences of the students. It is critical that, while giving students a clear picture of what is expected, the teacher leaves the potential of the task intact. He or she must be careful to not tell too much and consequently lower the challenge of the task to something routine, or to cut off the rich array of strategies that may evolve from a more open launch of the problem.
Explore
The nature of the problem suggests whether students work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem during the explore phase. The Teacher's Guide suggests an appropriate grouping. As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem-solving strategies.
It is inevitable that students will exhibit variation in their progress. The teacher's role during this phase is to move about the classroom, observing individual performance and encouraging on-task behavior. The teacher helps students persevere in their work by asking appropriate questions and providing confirmation and redirection where needed. For students who are interested in and capable of deeper investigation, the teacher may provide extra questions related to the problem. These questions are called Going Further and are provided in the explore discussion in the Teacher's Guide. Suggestions for helping students who may be struggling are also provided in the Teacher's Guide. The explore part of the instruction is an appropriate place to attend to differentiated learning.
The following questions can help the teacher prepare for the explore phase:
How will I organize the students to explore this problem? (Individuals? Pairs? Groups? Whole class?)
What materials will students need?
How should students record and report their work?
What different strategies can I anticipate they might use?
What questions can I ask to encourage student conversation, thinking, and learning?
What questions can I ask to focus their thinking if they become frustrated or off-task?
What questions can I ask to challenge students if the initial question is "answered"?
As the teacher moves about the classroom during the explore, she or he should attend to the following questions:
What difficulties are students having?
How can I help without giving away the solution?
What strategies are students using? Are they correct?
How will I use these strategies during the summary?
Summarize
It is during the summary that the teacher guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The summarize phase of instruction begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions as well as the strategies they used to approach the problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the problem and guides them in refining their strategies into efficient, effective, generalizable problem-solving techniques or algorithms.
Although the summary discussion is led by the teacher, students play a significant role. Ideally, they should pose conjectures, question each other, offer alternatives, provide reasons, refine their strategies and conjectures, and make connections. As a result of the discussion, students should become more skillful at using the ideas and techniques that come out of the experience with the problem.
If it is appropriate, the summary can end by posing a problem or two that checks students' understanding of the mathematical goal(s) that have been developed at this point in time. Check For Understanding questions occur occasionally in the summary in the Teacher's Guide. These questions help the teacher to assess the degree to which students are developing their mathematical knowledge. The following questions can help the teacher prepare for the summary:
How can I help the students make sense of and appreciate the variety of methods that may be used?
How can I orchestrate the discussion so that students summarize their thinking about the problem?
What questions can guide the discussion?
What concepts or strategies need to be emphasized?
What ideas do not need closure at this time?
What definitions or strategies do we need to generalize?
What connections and extensions can be made?
What new questions might arise and how do I handle them?
What can I do to follow up, practice, or apply the ideas after the summary?
Support for Classroom Teachers
When mathematical ideas are embedded in problem-based investigations of rich context, the teacher has a critical responsibility for ensuring that students abstract and generalize the important mathematical concepts and procedures from their experiences with the problems. In a problem-centered classroom, teachers take on new roles-moving from always being the one who does the mathematics to being the one who guides, interrogates, and facilitates the learner in doing and making sense of the mathematics.
The Teacher's Guides and Assessment Resources developed for Connected Mathematics provide these kinds of help for the teacher:
The Teacher's Guide for each unit engages teachers in a conversation about what is possible in the classroom around a particular lesson. Goals for each lesson are articulated. Suggestions are made about how to engage the students in the mathematics task, how to promote student thinking and reasoning during the exploration of the problem, and how to summarize with the students the important mathematics embedded in the problem. Support for this Launch-Explore- Summarize sequence occurs for each problem in the CMP curriculum.
An overview and elaboration of the mathematics of the unit is located at the beginning of each Teacher's Guide, along with examples and a rationale for the models and procedures used. This mathematical essay helps a teacher stand above the unit and see the mathematics from a perspective that includes the particular unit, connects to earlier units, and projects to where the mathematics goes in subsequent units and years.
Actual classroom scenarios are included to help stimulate teachers' imaginations about what is possible.
Questions to ask students at all stages of the lesson are included to help teachers support student learning.
Reflection questions are provided at the end of each investigation to help teachers assess what sense students are making of the 'big" ideas and to help students abstract, generalize, and record the mathematical ideas and techniques developed in the Investigation.
Diverse kinds of assessments are included in the student units and the Assessment Resources that mirror classroom practices as well as highlight important concepts, skills, techniques, and problem solving strategies.
Multiple kinds of assessment are included to help teachers see assessment and evaluation as a way to inform students of their progress, apprise parents of students' progress, and guide the decisions a teacher makes about lesson plans and classroom interactions. Components of CMP
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1. Define the standard concepts of real analysis: limit, continuity, differentiability, integrability, convergence of sequences and series. 2. Identify and give examples and non-examples (with justification) of the standard objects of real analysis: limits, continuous functions, differentiable functions, integrable functions, convergent sequences and convergent series. 3. Become aware of real-world applications in which the standard concepts and objects of real analysis play a central role. 4. Formulate conjectures and prove theorems about the standard concepts and objects of real analysis. 5. Determine how the standard concepts of real analysis relate to each other. 6. Understand the metric topology of real Euclidean space as it relates to the above.
REQUIREMENTS:
All students must have their own text. Assignments and exams are required by all faculty. Other requirements may include: projects, working in groups, class presentations, computer lab assignments or other forms of assessment.
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Mathematics A Discrete Introduction
9780534356385
ISBN:
0534356389
Pub Date: 2000 Publisher: Brooks/Cole
Summary: This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics. There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics
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The geometry of the circle and an introduction to three dimensional geometry is included. Additionally, coordinate geometry is reviewed, and then applied as a proof method, with frequent use of transformation geometry. Precalculus prepares students for a first course in Calculus, as well as introducing topics that will be needed in other Mathematics courses
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Getting Started Using the Technology at Your Disposal: One Problem, Three Different Approaches
Mary Sue Wyss
Abstract
Pascal's Pyramid is constructed out of toothpicks and gum drops. Observations of either the number of gum drops, toothpicks, tetrahedrons, or octahedrons in each level can produce data reflective of "change". Both second and third degree polynomials are generated. The three different approaches to analyzing the data include finite differences, use of the TI-81 and/or TI-82, and Excel.
Since each approach uses the same data set, the focus is directed on the best analytic method or "tool" of investigation for the data given. In addition, through this introductory exercise, students will become acquainted with their graphing calculator (matrix key) and spreadsheet software that utilizes graphs. Exploration and analysis is geared toward junior high Algebra students but could prove to be an enjoyable introductory exercise for upper level students and technically timid teachers.
Activity A: Finite Differences
For "nice" data sets, this is usually the most direct method of deducing the function. Finite differences reinforce pattern recognition and prepare students for sequences and series.
Step 1: Make a table of x-values and y-values to represent the levels of Pascal's Pyramid and the number of gum drops per level.
x
y
1
1
2
3
3
6
4
10
n
Table 1.A
Step 2: Make another table that shows the differences and ratios of y to x. Since the second difference taken is constant, we know we are dealing with a quadratic function. What is it?
x
y=f(x)
difference in f(x)
change in f(x)
1
1
2
3
2
1
3
6
3
1
4
10
4
1
n
1
Table 2.A
Step 3: By taking the differences, we were offered some valuable information about the characteristic nature of our function. Naturally, our function is more involved than just x2. Therefore, we may want to look at an alternative table such as ratios or multiples of y to arrive at the precise function. Let's make another table.
x
y
2.y
2.y rewritten
1
1
2
1 x 2
2
3
6
2 x 3
3
6
12
3 x 4
4
10
20
4 x 5
5
15
30
5 x 6
n
n (n+1)
Table 3.A
As a result of table 3.A, we see that 2y can be generalized in terms of n. We are very close to our answer. If we divide this generalization;
2y = n ( n + 1 )
then y = n (n + 1)
2
and we are done.
Activity B: Using the TI-81/82 Graphing Calculator
While finite differences may be the most direct route to finding our function, matrices will also work. Since the function is so "nice", this may be a good way to introduce students to the use of the matrix function key on the graphing calculator.
Step 1: We need to look at our data from table 1.A of Activity A. Given the matrix multiplication of [A] x = [B] where the scalar x = [A] -1[B], we find that [A]-1[B] produces the coefficients of our quadratic: y = ax2+bx+c. (We'll be using the first three points in our data set.)
To enter this into our calculator, begin by pressing . "Right arrow" over to EDIT and press . Our matrix is a 3 x 3. Press "3" and "3". Now we are ready to input our matrix given the following equations:
y = ax2+ bx + c
1 = 1a + 1b + c
3 = 4a + 2b + c
6 = 9a + 3b + c
Step 2: We want to exit from our new [A] matrix and create a 3 x 1 matrix [B]. To exit matrix [A], press . Again, arrow over to edit and "arrow down" to 2:[B] and . You want to make a 3 x 1 matrix. Put the "y-values" into [B].
Step 3: Press , to get back to the home screen. Press if home screen is not clear. Recall that from the scalar x=[A] -1[B]we get our coefficients for y = ax2+ bx + c. To let the calculator multiply the matrices, press then "down arrow" to 1:[A]:. Press . Since we want the inverse, press . The display to screen should be [A]-1. Now we want to go back to and "down arrow" to 2:[B]: and press . Your home screen should display the matrix [A]-1[B]
Step 4: Press to display the scalar x.
This tells us that a = 1/2, b = 1/2, and c=0 for all practical purposes.
Activity C: Using "Excel" Spreadsheets and Graphs
Excel offers us a quick way to see the behavior of the function. Through this method, students will learn how to incorporate a little guesswork by varying the parameters. The function we are using in this exercise is nice and known; however, most other sets we will be using later are not. With this exercise, students should be able to concentrate on how to set up a template and acquire a feel for parameterizing a function.
Step 1: We'll need to set up the same tables of data as in Activity A. Each column represents the table headings as follows.
A
B
C
D
E
1
Level (x)
Gum Drops (y)
ROC of f(x)
Change of f(x)
2
3
1
1
1
1
4
2
3
2
1
5
3
6
3
1
6
4
10
4
1
7
5
15
5
1
8
6
21
6
1
Table 1.C
Column D's heading ROC of f(x) refers to the rate of change of gum drops.
Step 2: Once you have the data in, you can select the graph icon in the top right corner. Continue by selecting the scatter plot and then press next. Select an area to place your graph and open a box for it. You should see the following display:
Graph 1.C
You can enhance the appearance of your graph by clicking twice on the graph and then accessing the axis title options. Whatever the case, it is apparent that the function is quadratic in nature for the data given. Students may put formulas into the cells B3 and C3 to create more data points and then re-graph to verify the quadratic nature of the function. The formulas appear below for cells B3 and C3.
B
C
1
Level (x)
Gum Drops (y)
2
1
1
3
=B3+1
=C3+B4
Table 2.C
Step 3: We will be using the same intuition as in Activity A to find the function that best fits the data. We know the function is of the form y = ax2+ bx + c. Let's begin by making a column heading entitled ax2 in column G. We can input the respective values for ax2 in by way of a formula later.
Step 4: To vary the parameter "a", we'll need to set up a cell with the "a" value in it. We'll set that up in the "A" column as shown below.
A
1
a=
2
1
Table 3.C
Step 5: We are now ready to input a formula into our column G that will generate the rest of the column without making the calculations ourselves. This column will be dependent on the number we have placed in cell A2. To start with we will take a=1. To put the equations into G4, use the cell display below.
G
1
ax^2+bx
2
3
1
4
=$A$3*B4^2
Table 4.C
After highlighting down the column (however far), and entering, we have a column of new values. We would like to graph these new values against x to see how well they compare to our function. (The $ symbol between A3 and after indicates that we want that value used as a constant.)
Step 6: To get a clear visual idea of how close our guess is to the real function, we'll graph by highlighting the x column and then press and keys which will allow you to go over to the G column and highlight that.
Step 7: After both columns are highlighted, select the graph icon again from the top right corner of the screen. Select another scattergram that has two graphs showing and open a window on your spreadsheet to display the graph.
Graph 2.C
Step 8: As we can see, the graphs don't match. We can change the values of our "a" parameter to vary the graph. Try some different values of "a" to see what seems best.
Step 9: As hard as we try, the estimated data does not fit well to the actual data. We may need to consider another parameter "b" from the equation y = ax2+ bx + c. This is easy to do by setting up another cell like we did for our "a" parameter. This can be done in cell A4 and A5 as follows.
A
4
b=
5
0.2
Table 5.C
Step 10: We want to change the equation in the G1 column to read ax2+ bx. After doing that, we want to go to G4 to add the "bx" to the equation. The equation should look as follows.
G
1
ax^2+bx
2
3
1
4
=$A$3*B4^2+$A$5*B4
Table 6.C
Toy with both parameters to investigate the affect on the graph. Hold one constant and vary the other. Try some extreme points to emphasize the change before arriving at the correct solution of a = .5, and b = .5.
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Hours of operation
How JavALab Courses Work
These courses take advantage of an advanced technology adapted to learning mathematics: Assessment and LEarning in Knowledge Spaces, or ALEKS. Students take an initial assessment
the first day of class that determines the mathematical objectives they have already mastered,
and sets up the objectives they will master during the course to fill their learning "pie." Students
commit at least three hours each week in the Javelina Algebra Lab (JavALab) and additional
hours outside the lab practicing in the Learning Mode. This adds pieces to the learning "pie."
Students also meet as a class once a week for 50 minutes. During this time instructors review
as a class, or individually, those topics with which students need help or further understanding.
For every 20 objectives students complete, or after each ten hours of time in ALEKS, students
take an automatic ALEKS Assessment. Assessments ensure mastery of the objectives and must
be taken in the JavALab.
Grading In JavALab Courses
There are a total of 184 objectives which cover all three courses. Grading is based on completion
and mastery of the required number of objectives outlined below for each course.
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Description
This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).
University Calculus, Early Transcendentals, Second Edition is the ideal choice for professors who want a streamlined text with plenty of exercises. This text helps students successfully generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.
The text is available with a robust MyMathLab® course–an online homework, tutorial, and study solution designed for today's students. In addition to interactive multimedia features like Java™ applets and animations, thousands of MathXL® exercises that reflect the richness of those in the text are available for students.
Table of Contents
1. Functions
1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Graphing with Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
2. Limits and Continuity
2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity; Asymptotes of Graphs
3. Differentiation
3.1 Tangents and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 The Derivative as a Rate of Change
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Functions and Logarithms
3.9 Inverse Trigonometric Functions
3.10 Related Rates
3.11 Linearization and Differentials
4. Applications of Derivatives
4.1 Extreme Values of Functions
4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test
4.4 Concavity and Curve Sketching
4.5 Indeterminate Forms and L'Hôpital's Rule
4.6 Applied Optimization
4.7 Newton's Method
4.8 Antiderivatives
5. Integration
5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Rule
5.6 Substitution and Area Between Curves
6. Applications of Definite Integrals
6.1 Volumes Using Cross-Sections
6.2 Volumes Using Cylindrical Shells
6.3 Arc Length
6.4 Areas of Surfaces of Revolution
6.5 Work
6.6 Moments and Centers of Mass
7. Integrals and Transcendental Functions
7.1 The Logarithm Defined as an Integral
7.2 Exponential Change and Separable Differential Equations
7.3 Hyperbolic Functions
8. Techniques of Integration
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.5 Integral Tables and Computer Algebra Systems
8.6 Numerical Integration
8.7 Improper Integrals
9. Infinite Sequences and Series
9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 The Ratio and Root Tests
9.6 Alternating Series, Absolute and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
9.10 The Binomial Series and Applications of Taylor Series
10. Parametric Equations and Polar Coordinates
10.1 Parametrizations of Plane Curves
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Graphing in Polar Coordinates
10.5 Areas and Lengths in Polar Coordinates
10.6 Conics in Polar Coordinates
11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
11.5 Lines and Planes in Space
11.6 Cylinders and Quadric Surfaces
12. Vector-Valued Functions and Motion in Space
12.1 Curves in Space and Their Tangents
12.2 Integrals of Vector Functions; Projectile Motion
12.3 Arc Length in Space
12.4 Curvature and Normal Vectors of a Curve
12.5 Tangential and Normal Components of Acceleration
12.6 Velocity and Acceleration in Polar Coordinates
13. Partial Derivatives
13.1 Functions of Several Variables
13.2 Limits and Continuity in Higher Dimensions
13.3 Partial Derivatives
13.4 The Chain Rule
13.5 Directional Derivatives and Gradient Vectors
13.6 Tangent Planes and Differentials
13.7 Extreme Values and Saddle Points
13.8 Lagrange Multipliers
14. Multiple Integrals
14.1 Double and Iterated Integrals over Rectangles
14.2 Double Integrals over General Regions
14.3 Area by Double Integration
14.4 Double Integrals in Polar Form
14.5 Triple Integrals in Rectangular Coordinates
14.6 Moments and Centers of Mass
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
14.8 Substitutions in Multiple Integrals
15. Integration in Vector Fields
15.1 Line Integrals
15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
15.3 Path Independence, Conservative Fields, and Potential Functions
15.4 Green's Theorem in the Plane
15.5 Surfaces and Area
15.6 Surface Integrals
15.7 Stokes' Theorem
15.8 The Divergence Theorem and a Unified Theory
16. First-Order Differential Equations (Online)
16.1 Solutions, Slope Fields, and Euler's Method
16.2 First-Order Linear Equations
16.3 Applications
16.4 Graphical Solutions of Autonomous Equations
16.5 Systems of Equations and Phase Planes
17. Second-Order Differential Equations (Online)
17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power Series Solutions
Appendices
1. Real Numbers and the Real Line
2. Mathematical Induction
3. Lines, Circles, and Parabolas
4. Conic Sections
5. Proofs of Limit Theorems
6. Commonly Occurring Limits
7. Theory of the Real Numbers
8. Complex Numbers
9. The Distributive Law for Vector Cross Products
10. The Mixed Derivative Theorem and the Increment Theorem
11. Taylor's Formula for Two Variables
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Providence, RI Statistics
...Despite its seminal importance in the modern world, calculus introduces only one truly new concept: the limit. The other two major tools of calculus - differentiation and integration - are simply application of the limit to different kinds of problems. Mastering calculus requires a strong foundation of algebra and trigonometry, followed by an in-depth understanding of limits
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Book description
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
work.
Matt A. Bernstein, PhD, is Professor of Radiologic
Physics at the Mayo Clinic, where he holds appointments in the
Departments of Radiology and Biomedical Engineering. A Fellow of the
International Society for Magnetic Resonance in Medicine (ISMRM) and
Editorial Board member of Magnetic Resonance in Medicine, Dr.
Bernstein has published over sixty journal articles, mainly in the
field of MRI physics.
William A. Friedman, PhD, is Emeritus Professor at the
University of Wisconsin and Affiliate Professor at the University of
Washington. A Fellow of the American Physical Society, Dr. Friedman
has over forty years of academic experience and has authored more than
one hundred journal articles in the field of nuclear physics.
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and engineering issues, often involving actual research data. Problems consist of a student page and an answer sheet. Students need to be familiar with scale drawing, geometry, speed-distance-time calculations and proportions
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Run a Quick Search on "Concepts of Modern Mathematics" by Ian Stewart to Browse Related Products:
Short Desription
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math"--groups, sets, subsets, topology, Boolean algebra, and more. By the time readers finish this book, they shall have a much clearer grasp of how modern mathematicians look at figures, function, and formulas, leading them to a better comprehension of the nature of the mathematics itself.
If You Enjoy "Concepts of Modern Mathematics (Paperback)", May We Also Recommend:
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Math Solver II is a scientific calculator. Math Solver II includes a step-by-step solution for any mathematical expression, to make work/homework more fun and easy. Also includes a Simple Mode, for... more
PANAGEOS .- level: Advanced ; language: English Plane Analytic Geometry Problem Solver, is for the user who already knows the subject and wants to verify his/hers solutions, or for the teacher orChildren can effectively learn math with friendly natural animals and/or worms. The comprehensive game of Space Tour, touring among various planets and the experience to fly over the surface of the... more
Calculate geometry problems with this tool. Geometry Solver 3D will solve analytic geometry problems easily. It will provide tools for calculations in 3D as well as graphic OpenGL demonstrations.... more
Math Mechanixs is an easy to use scientific and engineering FREE math software program. (FREE registration is required after 60 days). The typical tool for solving mathematical problem has been... more
STFMath is a multipurpose math utility, suitable not only for students, but also for engineers, professors, or anyone interested in math: functions (draw, analyze, evaluate), calculators (complex,... more
Children can effectively learn math with friendly natural animals and/or worms.The comprehensive game to rescue the princess frog from Witch's Castle is provided. The witch's dragons multiple to... more
Get into the pilot seat and learn about volume and surface area while blasting away space debris to save your ship! Galactic Geometry is a 3D educational game that offers an engaging environment... more
GEUP 3D is an interactive solid geometry software for math calculation and visualization. It allows to create dynamic and general constructions/applications visually by defining math elements. GEUP... more
Geometry calculates geometric figures such as spheres, triangles, cones, trapezoids, circles and cylinders. Also, it has an application in engineering to calculate the flow and geometry in an open... more
Math for kids of all ages. Also has times tables for kids.When you get the right answer you get a happy face. When it is wrong you get a sad face. Has 3 levels of difficulty to choose from.There... more
Magic Math Space Tour for ages 11-12 is a quiz-oriented CAI that provides an enjoyable environment for children to study math. Friendly animals and worms participate in the animations and introduce... more
Math Composer is a powerful yet easy to use tool for creating all your math documents. It is a simple way for math teachers and instructors to create math worksheets, tests, quizzes, and exams.... more
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Basic Geometry For College Students : An Overview Of The Fundamental Concepts Of Geometry - 03 edition
Summary: Intended to address the need for a concise overview of fundamental geometry topics. Sections 1-7 introduce such topics as angles, polygons, perimeter, area, and circles. In the second part of the text, Sections 8-11 cover congruent and similar triangles, special triangles, volume, and surface area.
Benefits:
A five-step problem-solving strategy throughout the book teaches students to an...show morealyze the problem, form an equation, solve the equation, state the conclusion, and check the result.
The greatest strength of the Tussy/Gustafson approach and the key to students' grasp of the language of mathematics is the STUDY SETS, found at the end of each section.
VOCABULARY, NOTATION and WRITING problems in the STUDY SETS are structured to improve students' ability to read, write, and communicate mathematical ideas.
CONCEPTS sections in the STUDY SETS reinforce major ideas and foster independent thinking.
PRACTICE sections in the STUDY SETS provide the drill and practice necessary for mastery of the mathematics.
APPLICATIONS in the STUDY SETS provide opportunities for students to apply what they've learned to real-life situations.
Many problems require students to present their solutions in the form of a chart, table, or graph. Students are also asked to read data displays to obtain information necessary to solve problems.
SELF CHECK problems, adjacent to worked examples, reinforce newly learned skills and help students build confidence by working a similar problem. Students can refer to the solution and Authors' Notes as they solve the Self Check. The answer to each Self Check is printed underneath the problem to give students instant feedback
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Mathematics majors whether planning on a career in industry or
in teaching. Open to all students.
Course Objectives:
A course in mathematical modeling differs from a course in applied
mathematics in one important way. Applied mathematics courses are
typically taught as mathematics in search of an application.
A mathematical modeling course is centered on real world situations in
search of some appropriate mathematics. Thus the following objectives
distinguish this course from other mathematics courses in the
curriculum:
To change the student's world view, so as to see the pervasiveness
of mathematics in the natural sciences.
To give teams of two or three students an opportunity to work together
to solve real-world problems of the kind that professional
applied mathematicians are paid to do.
To discover the usefulness of discrete deterministic models in
areas such as social choice, finance, and population growth.
To learn powerful ideas of mathematics like "transform-solve-invert"
and Polya-like strategies for attacking problems like looking
for analogies and solving just a useful part of a problem.
To learn to explain the mathematics that one has used to solve
a problem both in formal writing and in oral presentation.
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Survey Of Mathematics I –
mth361
(3 credits)
This is the first course of a two-part course sequence presenting a survey of mathematics. This course addresses the conceptual framework for mathematics. The focus of this course is on real number properties, patterns, operations, and algebraic reasoning and problem solving.
Real Numbers and Applications
Standards and Professional Organizations
Describe the standards and principles of mathematics as taught in K-12 schools.
Examine the role of professional mathematics organizations
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MATLAB is a powerful programme, which naturally lends itself to the rapid implementation of most numerical algorithms. This text, which uses MATLAB, gives a detailed overview of structured programming and numerical methods for the undergraduate student. The book covers numerical methods for solving a wide range of problems, from integration to the numerical solution of differential equations or the simulation of random processes. Each chapter includes extensive examples and tasks, at varying levels of complexity. For practice, the early chapters include programmes that require debugging by the reader, while full solutions are given for all the tasks. The book also includes: a glossary of MATLAB commands appendices of mathematical techniques used in numerical methods. Designed as a text for a first course in programming and algorithm design, as well as in numerical methods courses, the book will be of benefit to a wide range of students from mathematics and engineering, to commerce.
Table of Contents
Table of Contents
Simple calculations with MATLAB.
Writing scripts and functions.
Loops and conditional statements.
Root finding.
Interpolation and extrapolation.
Matrices.
Numerical integration.
Solving differential equations.
Simulations and random numbers.
Appendices.
A mathematical introduction to matrices.
Glossary of useful terms.
Solutions to tasks
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When it comes to college, you're going to find a lot of classes that are very tough. From Biology to Math, there are thousand's of students today that are struggling. What most don't realize is that you can go outside of the class and get help from other resources. Today, let's focus on some books you could use in order to help you get better with your Algebra classes.
Algebra for Dummies- I'm sure you're familiar with the "for dummies" series. This series in particular has a book on just about anything. When it comes to Math, they have a book as well. This book helps you discover everything from figuring out fractions to solving linear and quadratic equations. It makes things a little easier than your boring textbook.
Kiss my math- The kiss my math series is one of the better series out there. Rated by hundreds of consumer, this book has continued to average a 4 star rating on many store fronts. Even though this book focuses more on pre-algebra, it's a great start to help you better understand what's ahead of you. From step by step instructions to time-saving tips and tricks, this book educates you in many different ways.
MyMathLab Kit – If you want to steer clear of the books and you want a more interactive course, you'll probably want to look at the MyMathLab kit. This kit allows you to view interactive online courses that are almost like a classroom. You'll get review sheets, practice exames and case studies that you can use to help you better understand algebra.
College Algebra (4th Edition) - If you want a book that brings real world examples into the Algebra classroom, this may be the book that you want to check out. Written by Bob Blitzer, a professor who has recieved many teaching awards goes into detail on how to think "mathematically". It's a great book if you're looking for common sense answers.
When it comes to learning more about any math subject, most students just think they have to learn it on their own through their boring textbooks. There are so many resources out there and it doesn't hurt to spend an extra $20 to pass the class. Not only that, you'll also have a great resource to come back to at the end of the day. Check out some of the books and see which one best suits
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INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL ... (1) 2 (3) (2) 2 (4) 21 Students in a ninth grade class measured their heights, h, in ... Algebra Regents June 08.pdf
Curriculum Overview and Sample Lessons 9th GradeMath ** ... The following book is required for this course: Saxon Algebra I, An Incremental ...
... SUMMARY OF 9th GRADE ... course follows the New York State Standards for the new Integrated Algebra ... centers on Math A and B as defined by the New York State Standards.
While the K-7 CCSS effectively prepare students for algebra in 8 th grade, some standards from ... school-wide community of support for students; *Providing students a u0022math ...
Integrated Algebra 1 is a new text for high school algebra that continues the ... and mandated by the New York State Board of Regents in the New York State Mathematics ...
NYS Recommended Additions Math Standards for Grades 9-12 ... All of the New York State Mathematics Common ... to prepare students for Algebra I by 8th grade, and Common Core State Standards/CCSS Math 9_12 web.pdf
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Specification
Aims
Brief Description of the unit
The life sciences are arguably the greatest scientific adventure of the age. Over the last few decades a series of
revolutions in experimental technique have made it possible to ask very detailed questions about how life works, ranging
from the smallest, sub-cellular scales up through the organisation of tissues and the functioning of the brain
and, on the very largest scales, the evolution of species and ecosystems. Mathematics has so far played a small, but
honourable part in this development, especially by providing simple models designed to illuminate principles and test
broad hypotheses.
Although this course is still being written, it is likely to touch on several of the following topics.
Population models and broad questions of ecological and evolutionary stability: these topics are normally treated with
ODEs or, when one wants to include spatial organisation, PDEs. This area a good introduction to the "illustrative model" school
of mathematical biology.
Pattern selection and development of body plan in early life: here I would like to have the class read
a famous old paper Alan Turing's and then look at the sorts of things that modern work - both experimental
and theoretical - has to say about the same questions. The main tools here are, again, differential equations.
Analysis of regulatory networks: this follows naturally from the previous topic and begins to bring in some new
mathematical methods and ideas, especially from graph theory and probability. This is mathematical biology at its closest
to experimental data.
Molecular evolution and phylogenetics: this subject takes as its starting point biological sequence data (DNA or protein)
and asks questions such as: "How closely related are mice and men and when did they last have a common ancestor?". Here the
models are probabilistic and the questions have a statistical flavour.
The mathematics required for biology is not generally all that hard or deep (though there are exceptions: some of the
most exciting recent work in phylogenetics requires tools from algebraic geometry), but as the sketches above suggest
the range of tools is extremely broad. The point is that modern mathematical biology is genuinely applied maths: its
techniques are chosen to suit the biological problems, not the traditional disciplinary subdivisions. Although some
previous acquaintance with graph theory and probability would be helpful, this course is meant to be self-contained
and will only assume knowledge of differential equations.
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Accelerated Math is a specialty math class where students in the middle school accelerate to the next grade level. Classes are designed to accomplish a goal where 8th grade students successfully complete Algebra I, and are ready for geometry or Algebra 2 in high school.
Special Project
Middle school accelerated math students participate in a nationwide math contest called Mathfax. It sharpens the participating students test taking math skills that are needed to do well on college entrance exams. It consists of a series of four tests from November to March.
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Classes Taught by Ray Russell
This course is designed to teach the concepts of single variable calculus while strengthening students foundational math skills. The objective of the course is to develop a students understanding of calculus through methods and applications, to prepare them for future courses in the areas of math and science, to prepare students for the AP exam, to encourage an appreciation for mathematics and to make connections between mathematics and their world. The major topics of study throughout the year include limits, derivatives, indefinite integrals, and definite integrals.
This course contains a comprehensive review of the real and complex number system. Other topics include relations, graphs, linear and polynomial functions, linear equations and inequalities, verbal problems, and exponential and logarithmic functions. Continuing goals of this course are the enhancement of a student's ability to reason deductively and to understand the need for precision of language in mathematics.
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Mathematics Reform for the `Real World'
Beginning of article
The changes in the way that mathematics is taught in school
described in the Learning page article "Math Lessons for the Real
World," Nov. 9, are exactly the wrong type of educational reform in
light of ongoing efforts to make the United States more
technologically competitive with the rest of the world.
Mathematics is a foundation for every engineering, scientific,
and technical field of study.
The 1989 National Council of Teachers of Mathematics (NCTM)
standards endorsed by Thomas Romberg, director of the National
Center for Research in Mathematical Sciences Education, represent a
drastic watering down of the secondary school mathematics
curricula. They dismiss …
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An Introduction to Modern Mathematical Computing
With Mathematica
by Jonathan M. Borwein and Matthew P. Skerritt
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple, Mathematica, and Matlab.
An Introduction to Modern Mathematical Computing: With Mathematica looks beyond teaching the syntax and semantics of Mathematica and similar programs, and focuses on why they are necessary tools for anyone who engages in mathematics. It is an essential read for mathematicians, mathematics educators, computer scientists, engineers, scientists, and anyone who wishes to expand their knowledge of mathematics. This volume will also explain how to become an experimental mathematician, and will supply useful information about how to create better proofs.
The text covers material in elementary number theory, calculus, multivariable calculus, introductory linear algebra, and visualization and interactive geometric computation. It is intended for upper-undergraduate students, and as a reference guide for anyone who wishes to learn to use the Mathematica program.
Places primary importance on the mathematics, rather than being a 'how to' manual for making computations
Integrates numerous worked examples and introduces all key programming constructions
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Tag Archive for mathematics redesign course
MADISON, FL –North Florida Community College is offering a new Basic Mathematics Redesign course, which is already becoming popular among NFCC students. The new computer-based course offers student's self-paced learning through web-assisted software called MyMathLab. NFCC was one of five colleges in Florida to receive funding from the state through the Bill and Melinda Gates Foundation to fund the redesign project.
NFCC's Basic Mathematics course was redesigned using student-centered coursework, which incorporates new teaching strategies, technology, tutoring, and individual and group learning. Basic Mathematics is a refresher to refine and develop basic mathematical skills. The course provides instruction and practice in computation involving the following: arithmetic with whole numbers, fractions and decimals, ratio and proportion, operations with integers and percents and applications of all of the previous.
The goal of the redesign is to encourage students to take an active role in their own learning; giving them freedom to learn at their own pace through activities most suited to their particular learning styles. The redesign is based upon NCAT's Emporium Model of instruction, replacing classroom lectures with a learning resource center model featuring interactive computer software and on-demand personal assistance from faculty and peer tutors. NFCC's Learning Resource Center is available five days per week and staffed with peer tutors for a wide range of hours allowing students to work at their convenience.
Students looking to enroll in NFCC's Basic Mathematics Redesign course must get the instructor's approval prior to registration. For more information, contact NFCC Redesign Course Coordinator and Instructor Efrain Bonilla at (850) 973-1718 or bonillae@nfcc.edu.
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Math-1B
Students are expected to attend all classes on time. Students who are absent more than 3 times may be dropped from the class. However, it is the studentsí responsibility to drop by the appropriate deadline. Petitions to drop after the dead line will not be considered by the instructor.
Homework:
Homework (HW) will be assigned every day and will be collected at the beginning of the next class meeting. No late HW will be accepted. HW is the key to success in this class. Plan to devote a minimum of TWO hours to HW for each class hour.
Quizzes:
Three quizzes are given in class. No makeup quizzes. Quizzes problems are similar to homework problems, and lecture examples.
Exams:
Three one-hour midterm examinations. No makeups except for extenuating circumstances assuming the student notifies the instructor as soon as the emergency arises.
Final Exam:
One two-hour comprehensive examination. Any student missing the final will receive an F grade for the course.
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Classes
Classes
Math 35, Summer 2010, General View of Math
This class is meant to give non-"math and science" majors a general overview of important and/or interesting topics in mathematics.
Syllabus
The Course Syllabus contains important logistical information regarding this course,
including the grading scheme and a list of the topics covered. The syllabus also, contains detailed information regrading homework assignments, quizzes,
and exams. My classroom policies are contained here as well (for example, the attendance policy).
Primes
Here are the files for the "Distribution of the Primes" lecture. To access the files, you will need to go to
and download the Mathematica Player that will allow you to manipulate the files. After downloading the program, right click on the below links and save the documents
to your computer. After that you should be able to access them via the Mathematica Player:
Sieve of Eratosthenes as a Mathematica Notebook.
Prime Spirals as a Mathematica Notebook.
Here is a pdf copy of the Prime Spiral that I covered in class.
Finals Information
As mentioned in the syllabus, the requirements for the final paper are as follows.
-Three references must be cited (preferably in APA style, but this is not too important). One of the references must not come from the internet.
-The paper should be expository in style and will be graded on quality of presentation of the topic, clarity, etc.
Suggested topics are as follows.
-The application of mathematics in your major.
-A further exploration of a topic covered in class.
-Exposition of some mathematical topic. Exemplary titles would be something like: "A Brief History of Infinity", "How Prime Numbers are Used in Everyday Life", "Math: Discovered or Created?", "The Influence of Mathematics on Modern Culture."
-Any other topic that you ask me about and I approve.
I am looking for a coherent presentation that demonstrates that you've spent some time exploring how mathematics influences the world around you.
The paper will be due on or before midnight, Friday, August 13. I would be more than happy to read over any papers before that time or help in exploring a topic, etc.
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Aliens From the Planet Nomathus
Students will know the derivation of the quadratic formula, and additionally how and why to use it. With these skills they will solve equations and come up with a fun way to teach the quadratic formula to a class of alien students from the planet Nomathus.
Introduction
At 9 o'clock this morning, as you were walking into your second period
class, a huge silver UFO overheated and crashed onto the PE field!
As
the dust and steam settled, a silver sliding door opened and 3 aliens
from the planet Nomathus crawled out.
While the unsuspecting sixth
graders got changed in the locker rooms, the devious aliens crept down
the ramp to explore the strange new planet they found themselves on.
They made their way to room 217 and stood in the doorway to your
classroom. By the time their UFO cools down enough for them to take off
again, you are going to have the opportunity to teach them a lesson:
The Quadratic Formula.
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From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
The Sullivan/Struve/Mazzarella AlgebraSeries was written to motivate students to "do the math" outside of the classroom through a design and organization that models what you do inside the classroom. The left-to-right annotations in the examples provide a teacher's voice through every step of the problem-solving process. The Sullivan exercise sets, which begin with Quick Checks to reinforce each example, present problem types of every possible derivation with a gradual increase in difficulty level. The new "Do the Math" Workbook acts as a companion to the text and to MyMathLab® by providing short warm-up exercises, guided practice examples, and additional "Do the Math" practice exercises for every section of the text.
10. Graphs of Quadratic Equations in Two Variables and an Introduction to Functions
10.1 Quadratic Equations in Two Variables
10.2 Relations
Putting the Concepts Together (Sections 10.1—10.2)
10.3 An Introduction to Functions
Chapter 10 Activity: Discovering Shifting
Chapter 10 Review
Chapter 10 Test
Appendix A: Table of Square Roots
Appendix B: Geometry Review
Answers to Selected Exercises
Graphing Answers Section
Applications Index
Subject Index
Photo Credits
New to this edition
New and Updated Features
Quick Check Exercises, which follow every example, are now numbered as the first problems in each section's exercise set to make them easier to assign as homework. Quick Checks provide the platform for student to get "into the text." By starting their homework with these Exercises, students will be directed to the instructional material in that section, increasing their confidence and ability to work any math problem–particularly when they are away from the classroom. Answers to the Quick Check exercises have been included in the back of the text.
The exercise sets have been updated and re-designed in a 2-column format for better organization and more visual appeal.
The Annotated Instructor's Edition contains annotated answers placed next to their respective exercises.
Content Changes
The former Chapter 8, Introduction to Graphing and Equations of Lines, and Chapter 9, Systems of Linear Equations and Inequalities, have been moved to Chapters 3 and 4, allowing instructors to cover "everything linear" early in the course.
The former Section 8.7, Variation, is now Section 7.9, so that content on variation appears in the same chapter as rational expressions.
New to the Supplements Package
The Do the Math Workbook offers a collection of 5-Minute Warm-Up exercises, Guided Practice exercises, and Do the Math exercises for each section in the text. These worksheets can be used as in-class assignments, as an in-lab study assignment or for homework.
The Videos on DVD offer a lecture for every section of the text. All videos include optional subtitles in English and Spanish.
MyMathLab enhancements include:
Substantially increased coverage of exercises (including Chapter Review exercises) to give students more opportunity for practice.
Authors in Action Videos, made with Camtasia, take students into the classrooms of authors Michael Sullivan, Katherine Struve, and Janet Mazzarella.
Video lectures and chapter test solutions on video, now with optional subtitles in English and Spanish.
Translating Word Problems Animations to help students practice the translation step of solving word problems.
An Interactive English/Spanish glossary that offers definitions of important mathematical terms in both English and Spanish.
Features & benefits
Sullivan Examples and Showcase Examples provide students with superior guidance and instruction when they need it most–when they are away from the instructor and the classroom.
Sullivan examples feature an active two-column format in which annotations are provided to the left of the algebra, mirroring the way that we read. The annotations explain what the authors are about to do in each step instead of what was just done.
Showcase Examples provide how-to instruction in an easy-to-understand, 3-column format. The left column describes a step, the middle column provides a brief annotation, as needed, to explain the step, and the right column presents the algebra.
Placed at the conclusion of most examples, the Quick Check exercises provide students with immediate reinforcement and instant feedback to determine their understanding of the concepts presented in the examples.
Students learn algebra by doing algebra. Throughout the textbook, the exercise sets are grouped into eight categories–some of which appear only as needed:
"Preparing For..."problems are located at the opening of a section. These test students' grasp of the prerequisite material for each new section.
Quick Check Exercises immediately follow the examples, allowing students to practice and apply what they have just learned. These exercises are also assignable as homework, so students can easily refer back to the relevant example for extra help.
Building Skills exercises are drill problems that develop the students' understanding of the procedures and skills in working with the methods presented in the section. These exercises are tied to the section objectives and are often linked back to an example.
Mixed Practice exercises offer comprehensive skill assessment by asking students to relate multiple concepts or objectives. These exercise sets may also include problems from previous sections so that students must first recognize the problem-type before using the appropriate technique to solve it.
Applying the Concepts exercises ask students to apply the mathematical concepts to real-world situations.
Extending the Concepts exercises go beyond the basics, using a variety of problems to sharpen students' critical-thinking skills.
Explaining the Concepts problems ask students to explain the concepts in their own words.
Graphing calculator exercises are optional and may appear at the end of a section's exercise set.
Study Skills features are a regular theme throughout the book, anticipating students' needs and providing the voice of an instructor.
Section 1.1: Success in Mathematics introduces the basics of study skills, such as what to do during the first week of the semester; what to do before, during and after class; how to use the text effectively; and prepare for an exam.
In Words features help students understand definitions and theorems by putting them in plain English, just like an instructor would do in class.
Work Smart features identify common errors to avoid and encourage students to work more efficiently.
Work Smart: Study Skills boxes appear throughout the book to remind students to stay organized and to manage their time in the most effective way possible.
Test preparation features help students make the most of their study time.
Chapter Tests reflect the levels and types of exercises that students are likely to see on an exam, providing a valuable study tool that decreases anxiety and stress.
The Chapter Test Prep Video CD provides step-by-step solutions to every problem from the Chapter Tests, and is included with every new copy of the book. These videos provide guidance and support when students need the most help: the night before an exam.
The Big Picture: Putting It Together chapter openers summarize the concepts and techniques previously presented and then relate this material to the concepts about to be presented.
Author biography
Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.
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Polynomials can be used to model many real-world data. We examine how to evaluate polynomial functions and how to create a polynomial given a number of points.
Internet Activity
Activity 7.1p Click this link to view your assignment for this activity.
Adobe Acrobat Reader You will need Adobe Acrobat Reader to open and print the activity. To download the reader, click "Adobe Acrobat Reader" above.
Exploration
Polynomial Basics and Terms This site gives a step-by-step description of polynomials, beginning with a variable such as x. It then goes on to define some vocabulary associated with polynomials.
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Linear Algebra And Its Applications, Update - With Cd - 3rd edition
Summary: Linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of li...show morenear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. ...show less
David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.
As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter.
Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or University Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.
Light shelving wear with minimal damage to cover and bindings. Pages show minor use. Help save a tree. Buy all your used books from Green Earth Books. Read. Recycle and Reuse!911.99 +$3.99 s/h
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INTERMEDIATE ALGEBRA
FALL 2012
PURPOSE: Intermediate Algebrais the state wide prerequisite
for students who will be taking mathematics courses which will count
towards bachelors degrees and satisfy general education requirements.
A major goal of this course is to increase students' mathematical
fluency.
Homework is the most important part of the course. If you keep up
with the homework you will probably do well. If you do not, you
probably will not do well. The midterms and final exam will cover the
material on the homework. The final exam is the deadline for all late
work.
TENTATIVE TEST DATES:
Midterm 1
Expressions
Sept. 12
Midterm 2
Equations
Oct. 10
Midterm 3
Graphing
Nov. 7
Midterm 4
Exponentials, Logarithms, Etc.
Dec. 5
OFFICE
Dar 114N
OFFICE HOURS
MW 10 - 10:30
TTh 10 - 11:35
PHONE
664 - 2116
e-mail address: steve.wilson@sonoma.edu
url:
Students will need either a scientific or a graphing calculator
for this class.TI 89 or better are not allowed. The final exam is the deadline for late work.
Students are responsible for announcements made in class.
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igonometry
Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling ...Show synopsisGain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling TRIGONOMETRY 6e, International Edition. This book's proven approach presents contemporary concepts in brief, manageable sections using current, detailed examples and high-interest applications. Captivating illustrations drawn from Lance Armstrong's cycling success, the Ferris wheel, and even the human cannonball show trigonometry in action. Unique Historical Vignettes offer a fascinating glimpse at how many of the central ideas in trigonometry began. TRIGONOMETRY 6e, International Edition, uses a standard right-angle approach with an emphasis on the study skills most important for success both now and in advanced courses, such as calculus. The book's proven blend of exercises, fresh applications, and projects is combined with a simplified approach to graphing and the convenience of new Enhanced WebAssign--a leading, time-saving online homework tool--and the innovative CengageNOW teaching system. With TRIGONOMETRY 6e, International Edition, you'll find everything you need for a thorough understand of trigonometry concepts now and the solid foundation you need for future coursework and career success
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Customer Reviews for Mcgraw-hill Education Key To Algebra, Books 1-10
Key To Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language and examples are easy to follow. Word problems relate algebra to familiar situations, helping students understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system. This kit contains only Books 1-10. Answers Notes for Books 1-4Books 5-7 and Books 8-10 are available separately, as well as the Key to Algebra Reproducible Tests Key To Algebra, Books 1-10
Review 1 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
easy to use!
I purchased this for my oldest son, who is now about to graduate. He did very well with it although book 4 was a little challenging. It is well written and easy to understand. I will be using it next year with my other son. I believe he will do very well with it. The only problem I have is that some times in the teachers guide, the answer is provided with no explaination as to how the answer is achieved. Since there were only a few like that we just skipped them. Other than that, it is great! I have recommended it to several of my homeschooling friends, and will continue to do so for years to come.
Share this review:
+1point
1of1voted this as helpful.
Review 2 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
Date:October 12, 2005
Nancy Evans
I never had Algebra in school and never thought I could teach it! I was given your curriculum from an old homeschooler. The first day I looked at it I reviewed 1 and 1/2 books just to see if I could understand it, and I did! It gave me a new confidence teaching a subject I knew little about. Wow! Thank you key curriculum Press.
Share this review:
+4points
4of4voted this as helpful.
Review 3 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
Date:September 10, 2005
Donna
Now using it on student number 5. Easy to teach from and learn from and well retained information.
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Mathematics for Economists
Learning goals
In order to understand and apply modern economic theories and concepts as well as to meet the requirements for course study it is necessary for students to be able to use learn basic mathematical theories. This Course has the goal to provide students with these mathematical resources.
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Essential Mathematics uses Grasshopper to introduce design professionals to foundation mathematical concepts that are necessary for effective development of computational methods for 3D modeling and computer graphics.
It has three parts. The first discusses vector math including vector representation, operation, and line and plane equations. The second part reviews matrix operations and transformations. The third part includes a general review of parametric curves with special focus on NURBS curves and the concepts of continuity and curvature.
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ALGEBRA II
Meets - All Year1 Credit
6301ALGEBRA IILevel - HonorsGrades 9-10
Meets - All Year1 Credit
Prerequisite: Geometry
Algebra II briefly reviews the principles taught in Algebra I and further develops these ideas with more advanced topics.Concepts include solving and graphing: equations and inequalities, system of equations and inequalities, polynomials, quadratic equations and some higher degree equations.A study is made of functions (linear, quadratic, absolute value, exponential, logarithmic, and power), and the operation of functions and their composition. Topics also include complex numbers and determinants.Problem solving and practical applications are emphasized.Conics and matrices are also included at Level 1.A graphing calculator is required for this course.
Calendar
June 19, 2013
Metacomet School 4th Grade Promotion Ceremony9:30 AM
Bloomfield High School Graduation - Belding Theater at the Bushnell6:00 PM
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are a community/technical college or primary/secondary school teacher who wants to make a difference in your classroom, Your First Step to STEM Success can help you start using Mathematica in your classes at a significant discount. No matter if you teach a STEM subject like math, physics, biology, or chemistry, or a subject like social science, business, or finance, this program can give you the tools to engage your students and increase their understanding of the concepts you're teaching.
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Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see. Suggested prerequisites for this course are MA211: Linear Algebra, MA221: Differential Equations, and either MA302/CS101: Introduction to Computer Science, or a background in some programming language. Programming ideas will be illustrated in pseudocode and implemented in the open-source high-level computing environment. Upon successful completion of this course, the student will be able to: show how numbers are represented on the computer, and how errors from this representation affect arithmetic; analyze errors and have an understanding of error estimation; be able to use polynomials in several ways to approximate both functions and data, and to match the type of polynomial approximation to a given type of problem; be able to solve equations in one unknown real variable using iterative methods and to understand how long these methods take to converge to a solution; derive formulas to approximate the derivative of a function at a point, and formulas to compute the definite integral of a function of one or more variables; choose and apply any of several modern methods for solving systems of initial value problems based on properties of the problem. This free course may be completed online at any time. (Mathematics 213)
This module addresses processes of quality control. Quality control is the process of monitoring and maintaining the reliability, accuracy, and completeness of the data during the conduct of a project A quiz, thought provoking question, and links for further study are provided to create a lesson around the 18-minute video. Educators may use the platform to easily "Flip" or create their own lesson for use with their students of any age or level.
Ever
Defines what Out of Range Values are and how to account for them in data collection and statistical analysis.Competencies/Skills that HIBB Addresses: Understand how to minimize out of range values when creating new data sets.
Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.
This well as information for students and educators.
In this seminar, participants learn about the solution of hyperbolic and elliptic equations by discontinuous Galerkin methods. Applications include flow and transport in heterogeneous porous media and electromagnetic waves
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0321036468
9780321036469 in the new table of contents and consistent with current teaching practices, involves the early introduction of graphing lines in a rectangular coordinate system and functions. This organization provides students with increased exposure to basic graphing and function concepts, an integral part of later mathematics courses, throughout their study of intermediate algebra. It also allows the integration of interesting applications featuring real world data in the form of ordered pairs, tables, graphs, and equations. As a natural follow-up to the treatment of linear equations in Chapter 3, systems of linear equations are now presented in Chapter 4. Also consistent with this approach, graphs of quadratic equations are included earlier in the text when quadratic equations are solved rather than with the material on conic sections as in previous editions. The chapter on exponential and logarithmic functions appears earlier as well.If you choose not to cover graphing linear equations and functions earlier as the new edition suggests, you can defer Chapters 3 and 4 and cover them later after either Chapter 6 or 7. Section 5.3 and the material on graphing and functions in Sections 6.1, 6.4, 6.6, and 7.5 can easily be delayed or omitted. «Show less... Show more»
Rent Intermediate Algebra 8th Edition today, or search our site for other Hornsby
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Pre-Calculus A/B
Pre-Calculus A/B
In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by "A" and "B" sections). Students apply technology, modeling, and problem-solving skills to the study of trigonometric and circular functions, identities and inverses, and their applications, including the study of polar coordinates and complex numbers. Vectors in two and three dimensions are studied and applied. Problem simulations are explored in multiple representations—algebraic, graphic, and numeric. Quadratic relations are represented in polar, rectangular, and parametric forms. The concept of limit is applied to rational functions and to discrete functions such as infinite sequences and series. The formal definition of limit is applied to proofs of the continuity of functions and provides a bridge to calculus.
All courses are written to California Department of Education standards and to national standards, as applicable.
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Welcome
I am excited to be the instructor for the Basic Math Class this year. Please refer to the Course Syllabus link if you have questions regarding class policies and procedures. The Assignments/Projects link lets you know which chapters we will be covering for the upcoming assessment date. If you have any questions or need additional instruction call me to set up a tutoring appointment.
Course Description: This course is designed for students to understand the concepts needed for mastery of basic computational skills. Basic Math will focus on student proficiency in operations with whole numbers, fractions, decimals, percents, measurement, graphing, geometry, ratios, proportions, and equations.
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I would love to help you understand math on a deeper level. Please let me know how I can help!Linear Algebra is a field of mathematics that involves vector spaces and matrices are often used when a basis is given. Various operations can be performed on vectors such as vector addition and scalar multiplication.
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Your student will be taking Algebra 2 next year at PLD, and I
wanted to contact you to share some important information regarding this class.
The 2011-2012 school year was the first time we administered End of Course Exams
(EOCs) from the Kentucky Department of Education. These tests are a piece of
our schools accountability design. Equally important, the EOC exam counted as
10% of a studentís spring semester grade and next school year will count as
15%. Additionally, every student at PLD will take the ACT during their junior
year, and the math portion covers pre-algebra, algebra, geometry, advanced
algebra and trigonometry, so a studentís success in Algebra 2 can increase their
math ACT score. The math teachers at PLD are dedicated to helping your student
be successful on both the Algebra 2 EOC and the ACT.
Students are
allowed to use calculators on both the EOC and the ACT, and this year we had
over 400 students take both the EOC and the ACT. Unfortunately, we do not have
the resources to provide a graphingcalculator for every student. We
encourage you to make sure your student begins the year in August with a
graphing calculator. While these calculators can be purchased at many stores,
we would like to offer you a deal! We can purchase
calculators from a distributor at the discounted price of $105. If you are
interested in purchasing a TI-84 Plus (Texas Instruments) calculator through the
school, please contact
donnah.martin@fayette.kyschools.us
and she will take your order.
Alternatively, we do have approximately 150 graphing calculators that can be
checked out through the library to use for the entire year. On the first day of
school, math teachers will have check out forms that students can take home to
obtain a parent signature and return to school. Upon return of the forms, a
graphing calculator can be issued from the library, but due to a limited number
of calculators, this is on a first-come, first-served basis.
Some
additional materials that students will need to be successful in Algebra 2 are
graph paper, pencils, notebook (3-ring or spiral), paper and extra AAA
batteries. Thank you for your help in making sure that your child is equipped
with the supplies they need to succeed at PLD.
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Contents
Math45 tutorials
Math
Mathematics is probably the most universal discipline in our world today. Every nation uses some form of math and it is used across nearly all fields of study. Math plays a vital role in the natural sciences, engineering, biomedicine and social sciences. From simply counting numbers to equations in quantum mechanics, there is not end to the study of mathematics. And the beauty of mathematics is, as david Hilbert put it, "Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."
Math, with all its applications, is a language that gives foundation to many other disciplines. That's is why for most of the fields we want to study, whether you want to be a biomedical engineer, computer programmer or a microeconomics analyst, we need to be adept in the concepts of math. For the social sciences, statistics is a necessity for analyzing all the data collected. In physics and other natural sciences, algebra and calculus are going to have to be the dialect in which you work.
With all these different applications of mathematics, it is no surprise that some of the greatest minds the world has ever seen are mathematicians. From ancient minds such as Archimedes and Pythagoras to household names such as Sir Isaac Newton and Albert Einstein, most of the scientist that have contributed to our society had a firm grasp of mathematics.
Since math is such an integral subject in academics, great emphasis is put on the discipline for students to excel. There are many awards and competitions based around the different skills in mathematics in the United States.Here is a list of some prestigious national competitions. (
American Invitational Mathematics Examination (AIME)
American Mathematics Contest 10 (AMC->10)
American Mathematics Contest 12 (AMC->12), formerly the American High School Mathematics Examination (AHSME)
With math being such a universal and integral area of study for mathematics, it is no wonder that there are a countless number of fields within the discipline. Whether you are trying to learn the intricacies of game theory or solving complex physics equations, you might find yourself struggling with new concepts. If you feel that you could use some help, and think you might need a math tutor, Tutorspree can help you connect with private tutors that can walk you through any mathematical problem that you are having trouble with.
We have some of the most talented math tutors and they are capable of creating a tutoring lesson plan that can help you accomplish your goals in mathematics whether it be learning how to solve inequalities for a algebra test or finding the area under a curve for your AP Calculus class.
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Here is a collection of math assessments written especially for high school. They were created with Wyoming Math Standards in mind, but since they are based on the NCTM standards any teacher from any state will probably find them useful.
Each assessment is written to be a short, quick assignment that will give the teacher an easy way to see progress in different areas. Wyoming teachers can think of these as 'mini BOE activities'. Most will take only a few minutes to complete, thus you don't have to make big changes in your current curriculum. We also tried to base these on real-life applications so students can see the relevance in everyday life.
There are a total of 60 assessments written for Algebra 1, Algebra 2, Geometry, and Trigonometry. You can use as many or as few as you would like.
Ideas and suggestions are welcome. We would like to keep updating and improving these exercises. Send suggestions to Jim Hoffman at hoffman@bgh4.k12.wy.us
Wyoming Math Standards:
1-Number Operations and Concepts
2-Geometry
3-Measurement
4-Algebra
5-Data Analysis and Probability
Each of the assessments has a short description including math skills used and standards assessed. You can download the files in Word format (.doc) and make any changes you like. Just click the title to download.
Trigonometry
Stock Options Graph Analysis: "Stock options" are not the same as stocks Stock options are agreements to buy or sell stocks at a later date…(math skills used: analyzing graphs, piecewise functions / standards 4,5)
Fire Trucks to Fill: Captain Don is in charge of directing fire trucks for a large grass fire. He currently has eight trucks coming…(math skills used: combined rates / standards 1,4,5)
Discus Sector: Discus is one of the most exciting events in track and field due to the speed and distances involved. It also makes…(math skills used: sectors / standards 2,3,4)
Seven Game Series: In many sports the champion is decided using a 7-game series. This means the first team to win four…(math skills used: probability / standards 1,4,5)
Mixed Up Pizza Order: Savanna called to order a pizza. The clerk at the store asked which toppings Savanna would like. There are 5 toppings…(math skills used: probability, factorial notation, writing expressions / standards 1,4,5)
Construction Workers Needed: The foreman at the construction site had 15 workers for 12 days to finish the first project. He knows the second project…(math skills used: related rates / standards 4)
Chain Reaction: Robin completed a chemistry experiment where a solution was placed in a test tube. Next an electric current…(math skills used: equation of a line, experimental data, best fit lines / standards 4,5)
Space Probes: Scientists are predicting a comet will collide with an asteroid in 30 days. Three different probes can be sent…(math skills used: equation of a line / standards 1,4,5)
Batter Up: Troy is a very good batter. He averages a hit every one out of three times he comes to bat. If Troy batted twice…(math skills used: probability / standards 5)
WiFi Access: The owner of a campground would like to install WiFi (wireless internet) access for his customers. He currently…(math skills used: distance formula, midpoint formula / standards 2,3)
Golden Corrals: Robert has thirty corral panels that measure 10 feet each. He originally set up the corral in a rectangular shape…(math skills used: Pythagorean thm, perimeter, area / standards 1,2,3)
Experimental Data: The data points in the table below came from an experiment that involved hydrogen (H) and carbon (C). All measurements…(math skills used: equation of a line, experimental data, best fit lines / standards 4,5)
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credit retrieval course is for students who have already taken this class and not earned credit. Students enrolled in this course will use an online curriculum called Compass Learning Odyssey (CLO). Within the CLO, students will take objective-based assessments which indicate what standards have been met and what skills need to be practiced and demonstrated by the student. Based on the results of the this objective-based assessment, an individual plan (called a CLO learning path) will developed by the teacher and communicated to the student. Successful completion of the CLO learning paths and the final summative assessment earns a passing grade (C) and .5 credit in Algebra 1. The second semester of Algebra 2 covers the following mathematical topics: radical functions, exponential and logarithmic functions, probability and statistics, systems of equations and inequalities, matrices, conic sections, and sequences and series. This course helps meet the state minimum requirements of 2.0 Mathematics credits. Please check with your district for more specific requirements.
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Study of algebraic concepts including linear and quadratic equations, inequalities and systems; polynomials; rational, exponential and logarithmic functions with emphasis on their numerical, graphical and algebraic properties and their applications. Prerequisite: Grade G.E.
Prerequisite(s) / Corequisite(s):
Grade
Course Rotation for Day Program:
Offered Fall and Spring.
Text(s):
Most current editions of the following:
College Algebra
By R. Blitzer (Prentice Hall) Recommended
College Algebra
By Beecher, Penna, and Bittinger (Addison-Wesley) Recommended
Course Objectives
To communicate mathematically in both written and verbal forms.
To reason with symbolic and graphical representations.
To use mathematics to solve real-world problems.
To use appropriate technology, such as graphing calculators and computers, to enhance their mathematical understanding.
To understand intuitively and formally the mathematical idea of a function and its real world applications.
Measurable Learning Outcomes:
• Simplify exponential, rational, and radical expressions and solve equations containing such expressions. • Solve linear, quadratic and polynomial equations and inequalities in both real number and complex number domains. • Solve equations involving absolute values. • Add, subtract, multiply and divide complex numbers. • Find and graph equations of lines in both point-slope and slope-intercept form. • Find equations for circles and graph circles in the Cartesian Plane. • Determine if a relation is a function. • Identify the domain and range of polynomial, radical, rational, exponential, logarithmic and piecewise-defined functions, and evaluate their values. • Graph polynomial, radical, rational, exponential, logarithmic and piecewise-defined functions. • Use the graph of a function to identify characteristics of the function such as specific values and symmetry. • Recognize graphs of common functions and graph transformations of these common functions. • Combine functions arithmetically and through composition and identify the domain of the resulting functions. • Describe and explain the fundamental concepts associated with inverse functions including the definition of one-to-one functions and the graphical interpretation of inverses. • Identify characteristics of the graphs of polynomial functions including end behavior and degree. • Apply the Fundamental Theorem of Algebra and related results to obtain a complete factorization of a polynomial function. • Identify vertical, horizontal and slant asymptotes of rational functions. • Simplify exponential and logarithmic expressions and solve exponential and logarithmic equations. • Solve systems of linear equations in two and three variables and nonlinear systems in two variables. • Solve real-world problems using a variety of linear, polynomial, rational, exponential and logarithmic models
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Grade 2 - The Worktext provides 2 colorful pages to practice the skills taught in the lesson. Understanding is emphasizedthrough the use of manipulatives then pictured on the worktext page before progressing to the abstract. A review of previously taught concepts is included at the bottom of the second page. Matt and Paddy are pictured throughout and make learning math fun with a variety of activities. A Chapter Review, a Cumulative Review, and a note to theparent are included for each chapter.
The Worktext provides two teacher-directed pages to review the skills taught in the lesson and to give individual help where needed. While emphasizing the farm themes introduced in the lessons, the book provides a variety of activities. A chapter review, a cumulative review, and a note to the parent are included at the end of each chapter.
This is a traditional geometry text, requiring the students to prove theorems. It is biblically based throughout and contains one lesson per chapter, relating Geometry and Scripture. Different colors and shading are used to distinguish among postulates, definitions, theorems, and constructions. Exercises are divided into three levels of difficulty. Dominion Thru Math exercises, scattered through each chapter, relate to the chapter openers, and offer the opportunity for students to the use technology in problem solving.
Analytic Geometry features, one per chapter, help students to make the algebra-geometry connection. Geometry Around Us features reveal some of Geometry's secret hideouts. Mind over Math brain teasers ar ... more
Math 4 Reviews provides two pages of review for each lesson. The first page reviews concepts taught in the lesson for the day. The second page reviews concepts taught in previous lessons and provides facts practice. A Chapter Review is included at the end of each chapter. The pages may be used any time after the lesson has been taught.
Full-color reduced student pages are contained on each page of the teacher's edition. Margins contain full solutions to both proofs and computational problems. Answers to cumulative review exercises contain the section number from which the question was taken. The margin contains section objectives and vocabulary.
Recommended assignments are given in three tracks: remedial, average, and honors classes. Resources are listed for each section including appendixes, quizzes from the test packet, activities in the Activity Manual and other resources. The bottom margin contains suggestions for presenting the lesson, including motivational ideas, and common student errors. Additional problems provide more examples, in-class ... more
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This interactive course covers the basics of geometry for high-school and senior high-school students. From the basics of what are points, and lines, this course goes all the day to explain dynamically and interactively what are similarities and dilatations.
This Interactive Learning App was developed by experienced teachers who have fine-tuned how to visually teach to students these fun concepts. An emphasis is put on interactive and dynamic learning.
Like all of our courses, it is meant to be fun and engaging and to allow the learner to progress by being challenged throughout!
The most complete interactive Trigonometry course on the web (or everywhere).
This course provides really solid training in the topic of high-school Trigonometry. What is viewed as a dry topic, is explained in an engaging and interactive way for students to learn and absorb what should be an important topic to learn, for students vying for scientific fields.
This topic starts from the basics of 'trig', to them explain the basics of the different important laws, as well as 'trig' functions and identities.
No other online Trigonometry course we know of does it so easily and gets the students learning, better and faster.
Probability is one of those fun topics that many students have a hard time with. This topic is more important that many think, as it teaches systematic and sequenced thinking.
In this fun and interactive course, the student will go on a journey to master high-school probability.
From understanding the basics of what outcomes are to computing basic linear probability, to then end with Compound random experiments.
Our collective teaching experience of over 100 years has helped us bring it down to basics, to help the student think through the process in an organized way. This approach is evident in all the courses on this site or on the mobile app stores.
Statistics is normally a very dry topic, that is meant as a 'toolbox' for students to almost memorize. At the right time, the right 'swiss army knife' is brought out to solve the problem at hand.
This course deals with the topic in a different way! The student progresses through the learning at a steady pace, while 'absorbing' the notions through strong visuals and interactions.
For example, one of the hardest topics to learn in stats is correlation. In this course, it will be shown through interactive learning where the student will understand it naturally by watching the examples and going through the directed exercises.
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Casio Takes New Approach to Graphing Calculator for Students
Casio's Prizm fx-CG10 plots graphs over full-color images to help students visualize concepts.
Casio Education has introduced the Prizm fx-CG10, a new concept in educational graphing calculators that aims to impart mathematical concepts in addition to providing standard graphing functions. Using a new tool known as Picture Plot, the Prizm enables users to plot graphs over full-color photographic images, such as an Egyptian pyramid or the jets of an outdoor fountain, as way of relating complex mathematical functions to real-world concepts such as design and engineering.
Casio also offers teachers online training using streaming video and downloadable supplemental activities, as well as a loaner program, which enables interested educators to try the Prizm for 30 days. An application for the program is
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The third edition of Languages and Machines: An Introduction to the Theory of Computer Science provides readers with a mathematically sound presentation of the theory of computer science at a level suitable for junior and senior level computer science majors. The theoretical concepts a...
Mathematics on the Internet: A Resource for K-12 Teachers, third edition, helps teacher educators, college students preparing to become mathematics teachers, and teachers in elementary, middle, and high schools to become better acquainted with some of the resource materials and information available...
For non-majors introductory energy courses in the departments of Physics, Geology, and Geography. The most complete book of its kind on the market, this text focuses on energy needs, trends, and long-term prospects and resource supplies. It addresses all the various issues involved w...
Far more "user friendly" than the vast majority of similar books, this text is truly written with the "beginning" reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize "Active Reading," a s...
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Skills Improvement Service (LSIS), this case study tackles the theme of progression through STEM subjects. By Newham Adult Learning Service, it describes an action research project that aimed to capture progression and learner voice data from a sample of learners who had recently completed a level two mathematicsA Mathematics Matters case study which looks at how advances in statistics allow us to analyse risks and consequences and so make informed decisions. Risks are an unavoidable part of modern life, but mathematicians and statisticians have developed a variety of methods to help mitigate its effects. These techniques enable hospitals, mathematicians work with epidemiologists to understand the spread of infections and mitigate their effects. Epidemics can threaten the can help industry to manage their use of fluids. Many industrial processes involve the complex movement of fluids, but predicting fluid behaviour can often be difficult. Mathematical models of fluid flow can help to improve manufacturing efficiency and reduce costs, looks at how Formula One teams use mathematical methods such as fluid mechanics and Navier-Stokes equations to improve performance. Every second counts in the fast-paced world of Formula One, so race teams use advanced mathematics to squeeze the best performance out of their cars. Computational…
This Mathematics Matters case study describes how mathematicians help to boost efficiency in the energy industry by mapping buried oil reserves. As oil supplies become harder and more expensive to reach, it's essential that we maximise the yield from available reservoirs in any way possible. Mathematicians are contributing…
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When 'studying calculus, you should have a good understanding of the following tables of formulas so you can efficiently and correctly solve calculus problems. An introduction to the basic concepts of calculus. The derivative ... The derivative, then takes a type of formula and turns it into another simiilar type of formula.
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academics
Mathematics
Pitzer's mathematics courses are designed to serve three purposes: general education; service to courses in social, behavioral and natural sciences; and the basis for the mathematics major.
Pitzer Advisers: D. Bachman, J. Grabiner, J. Hoste.
General Education in Mathematics
What is mathematics? What are its major methods and conclusions? How is it related to other subjects? What do modern mathematicians do? Several Pitzer courses specifically address these questions. These courses (described below) are: Mathematics 1, Mathematics, Philosophy and the "Real World"; Mathematics 5, Rubik's Cube and Other Mathematical Puzzles; Mathematics 6, Two Player Games; Mathematics 7, The Mathematics of Gambling, Mathematics, Art and Aesthetics; Mathematics 10, The Mathematical Mystery Tour; Mathematics 11, Theories of Electoral Systems; Mathematics 15, Mathematics for Teachers I: Number and Operation; Mathematics 16, Mathematics for Teachers II: Geometry and Data. These courses cover mathematical material that is exciting and sophisticated and yet accessible to students with a standard high school education in mathematics. As such they offer students an excellent opportunity to break fresh ground in kinds of mathematics they are not likely to have seen before. All of these courses, in addition to those in the precalculus and calculus sequences, meet Pitzer's Educational Objective in Formal Reasoning.
The Precalculus and Calculus Sequences
Mathematics 25, Precalculus, is designed to prepare students for Calculus I. The course reviews linear, quadratic and polynomial functions, before introducing the exponential, logarithmic and trigonometric functions. These are the functions most widely used in the quantitative social sciences and natural sciences. Mathematics 25 does not fulfill the Quantitative Reasoning Requirement.
Mathematics 30, 31 and 32 comprise the calculus sequence. The calculus, since it studies motion and change, is the key mathematical tool in understanding growth, decay and motion in the physical, biological, and social sciences. Pitzer offers Mathematics 30, 31 and 32 each year. Calculus is also offered at the other Claremont Colleges.
We also offer more advanced courses as part of The Claremont Colleges' Intercollegiate Mathematics program.
Requirements for the Major
A major in mathematics can be obtained by taking courses at Pitzer and the other Claremont Colleges.
A student must take a total of 13 courses for the Mathematics major, distributed as follows:
I. Calculus (3 courses):
Three semesters of calculus (Math 30, 31 and 32) with grades of C or better in each course. In some cases, a suitable score on the Pitzer Mathematics Placement exam, or Calculus AP exam, may be substituted for one or more of these courses.
III. Depth and Breadth (5 courses)
Five additional upper division mathematics courses (numbered 100 or above) chosen in consultation with the adviser. Ideally, these courses will expose the student to the major areas of mathematics as well as provide depth in at least one area.
IV. Applications and Connections (2 courses)
Two courses outside of mathematics that emphasize the application of mathematics or its connections to other disciplines: for example, courses in Computer Science, Science, Engineering, and History or Philosophy of Mathematics. These courses will be chosen in consultation with the adviser and normally will have mathematics courses from I, II, or III as prerequisites.
V. Colloquium
Students must attend the Mathematics Colloquium at least four times per semester for a total of two semesters, normally in the Senior year, and provide a written summary of the attended talks to their mathematics adviser.
Combined Programs: Pitzer College and Claremont Graduate University offer combined programs leading to both a bachelor of arts degree and a Master of Arts degree in applied mathematics, scientific computing, statistics and operations research, The Teaching of Mathematics, or Pure Mathematics. Students who are interested in one or more of these programs should consult with the mathematics faculty early in their undergraduate years.
Minor: The mathematics minor requires the student to take six graded courses: Mathematics 31, Mathematics 32, Mathematics 100, a course in linear algebra and two additional courses (which cannot include courses designed to prepare students for calculus) in Mathematics, at least one of which must be upper-division (numbered 100 or above), to be chosen by the student in consultation with a member of the Mathematics faculty. Students who satisfy the requirement for Calculus II and/or III by placement or by AP credit may constitute the 6 required letter-graded courses by additional mathematics courses (which cannot include course designed to prepare students for calculus), by computer science courses, or by courses with mathematics prerequisites in science, economics, or history and philosophy of mathematics.
In addition, students must attend the Mathematics Colloquium at least four times and provide a written summary of the attended talks to a member of the Mathematics faculty.
A catalog, "Mathematics Courses in Claremont," which lists all mathematics courses offered in The Claremont Colleges, is prepared each year by the Mathematics Field Committee. Students who want mathematics courses other than those listed below should consult this catalog. Copies are available in the office of the Registrar, from the mathematics faculty and on the World Wide Web.
Honors: Students will be recommended for Honors at graduation if their overall grade-point average is 3.5 or above, if their grade-point average in Mathematics is 3.5 or above and if they satisfactorily complete a Senior Exercise of honors quality. The Senior Thesis will be designed by the students and their Pitzer mathematics adviser, with the cooperation, if appropriate, of mathematics faculty elsewhere in Claremont.
AP Credit: A student who has a score of 4 or 5 on the Mathematics Calculus AB examination will receive credit for Mathematics 30 after passing Mathematics 31. Similarly, a student with a score of 4 or 5 on the Calculus BC exam will receive credit for Mathematics 30 and 31 after passing Mathematics 32. All new students are advised to take the math placement exam before registering for math 30, 31, or 32, regardless of their AP scores.
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Mathematics
Middle School mathematics classes equip students with the mathematical skills of a competent citizen in today's world. These skills include the ability to model situations mathematically, to estimate and compare magnitudes, to interpret graphs and statistics, to calculate probabilities, to evaluate numerical and spatial conclusions, to solve problems mentally as well as with paper, calculator, and computer, and to communicate effectively in these areas. Finally, while much of the above is exercised in the context of individual work, we have the further goal of fostering the skills and value of doing mathematics cooperatively with others.
Algebra I and Algebra I Honors: A rigorous high school-level first-year algebra course with emphasis on theory and application beyond mechanical processes. Problem solving is integral to both regular and honors level courses.
Geometry Honors: A high school course offered on the middle school campus for students who have completed Algebra I or Algebra I Honors. The study of geometry provides students with the opportunity to develop mathematic reasoning. Reasoning mathematically means developing and testing conjectures through deduction. Teaching students to make conjectures requires a spirit of experimentation and exploration in the classroom. Students will learn how to follow a proof and to determine whether a proof is valid or invalid. Initially, students will learn to write simple proofs and then advance to writing more difficult proofs. Algebra skills will also be integrated throughout each chapter and reinforced within the geometry exercises.
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Course Communities
Kepler: The Volume of a Wine Barrel
Course Topic(s):
One-Variable Calculus | History of Calculus
In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. This article provides you with visual imagery, much of it animated (via Java applets), to help share Kepler's ideas with your students.
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This is an instruction
system for a modern course in Trigonometry. It is designed for students who have
successfully completed Beginning, Elementary, and Intermediate Algebra courses.
The instruction emphasizes the Circular Functions. Other topics are developed
from the basic six circular functions.
Every objective
in the course is thoroughly explained and developed. Numerous examples illustrate
every concept and procedure. Student involvement is guaranteed as the presentation
invites the student to work through partial examples. Each unit of material ends
with an exercise specifically designed to evaluate the extent to which the objectives
have been learned and encourage re-study of any skills that were not mastered.
The instruction
is dependent upon reasonable reading skills and conscientious study habits. With
those skills and attitudes in place, the student is assured a successful experience
in learning those concepts associated with Trigonometry.
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Curriculum and Requirements
Related Links
For well over two thousand years, mathematics has been a part of the human search for understanding. Mathematical discoveries have come both from the attempt to describe the natural world and from the desire to arrive at a form of inescapable truth through careful reasoning that begins with a small set of self-evident assumptions Learning to think in mathematical terms is an essential part of becoming a liberally educated person.
Mathematics is an engaging field, rich in beauty, with powerful applications to other subjects. Thus we strive to ensure that Kenyon students encounter and learn to solve problems using a number of contrasting but complementary mathematical perspectives: continuous and discrete, algebraic and geometric, deterministic and stochastic, theoretical and applied. In our courses we stress mathematical thinking and communication skills. And in courses where it makes sense to incorporate technological tools, our students learn to solve mathematical problems using computer algebra systems, statistical packages, and computer programming languages.
New Students
For those students who want only an introduction to mathematics, or perhaps a course to satisfy a distribution requirement, selection from MATH 105, 106, 111, 116, 128 and SCMP 118 is appropriate. Students who think they might want to continue the study of mathematics beyond one year, either by pursuing a major or minor in mathematics or as a foundation for courses in other disciplines, usually begin with the calculus sequence (MATH 111, 112, and 213). Students who have already had calculus or who want to take more than one math course may choose to begin with the Elements of Statistics (MATH 106) and Data Analysis (MATH 206) or Introduction to Programming (SCMP 118). A few especially well-prepared students take Linear Algebra (MATH 224) or Foundations (MATH 222) in their first year. (Please see the department chair for further information.)
MATH 111 is an introductory course in calculus. Students who have completed a substantial course in calculus might qualify for one of the successor courses, MATH 112 or 213. MATH 106 is an introduction to statistics, which focuses on quantitative reasoning skills and the analysis of data. SCMP 118 introduces students to computer programming.
To facilitate proper placement of students in calculus courses, the department offers placement tests that help students decide which level of calculus course is appropriate for them. This and other entrance information is used during the orientation period to give students advice about course selection in mathematics. We encourage all students who do not have Advanced Placement credit to take the placement exam that is appropriate for them.
The ready availability of powerful computers has made the computer one of the primary tools of the mathematician. Students will be expected to use appropriate computer software in many of the mathematics courses. However, no prior experience with the software packages or programming is expected, except in advanced courses that presuppose earlier courses in which use of the software or programming was taught.
Course Requirements for the Major
There are two concentrations within the mathematics major: classical mathematics and statistics. The coursework required for completion of the major in each concentration is given below.
Classical Mathematics A student must have credit for the following core courses:
Three semesters of calculus (MATH 111, 112, 213, or the equivalent)
One semester of statistics (MATH 106 or 436, or the equivalent)
SCMP 118 Introduction to Programming
MATH 222 Foundations
MATH 224 Linear Algebra I
MATH 335 Abstract Algebra I or MATH 341 Real Analysis I
In addition, majors must have credit for at least three otherelective courses selected with the consent of the department. MATH 110 may not be used to satisfy the requirements for the major.
Statistics A student must have credit for the following core courses:
Three semesters of calculus (MATH 111, 112, 213 or the equivalent)
SCMP 118 Introduction to Programming
MATH 222 Foundations
MATH 224 Linear Algebra I
MATH 336 Probability
MATH 341 Real Analysis I
MATH 416 Linear Regression Models or MATH 436 Mathematical Statistics
In addition to the core courses, majors must also have credit for two elective courses from the following list:
MATH 106 Elements of Statistics
MATH 206 Data Analysis
MATH 216 Nonparametric Statistics
MATH 236 Random Structures
MATH 416 Linear Regression Models
MATH 436 Mathematical Statistics
Applications of Math Requirement
Mathematics is a vital component in the methods used by other disciplines, and the applied math requirement is designed to expose majors to this vitality. There are two ways to satisfy the requirement:
a) Earn credit for two courses (at least 1 unit) from a single department or program that use mathematics in significant ways. Typically, majors will choose a two-course sequence from the following list; other two-course sequences require departmental approval:
PHYS 140/145
ECON 101/102
PSYC 200 together with a 400-level Research Methods in Psychology course
b) Earn credit for a single math course that focuses on the development and analysis of mathematical models used to answer questions arising in other fields. The following courses satisfy the requirement, but other courses may satisfy the requirement with approval of the department:
MATH 258 Mathematical Biology
MATH 347 Mathematical Models
Classical mathematics majors may also use MATH 206, MATH 216, MATH 226, or MATH 416 to satisfy the requirement. Additionally, students choosing this option may not use the applied math course as one of the elective courses required for the major.
Depth Requirement
Majors are expected to attain a depth of study within mathematics, as well as breadth. Therefore majors should earn credit in one of four two-course upper-level sequences:
MATH 335/435 Abstract Algebra I & II
MATH 341/441 Real Analysis I & II
MATH 336/436 Probability and Mathematical Statistics
MATH 336/416 Probability and Linear Regression Models
Other two-course sequences may satisfy the requirement with approval from the department.
Senior Exercise
The Senior Exercise begins promptly in the fall of the senior year with independent study on a topic of interest to the student and approved by the department. The independent study culminates in the writing of a paper, which is due in November. (Juniors are encouraged to begin thinking about possible topics before they leave for the summer.) Students are also required to take the Major Field Test in Mathematics produced by the Educational Testing Service. Evaluation of the Senior Exercise is based on the student's performance on the paper and the standardized exam. A detailed guide on the Senior Exercise is available on the math department Web site under the link "mathematics academic program."
Suggestions for Majoring in Mathematics
Students wishing to keep open the option of a major in mathematics typically begin with the study of calculus and normally complete the calculus sequence, MATH 222 (Foundations), and either SCMP 118 or MATH 106 by the end of the sophomore year. A major is usually declared no later than the second semester of the sophomore year. Those considering a mathematics major should consult with a member of the mathematics department to plan their course of study.
The requirements for the major are minimal. Anyone who is planning a career in the mathematical sciences, or who intends to read for honors, is encouraged to consult with one or more members of the department concerning further studies that would be appropriate. Similarly, any student who wishes to propose a variation of the major program is encouraged to discuss the plan with a member of the department prior to submitting a written proposal for a decision by the department.
Students who are interested in teaching mathematics at the high-school level should take MATH 230 (Geometry) and MATH 335 (Abstract Algebra I), since these courses are required for certification in most states, including Ohio.
Honors in Mathematics
Eligibility
To be eligible to enroll in the Mathematics Honors Seminar, by the end of junior year students must have completed one depth sequence (MATH 335-435, MATH 336-416, MATH 336-436, MATH 341-441) and have earned a GPA of at least 3.33, with a GPA in Kenyon mathematics courses of at least 3.6. The student must also have, in the estimation of the mathematics faculty, a reasonable expectation of fulfilling the requirements for Honors, listed below.
To earn Honors in mathematics, a student must: (1) Complete two depth sequences (see list above); (2) Complete at least six 0.5-unit courses in mathematics numbered 300 or above; (3) Pass the Senior Exercise in the fall semester; (4) Pass the Mathematics Honors Seminar MATH 498; (5) Present the results of independent work in MATH 498 to a committee consisting of an outside examiner and members of the Kenyon Mathematics Department; (6) successfully complete an examination written by an outside examiner covering material from MATH 498 and previous mathematics courses; (7) Maintain an overall Kenyon GPA of at least 3.33; (8) Maintain a Mathematics Department GPA of at least 3.6.
Awarding Honors
Based on performance in all of the above-mentioned areas, the department (in consultation with the outside examiner) can elect to award Honors, High Honors, or Highest Honors; or not to award honors at all.
Requirements for the Minors
There are two minors in mathematics. Each minor deals with core material of a part of the discipline, and each reflects the logically structured nature of mathematics through a pattern of prerequisites. A minor consists of satisfactory completion of the courses indicated.
Statistics Five courses in statistics from the following: MATH 106 or 116, 206, 216, 236, 336, 416, 436. (Students may count at most one statistics course from another department. For example, ECON 375 or PSYC 200 may be substituted for one of the courses listed above.)
Our goal is to provide a solid introduction to basic statistical methods, including data analysis, design and analysis of experiments, statistical inference, and statistical models, using professional software such as Minitab, SAS, Maple, and R.
Deviations from the list of approved minor courses must be ratified by the Mathematics Department. Students considering a minor in mathematics or statistics are urged to speak with a member of the department about the selection of courses.
Cross-listed course The following course is cross-listed in biology and will satisfy the natural science requirement: MATH 258 Mathematical Biology
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SpeedStudy 8th Grade Math PC Mac New Sealed
New in Retail Box
This item ships as brand new and sealed in retail box. Item as shown in photo.
Specifications
Quantity in stock: Only 9 left, get yours while they last! Condition: New Manufacturer: SelectSoft Publishing UPC: 798936830081
Description
Features 25 standards-based lessons with skill-building animations
Reinforce learning with 300+ interactive quiz questions
Includes searchable database of over 500 key terms
Boost grades and test scores! Using step-by-step animations, real-time quizzes and a fun 3-D interface, Quickstudy gives students the tools they need to master key math concepts with over 25 lessons. Take the stress out of 7th Grade middle school math
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Book Description: Inside the Book:Preliminaries and Basic OperationsSigned Numbers, Frac-tions, and PercentsTerminology, Sets, and ExpressionsEquations, Ratios, and ProportionsEquations with Two Vari-ablesMonomials, Polynomials, and FactoringAlgebraic FractionsInequalities, Graphing, and Absolute ValueCoordinate GeometryFunctions and VariationsRoots and RadicalsQuadratic EquationsWord ProblemsReview QuestionsResource CenterGlossaryWhy CliffsNotes?Go with the name you know and trust...Get the information you need—fast!CliffsNotes Quick Review guides give you a clear, concise, easy-to-use review of the basics. Introducing each topic, defining key terms, and carefully walking you through sample problems, this guide helps you grasp and understand the important concepts needed to succeed.Master the Basics–FastComplete coverage of core conceptsEasy topic-by-topic organizationAccess hundreds of practice problems at CliffsNotes.com
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
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We will provide students with experiences that will enhance their ability to understand mathematics and the mathematical procedures necessary to make informed judgments on issues, to act as wise consumers, and to come to logical determinations as they pertain to personal and professional endeavors.
The purpose of the mathematics curriculum at Assabet Valley is to:
Provide a rigorous and relevant course of studies to meet the needs of all students Prepare all students for all graduation requirements of the Commonwealth of Massachusetts and of Assabet Valley Regional Technical High School Instruct students in how to reason, solve problems and to produce a level of competence required for their high school years and their adult lives Provide a rigorous and relevant course of studies to meet the needs of all students
Our curriculum provides students with the opportunities to develop a foundation from which they can pursue a profession and/or further their education at a higher level, such as two or four year colleges.
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Understanding Mathematics: From Counting to Calculus
Retail Price:
$24.95$21.21
Product ID - MM0221 | Availability - Now Shipping
Understanding Mathematics: From Counting to Calculus is an easy-to-read, non-technical book—beginning with counting and building up to more advanced math topics like calculus. Hundreds of detailed examples, shaded step-by-step boxes, and pictures emphasizing important concepts are included.
More Details
Understanding Mathematics is a comprehensive, easy-to-read, non-technical discussion covering a broad range of math topics ranging from counting to calculus. These math fundamentals, normally taught from first grade through college, are covered in detail with a special emphasis on real world examples and practical applications. Most importantly, this text provides an explanation of both the "why" and the "how" of math. The author conferred with teachers and students for feedback while writing the book, creating an end product that is a concise and easy-to-follow, step-by-step process of studying arithmetic, fractions, percentages, negative numbers, exponents, algebra, solving equations, functions, graphing, geometry, trigonometry, logarithms, complex numbers, calculus, and derivatives. Your student is sure to grasp the fundamentals of all these topics with the many bright illustrations and simple language contained within this 350-page book.
This book is perfect for homeschool families, any student who is struggling with understanding math concepts, and also adults who remain uncomfortable using math or explaining it to others. You will find it extremely useful for many years! Act now and order Understanding Mathematics
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Algebra II
Chapter 8: Sequences and Series - Qest on Friday, May 3. The students explore finding sums (series) of sequences, whether geometric or arithmetic. These can be found in many places in the world, such as building a pattern with bricks, etc. and needing to know how many total bricks are needed for the project.
Chapter 10: Introduction to Limits in Calculus: This includes introducing key vocabulary, working with function continuity, and learning differnt techniques to calculate the limit of a graph at a given value of x. -Quest on Thursday, May 16.
Pre-Algebra
Chapter 10-12: The students will be reviewing topics in Chapters 10-12. We will be practicing these on IXL, an online program that keeps track of students' progress and provides feedback. The IXL standards assigned are listed in the downloads and will be graded on May 15th. The students will be reviewing Surface Area and Volume of 3D figures, Probability & Graphs, Angles, and Transformations.
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MERLOT Search - category=2513&materialType=Drill%20and%20Practice
A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Tue, 18 Jun 2013 22:26:43 PDTTue, 18 Jun 2013 22:26:43 PDTMERLOT Search - category=2513&materialType=Drill%20and%20Practice
4434Graphing the line y = mx + b
This learning object gives the student the equation y = mx + b and first asks the student to move the line to the correct y-intercept and then rotate for the correct slopeFinding the Domain of a Function
This applet guides the user through the process of finding the domain of a function. Hints and feedback are plentiful and useful. New problems are generated at the click of a button.Exponent Rules
This site generates problems that test students' understanding of exponent rules. Hints and feedback are availableFinding the Domain and Range of a Function
Find the domain and range of a function given its graph.Level of Measurement
This module helps students identify level of measurement by giving them ten exercises in which they must determine whether a variable is being measured at the nominal, ordinal, or interval-ratio level.COW -- Calculus on the Web
This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus, Calculus I - III, Linear Algebra, Number Theory, and Abstract Algebra. The last two subject areas -- referred to as "books" on the site -- are under construction. To each topic within a book (for example, Epsilon and Delta within Calculus I) there is a "module" of approximately 20 to 30 problems. Each module also includes a help page of background material. The modules are interactive to some extent and often provide suggestions when wrong answers are entered.Discrete Math Resources
This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.Classroom Activities for Calculus
This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of what I know about group learning and how I use the activities. Many activities are quick combinations of discovery and practice. The statistics gets a bit lengthy, but I thought I'd include it anyway. As far as I recall, my text is only mentioned once and this posting should not be considered a commercial. Use the activities any way you want.Matrix Multiplier
This site contains a tool that allows a user to rapidly compute the product (or other formula) of two matrices.Inference for Means Activity
This activity enables students to learn about confidence intervals and hypothesis tests for a population mean. It focuses on the t-distribution, the assumptions for using it, and graphical displays. The activity also focuses on how to interpretations a confidence interval, a p-value, and a hypothesis test.
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Abstract
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in- depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
bazlov
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The philosophy behind our courses
Learning to do mathematics is not unlike
learning how to dance, or play the piano, or golf, or play hockey
or basketball. To be good at any of these activities, one must
spend hours in repetitious practice of laws of exponents or
pirouettes or scales, or a golf swing or skating backwards or
dribbling. You can participate recreationally without this level of
commitment to the activity but universities aren't about a
"recreational" involvement with learning. This is the
basis for our philosophy of learning mathematics.
Mathematics is a subject which builds upon
itself, not unlike a house. If you are building a house, the first
thing you put in is a foundation, then you put up some walls, and
finally you put on the roof. In a similar fashion, when you are
learning mathematics, first you learn some addition facts, and then
you use that knowledge to learn how to multiply, and then you use
your knowledge of multiplication to learn about division. All of
mathematics is like that, so if someone misses something early on
in his/her schooling because s/he is sick or moves or whatever,
then it makes it very difficult for him/her to learn any
mathematics which comes after that that uses the knowledge s/he
doesn't have. This is the primary reason why many people do poorly
in mathematics.
To avoid this happening in our program, we use
the mastery concept of learning. This means you do
not go on to study higher levels of mathematics until you have
demonstrated a good, solid knowldedge of every bit of mathematics
required to do the next level. This entails continuous assessment
and high pass standards, often as high as 80%. [This is not the
case for the Math 1051 course that is offered at the MLC as part of
the accelerated M103F/M1051 course.]
Our learning materials place emphasis on
building essential mathematics skills and fostering independent
study habits. The learning and exercise sequence will ensure that
new terms, concepts and proceses are well understood before they
are used in solving more complex problems. Explanations are given
which relate new concepts and skills to what is already known and
fundamental skills are used to solve relevant practical
problems.
Our M10XF and M1090 courses are NOT self-paced.
The textbooks used are written in a 'self-study' style so that
students can learn much of the content on their own. But the
classroom experience is essential for the student to put the
mathematics in context so that s/he knows how to use the
mathematics effectively and meaningfully. Class sizes are kept
small to allow students enough individual attention but students
are expected to work on their own for at least 8-10 hours
each week.
"A familiarity with mathematics is nice.
Understanding mathematical concepts is fine. But to participate in
post-secondary courses involving mathematics, there is an
expectation that the student can do mathematics.
This does not come with mere familiarity and/or understanding; this
comes with hours of practice, much of which is repetitive."
"Many people who have never had the occasion to learn what
mathematics is, confuse it with arithmetic and consider it a dry
and arid science. In actual fact it is the science which demands
the utmost imagination. One of the foremost mathematicians of our
century says very justly that it is impossible to be a
mathematician without also being a poet in spirit. It goes without
saying that to understand the truth of this statement one must
repudiate the old prejudice by which poets are suppose to fabricate
what does not exist, and that imagination is the same as "making
things up". It seems to me that the poet must see what others do
not see, must see more deeply than other people. And the
mathematician must do the same."
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This
class is open to all homeschooled students in 9th - 12th grades and who have
successfully completed Algebra 2. Academic performance should be average or
above while a passion for math is not required. Assuming you have met the
Algebra 2 requirement and the class is not full, you will be accepted into the
class.
AP
Statistics is not your typical math class and often you will need to think
critically and intuitively to address the statistical issues presented to you.
While this class is neither reading nor writing intensive you will be required
to do some of both. Past students report they spend 1 to 2 hours per day on AP
Statistics.
Why should you take statistics?
Statistics is the most widely applicable
branch of mathematics and is used by more people than any other kind of
math.AP Statistics is a great option
for students headed to a math- or science-related major, and who are looking
for another math course before graduation.
For students not headed into a math- or
science-related major, statistics is a useful and practical topic in today's
society and some argue that these students are better served by taking statistics
than calculus. The course does not depend heavily on advanced mathematical
computation but rather you are asked to use your critical thinking skills to
explain concepts and interpret results. To cement these concepts and assist you
with interpreting results hands-on investigations are used throughout the
course. Technology, such as the graphing calculator and statistical software,
is used to lower the drudgery of computation.
Class Meeting Time: Students do not "meet" at a scheduled
time, but work asynchronously to do their studying within their own
schedule.The Daily Message is posted
prior to midnight EST for the following school day permitting students in the Far East to work on today's assignment, today. Class
assignments for the upcoming two to three weeks are posted online permitting
students to work ahead if needed. Past families have found that I am very
accommodating to student and family travel plans and special events.
Course Format:
AP Statistics is a college level introductory
course in statistics in which students will learn to collect, organize,
analyze, and interpret data. These broad conceptual themes are:
Exploring
Data
Producing
Models Using Probability and Simulation
3.Experimental Design
4.Statistical Inference
Our class day begins with a Daily Message posting which expounds on the
day's statistical concepts. On a daily basis we read a few pages from our text
and apply these new concepts to problems. Students are able to daily test their
knowledge through multiple choice questions. Throughout the course we have
hands-on data collection assignments where we learn to apply what we are
learning to real data. These assignments never require the student to survey
neighbors or strangers and can be done from within the home. At the end of
every chapter the student has a multiple choice exam and a Free-Response
component that develops their ability to "pull all the pieces together."
Students are encouraged to ask questions of their peers and of me on our
communication board. The students utilize the online discussion boards to
interact with classmates, to post any questions they have from the reading material
and homework assignments, to answer classmates questions and most importantly
to discuss the interpretation of ourresults. The class operates asynchronously and I am available for live
chats on an as-needed basis.
Assessment:Student assessment will consist of a combination of
class participation, homework, hands-on activities, multiple choice and free
response exams. The exams are graded using a scoring guideline in the same
manner as the AP exam is scored. My experience with designing scoring rubrics
and assessing student responses will help me ensure that the students taking
this course are well-prepared for a good score on the AP® Statistics exam next
spring!
3.2007
& 2002 AP Stat College Board Released exam. (These books are purchased in
bulk by Mrs. Matheny and then repurchased by the students in March 2013, $10)
Instructor Qualifications:
I earned a BS and MS in Ceramic Engineering
from The Ohio State University and an MBA from ClarkUniversity.
Prior to homeschooling , I worked full-time for twenty
years in industry as a Research Engineer and later as a Manager of Engineering.
In addition, I hold five US Patents. During these years I found statistical
methods to be a very valuable tool and an integral part of my work life. While
in Worcester, MA,
I was an adjunct professor for several years teaching both Statistics, and
Production & Operations Management at both AssumptionCollege and AnnaMariaCollege. For the past fifteen years I
have been a home schooling mom to my two sons; one is now in college and the
other is in high school. This will be my fifth year teaching AP Statistics
on-line through PA Homeschoolers. I'm looking forward to this coming year!
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You are on Coach Snider's website. I teach Support Coordinate Algebra and Coordinate Algebra. I hope you find this website useful.
706-632-2081 Fannin County High School jsnider@fannin.k12.ga.us- email
I have fourth block planning if you need to contact me.
Thanks,
Coach Snider
EOCT updated April 19, 2013
Students be preparing in freshman success and at home for your EOCT in Coordinate Algebra. Any old tests and online tests you can find will be a big help when studying. Many of the practice tests...
This is the first course in a sequence of courses designed to provide students with a rigorous program of study in mathematics. It includes the following: relationships between quantities, reasoning with equations and inequalities, linear and exponential functions, describing data, transformations in the coordinate plane, and connecting algebra and geometry through coordinates.
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Class Downloads
Quadrilateral Characteristics
(78.27 KB)
Translating Expressions
(349.73 KB)
Inequality
(293.58 KB)
Consecutive integers
(218.7 KB)
Tutoring Schedule
(583.47 KB)
Inequalities 2
(175.86 KB)
Solving Linear Inequalities
(111.83 KB)
Solving Equations
(364.43 KB)
Coordinate Algrebra PPT's
Unit Analysis
(221.31 KB)
Metric System
(1.27 MB)
Customary System
(592.38 KB)
Conversion Factors
(389.1 KB)
Percents
(248.39 KB)
Algrebra Syllabus
(187.9 KB)
Math 1
Adding/Subtracting Polynomials
(273.92 KB)
Dividing Polynomials
(437.25 KB)
Factoring Trinomials
(724.99 KB)
GCF Factoring
(273.41 KB)
Multiplying Monomials
(232.96 KB)
Multiplying Polynomials
(530.94 KB)
Pascal's Triangle
(216.91 KB)
Review Self-Test
(161.99 KB)
This does not include Pascal's Triangles for Review. Your student has received a worksheet with problems over this topic.
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This textbook, aimed at undergraduate mathematicians, covers the main topics in number theory; that is properties of ordinary numbers and fractions. Many modern aspects are covered, including (briefly) the latest work on Fermat's last theorem. Both elementary and more advanced topics are included, with large problem sections and hints on their solution. The current reprinting of this edition not only includes some minor corrections but also an extra 50 pages containing the latest information on some conjectures, some new facts (for instance about Mersenne primes), new proofs and problems as well as a number of minor
corrections.
Readership: Third year and postgraduate students taking a course in number theory.
H. E. Rose, Lecturer in Mathematics, University of Bristol
"It is of interest both to students and teachers working in this field." - EMS Newsletter, No. 21, 1996
"An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory." - American Mathematical
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Special Features
Dynamic Grapher Choose a parameter of a function and investigate how it effects the function. Have students problem-solve to find what is happening and why.
Advanced Statistic functions
Hypothesis testing functions include:
1- and 2-Sample z-tests. F-tests, and t-tests
1- and 2-Proportion z-tests
Linear regression t-test
Chi-Square test
Confidence interval functions include:
1- and 2- Sample z-intervals, and t-intervals
1- and 2-Proportion z-intervals
CONICS CONICS are now a problem solving activity. Find the conic you want, enter the parameter, then draw it. Then find out all the critical points and information on the conic using the Graph-Solver. Discover how the critical points are related to the function.
Financial & Business Functions
The "PLUS" is all business when it comes to advanced financial calculations. It can quickly calculate Time-Value-of-Money (TVM), simple and compound interest, cash flowsm and amortization. It also performs conversions and calculations for cost/sell/margin, days, and bonds.
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Lecture 5: WildLinAlg5:Change of coordinates and determinants
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Lecture Details :
In this video we discuss the fundamental problem of Linear Algebra, namely how to invert a linear change of coordinates. We also introduce determinants, via bi-vectors and tri-vectors.
Course Description :
This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.
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Euclidean plane geometry is one of the oldest and most beautiful of subjects in mathematics, and Methods for Euclidean Geometry explores the application of a broad range of mathematical techniques to the solution of Euclidean problems.
The book presents numerous problems of varying difficulty and diverse methods for solving them. More than a third of the book is devoted to problem statements, hints, and complete solutions. Some exercises are repeated in several chapters so that students can understand that there are various ways to solve them.
The book offers a unique and refreshing approach to teaching Euclidean geometry, which can serve to enhance students' understanding of mathematics as a whole.
Having completed a survey of lines, polygons, circles, and angles, we come to another collection of well-known figures in the plane: ellipses, parabolas, and hyperbolas. In what situations do these figures appear? What is our motivation for studying them?
One way in which these figures arise quite naturally is when we try to find answers to questions of the type, "What is the set of all points (loci) of a plane that satisfy a given property?" Another is when we wish to understand the trajectory of a moving point. Yet a third situation occurs when we seek to describe the intersection of two surfaces in space.
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Category theory is a branch of mathematics that emerged in the 1950s to understand how the different areas of mathematics relate to each other. Today, its influence pervades nearly all of mathematics, in addition to being an important area of study in its own right. This course will cover the basic concepts of category theory, with an emphasis on intuition and examples.
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Mr. W Schapiro Math Concepts MA 60
MA 60 Math concepts is a skills class designed to support the student in being successful in their Algebra class (MA 28). The emphasis of this class is to reinforce basic skills along with the newly learned concepts in algebra. Having the extra class period gives students more time for guided practice.
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Geometry of Quantum Theory. Varadarajan, V.S. This is a book about the mathematical foundations of quantum theory. Its aim is to develop the conceptual basis of modern quantum theory from general principles using the resources and techniques of modern mathematics.
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Description
For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus.
The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Preface
1 First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
1.7 Population Models
1.8 Acceleration-Velocity Models
2 Linear Equations of Higher Order
2.1 Introduction: Second-Order Linear Equations
2.2 General Solutions of Linear Equations
2.3 Homogeneous Equations with Constant Coefficients
2.4 Mechanical Vibrations
2.5 Nonhomogeneous Equations and Undetermined Coefficients
2.6 Forced Oscillations and Resonance
2.7 Electrical Circuits
2.8 Endpoint Problems and Eigenvalues
3 Power Series Methods
3.1 Introduction and Review of Power Series
3.2 Series Solutions Near Ordinary Points
3.3 Regular Singular Points
3.4 Method of Frobenius: The Exceptional Cases
3.5 Bessel's Equation
3.6 Applications of Bessel Functions
4 Laplace Transform Methods
4.1 Laplace Transforms and Inverse Transforms
4.2 Transformation of Initial Value Problems
4.3 Translation and Partial Fractions
4.4 Derivatives, Integrals, and Products of Transforms
4.5 Periodic and Piecewise Continuous Input Functions
4.6 Impulses and Delta Functions
5 Linear Systems of Differential Equations
5.1 First-Order Systems and Applications
5.2 The Method of Elimination
5.3 Matrices and Linear Systems
5.4 The Eigenvalue Method for Homogeneous Systems
5.5 Second-Order Systems and Mechanical Applications
5.6 Multiple Eigenvalue Solutions
5.7 Matrix Exponentials and Linear Systems
5.8 Nonhomogeneous Linear Systems
6 Numerical Methods
6.1 Numerical Approximation: Euler's Method
6.2 A Closer Look at the Euler Method
6.3 The Runge-Kutta Method
6.4 Numerical Methods for Systems
7 Nonlinear Systems and Phenomena
7.1 Equilibrium Solutions and Stability
7.2 Stability and the Phase Plane
7.3 Linear and Almost Linear Systems
7.4 Ecological Models: Predators and Competitors
7.5 Nonlinear Mechanical Systems
7.6 Chaos in Dynamical Systems
8 Fourier Series Methods
8.1 Periodic Functions and Trigonometric Series
8.2 General Fourier Series and Convergence
8.3 Fourier Sine and Cosine Series
8.4 Applications of Fourier Series
8.5 Heat Conduction and Separation of Variables
8.6 Vibrating Strings and the One-Dimensional Wave Equation
8.7 Steady-State Temperature and Laplace's Equation
9 Eigenvalues and Boundary Value Problems
9.1 Sturm-Liouville Problems and Eigenfunction Expansions
9.2 Applications of Eigenfunction Series
9.3 Steady Periodic Solutions and Natural Frequencies
9.4 Cylindrical Coordinate Problems
9.5 Higher-Dimensional Phenomena
References for Further Study
Appendix: Existence and Uniqueness of Solutions
Answers to Selected Problems
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Oh no, not yet another introduction to elementary number theory! Like so many other books, this one treats topics that have become standard in recent years (the six chapters cover primes, congruences, public-key cryptography, quadratic reciprocity, continued fractions and elliptic curves), and it has exercises with selected solutions. \par One cannot expect fantastic new proofs in an area which has been covered in countless textbooks, and so such a book has to be judged by its exposition. In this respect, the author succeeds admirably: the book is written in an entertaining style; it even contains a few jokes, such as Lenstra's proof that there are infinitely many composite numbers, and subjects that are usually quite dry are presented in a lively way. In fact, my favorite chapter in this book is the one on continued fractions. In (too) many sources, discussing continued fractions means going through an almost endless string of identities proved by induction. The basic relations are proved here, too, but then the text quickly moves on to interesting problems, such as Euler's expansion of $e$ or problems concerning the continued fractions of algebraic numbers of degree $>2$. \par What distinguishes this text from other books is the computational approach, which the author takes seriously. He uses the software system Sage developed by himself throughout the book, from computing greatest common divisors to proving the associativity of the group law on an elliptic curve, or for determining its rank. It doesn't take much to predict that software systems will play an ever increasing role in the future of mathematics, and having a text explaining a powerful system such as Sage has two advantages: it gives the students a tool to do calculations that illustrate even the most abstract concepts, and, simultaneously, introduces them to an open source software that can later be applied profitably for studying research problems. \par I have noticed only one error: there is a (small but serious) gap in the proof of quadratic reciprocity via Gauss sums (if $R \subset S$ are rings and if the congruence $a \equiv b \bmod q$, where $a, b, q \in R$, holds in $S$, then it does not necessarily hold in $R$; this conclusion is in general not valid if e.g. $q$ becomes a unit in $S$), and closing this gap requires a little algebraic number theory (or the introduction of finite fields). \par Yet another introduction to number theory? Yes, but an excellent one, with the additional bonus of a) presenting material that can be covered in one semester, and b) introducing the readers to a powerful software system. [Franz Lemmermeyer (Jagstzell)]
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Purchasing Options
Features
Discusses three common numerical areas: interpolation and quadratures, linear and nonlinear solvers, and finite differences
Explains the most fundamental and universal concepts, including error, efficiency, complexity, stability, and convergence
Addresses advanced topics, such as intrinsic accuracy limits, saturation of numerical methods by smoothness, and the method of difference potentials
Provides rigorous proofs for all important mathematical results
Includes numerous examples and exercises to illustrate key theoretical ideas and to enable independent study
Contains a solutions manual for qualifying instructors
Summary
A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study.
An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon's potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation.
By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.
Editorial Reviews
"… presents the general methodology and principles of numerical analysis, illustrating the key concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on hoe to efficiently represent mathematical models for computer-based study. … this book provides a pedagogical account of the fundamentals of numerical analysis. … provides a foundation link to more specialized computational work in mathematics, science, and engineering. … Discusses three common numerical areas: interpolation and quadratures, linear and nonlinear solvers, and finite differences. Explains the most fundamental and universal concepts, including error, efficiency, complexity, stability, and convergence. Addresses advance topics, such as intrinsic accuracy limits, saturation of numerical methods by smoothness, and the method of difference potentials. Provides rigorous proofs for all important mathematical results. Includes numerous examples and exercises to illustrate key theoretical ideas and to enable independent study. " — In Mathematical Reviews, Issue 2007g
"It is an excellent book, having a wide spectrum of classical and advanced topics. The book has all the advantages of the Russian viewpoint as well as the Western one." —David Gottlieb, Brown University, Providence, Rhode Island, USA
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