Pearson - Mathematical Ideas, 11/E - Charles D. Miller, Vern E. Heeren & John Hornsby

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Description

One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solution--bringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies this same strategy of engaging students through descriptions of video clips from popular cinema and television to the textbook. Alongside fresh data and tools, this Eleventh Edition uses up-to-the-minute images as well as old favorites of math being done in Hollywood. In addition, examples are clarified with additional annotations, the margin notes have been freshened, and Chapter 14: Personal Financial Management has been updated to meet the needs of today's students. With great care and effort, Vern Heeren and John Hornsby have crafted this new edition to serve the needs of today's students and instructors.

Features

Varied Exercise Sets The authors present a variety of exercises including drill, conceptual, and applied problems. They use graphs, tables, and charts when appropriate. Most sections include a few challenging exercises that require students to extend the ideas presented in the section. To address the issue of writing across the curriculum, most exercise sets require the student to answer a number of exercises by writing a few sentences.

For Group Discussion or Individual Investigation These entries, retitled in this edition, encourage students to discuss their reasoning processes. Students gain a deeper understanding of key mathematical concepts by taking what they've just learned one step further.

Problem-Solving Hints Special paragraphs labeled Problem-Solving Hints relate the discussion of problem-solving strategies to techniques presented earlier in the chapter.

Collaborative Investigations In response to instructor requests, we continue to address the issue of cooperative learning in the end-of-chapter feature Collaborative Investigation. These exercises can be done in small groups or with the whole class, and are designed to promote communication about mathematics topics.

New To This Edition

Every chapter now begins with an application taken from a movie or television program showing good, bad, and ugly mathematics--because students can learn from all three. For example, Chapter 1 begins with the accurate and infamous scene from Die Hard with a Vengance where the characters played by Bruce Willis and Samuel L. Jackson must solve a math problem involving jugs of water to keep a bomb from exploding.
In this edition, the authors have clarified the outline format of the text. Within each section, the sub-sections are now titled, making it much easier to find key concepts. Each example is also titled, allowing students to easily see the key concept presented and helping instructors determine which material to review in class.
Numerous carefully written examples illustrate concepts and skills introduced, and give students step-by-step directions for solving similar problems. New annotations clarify these examples. They prepare students for the exercises that follow.
Margin notes have long been a popular feature of this text and this edition will be no exception. Popular notes, especially ones related to lives of mathematicians, historical vignettes, stamp and coin reproductions, anecdotes, newspaper and magazine articles, and current research in mathematics remain, but new notes have been added. Most new notes focus on the movie and television theme of this edition. These tidbits remind students that math can be fun and interesting.
For the first time, this text is available with an Annotated Instructor’s Edition. Answers are shown on exercise pages, when possible, and when space does not allow, answers are found in the back of the text.

Table of Contents

1 The Art of Problem Solving

1.1 Solving Problems by Inductive Reasoning

1.2 An Application of Inductive Reasoning: Number Patterns

1.3 Strategies for Problem Solving

1.4 Calculating, Estimating, and Reading Graphs

Extension: Using Writing to Learn About Mathematics

Collaborative Investigation: Discovering Patterns in Pascal’s Triangle

Chapter 1 Test

2 The Basic Concepts of Set Theory

2.1 Symbols and Terminology

2.2 Venn Diagrams and Subsets

2.3 Set Operations and Cartesian Products

2.4 Surveys and Cardinal Numbers

2.5 Infinite Sets and Their Cardinalities

Collaborative Investigation: Surveying the Members of your Class

Chapter 2 Test

3 Introduction to Logic

3.1 Statements and Quantifiers

3.2 Truth Tables and Equivalent Statements

3.3 The Conditional and Circuits

3.4 More on the Conditional

3.5 Analyzing Arguments with Euler Diagrams

Extension: Logic Problems and Sodoku

3.6 Analyzing Arguments with Truth Tables

Collaborative Investigation: Logic Problems and Sodoku Revisited

Chapter 3 Test

4 Numeration and Mathematical Systems

4.1 Historical Numeration Systems

4.2 Arithmetic in the Hindu-Arabic System

4.3 Conversion between Number Bases

4.4 Clock Arithmetic and Modular Systems

4.5 Properties of Mathematical Systems

4.6 Groups

Collaborative Investigation: A Perpetual Calendar Algorithm

Chapter 4 Test

5 Number Theory

5.1 Prime and Composite Numbers

5.2 Selected Topics from Number Theory

5.3 Greatest Common Factor and Least Common Multiple

Extension: Modern Cryptography

5.4 The Fibonacci Sequence and the Golden Ratio

Extension: Magic Squares

Collaborative Investigation: Investigating an Interesting Property of Number Squares

Chapter 5 Test

6 The Real Numbers and Their Representations

6.1 Real Numbers, Order, and Absolute Value

6.2 Operations, Properties, and Applications of Real Numbers

6.3 Rational Numbers and Decimal Representation

6.4 Irrational Numbers and Decimal Representation

6.5 Applications of Decimals and Percents

Extension: Complex Numbers

Collaborative Investigation: Budgeting to Buy a Car

Chapter 6 Test

7 The Basic Concepts of Algebra

7.1 Linear Equations

7.2 Applications of Linear Equations

7.3 Ratio, Proportion, and Variation

7.4 Linear Inequalities

7.5 Properties of Exponents and Scientific Notation

7.6 Polynomials and Factoring

7.7 Quadratic Equations and Applications

Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?

Chapter 7 Test

8 Graphs, Functions, and Systems of Equations and Inequalities

8.1 The Rectangular Coordinate System and Circles

8.2 Lines and Their Slopes

8.3 Equations of Lines and Linear Models

8.4 An Introduction to Functions: Linear Functions, Applications, and Models

8.5 Quadratic Functions, Applications, and Models

8.6 Exponential and Logarithmic Functions, Applications, and Models

8.7 Systems of Equations and Applications

Extension: Using Matrix Row Operations to Solve Systems

8.8 Linear Inequalities, Systems, and Linear Programming

Collaborative Investigation: Living with AIDS

Chapter 8 Test

9 Geometry

9.1 Points, Lines, Planes, and Angles

9.2 Curves, Polygons, and Circles

Extension: Geometric Constructions

9.3 Perimeter, Area, and Circumference

9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem

9.5 Space Figures, Volume, and Surface Area

9.6 Transformational Geometry

9.7 Non-Euclidean Geometry, Topology, and Networks

9.8 Chaos and Fractal Geometry

Collaborative Investigation: Generalizing the Angle Sum Concept

Chapter 9 Test

10 Trigonometry

10.1 Angles and Their Measures

10.2 Trigonometric Functions of Angles

10.3 Trigonometric Identities

10.4 Right Triangles and Function Values

10.5 Applications of Right Triangles

10.6 The Laws of Sines and Cosines: Area Formulas

Collaborative Investigation: Making a Point about Trigonometric Function Values

Chapter 10 Test

11 Counting Methods

11.1 Counting by Systematic Listing

11.2 Using the Fundamental Counting Principle

11.3 Using Permutations and Combinations

11.4 Using Pascal’s Triangle

11.5 Counting Problems Involving “Not” and “Or”

Collaborative Investigation: Solving a Traveling Salesman Problem

Chapter 11 Test

12 Probability

12.1 Basic Concepts

12.2 Events Involving “Not” and “Or”

12.3 Conditional Probability; Events Involving “And”

12.4 Binomial Probability

12.5 Expected Value

Extension: Estimating Probabilities by Simulation

Collaborative Investigation: Finding Empirical Values of π

Chapter 12 Test

13 Statistics

13.1 Frequency Distributions and Graphs

13.2 Measures of Central Tendency

13.3 Measures of Dispersion

13.4 Measures of Position

13.5 The Normal Distribution

Extension: How to Lie with Statistics

13.6 Regression and Correlation

Collaborative Investigation: Combining Sets of Data

Chapter 13 Test

14 Personal Financial Management

14.1 The Time Value of Money

Extension: Annuities

14.2 Installment Buying

14.3 Truth in Lending

14.4 The Costs and Advantages of Home Ownership

14.5 Investing

Collaborative Investigation: To Buy or to Rent?

Chapter 14 Test

Courses

Liberal Arts Mathematics (Mathematics)

Previous Edition(s)

Mathematical Ideas, 10/E
Miller, Heeren & Hornsby
©2004 | Pearson | Cloth; 944 pp | Instock
ISBN-10: 0321168089 | ISBN-13: 9780321168085
Suggested retail price: $153.33 Net price: $115.00 (What's this?)Brief Description |
The tenth edition of Mathematical Ideas is the best ever! We have continued with the features and pedagogy that have made this book so successful over the years and at the same time, we've spent a considerable amount of time to incorporate fresh data, new photos, and new content (by way of a new chapter on trigonometry). We have tried to reflect the needs of our users—both long-time readers and those new to the Math Ideas way of teaching liberal arts math. We hope you'll be pleased with the results.

Like its predecessors, this edition has been designed with a variety of students in mind. It is well-suited for several courses, including the aforementioned liberal arts audience, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle school teachers. Ample topics are included for a two-term course, yet the variety of topics and flexibility of sequence make the text suitable for shorter courses as well. Our main objectives continue to be to provide comprehensive coverage of topics, appropriate organization, clear exposition, an abundance of examples, and well-planned exercise sets with numerous applications.
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In this section:

Author Bios

Author Bios

Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.

John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country.

Websites and Online Courses

In this section:

Websites and Online Courses

MyMathLab with eBook -- Instant Access -- for Mathematical Ideas and Mathematical Ideas Expanded, 11/E
Miller, Heeren & Hornsby
©2008 | On-line Supplement; 1088 pp | Access Code Required | Live
ISBN-10: 0321369645 | ISBN-13: 9780321369642
Online purchase price: $82.00 | Students, buy access Take a Tour | More Info

MyMathLabPlus for Mathematical Ideas Expanded Edition, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Website; 1088 pp | Live
ISBN-10: 032171654X | ISBN-13: 9780321716545
Online purchase price: $92.00More Info

In this section:

Instructor Resources

Downloadable Instructor Resources
Other Instructor Resources

Student Resources

Websites and online courses
Other student resources

eLearning & Assessment

Websites and Online Courses

Course & Discipline Resources

For the Mathematics Discipline

Active Learning Questions (Download only) for Mathematical Ideas, 11/E
Miller
©2008 | Pearson | On-line Supplement | Live
ISBN-10: 0321498127 | ISBN-13: 9780321498120

Insider's Guide for Mathematical Ideas 11e and Mathematical Ideas Expanded Edition, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Paper; 201 pp | Instock
ISBN-10: 0321490908 | ISBN-13: 9780321490902

Instructor's Solutions Manual for Mathematical Ideas, 11/E
Larson
©2008 | Pearson | Paper; 672 pp | Instock
ISBN-10: 032136970X | ISBN-13: 9780321369703

Instructor's Testing Manual for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Paper; 384 pp | Instock
ISBN-10: 0321369696 | ISBN-13: 9780321369697

PowerPoint Slides (Download only) for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | On-line Supplement | Live
ISBN-10: 032136967X | ISBN-13: 9780321369673

TestGen® Computerized Test Bank for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321369661 | ISBN-13: 9780321369666
Suggested retail price: $0.00Net price: $0.00 (What's this?)

Websites and online courses

Annotated Instructor's Edition for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Cloth | Instock
ISBN-10: 0321361474 | ISBN-13: 9780321361479
More Info

MathXL -- Instant Access -- for Mathematical Ideas and Mathematical Ideas Expanded, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | On-line Supplement | Live
ISBN-10: 0321369653 | ISBN-13: 9780321369659
More Info

Other student resources

MathXL Tutorials on CD for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321369726 | ISBN-13: 9780321369727
Net price: $20.00 (What's this?)More Info

Student Study Guide and Solutions Manual for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Paper; 464 pp | Instock
ISBN-10: 0321369718 | ISBN-13: 9780321369710
Net price: $27.50 (What's this?)More Info

Video Lectures on CD with Optional Captioning for Mathematical Ideas, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321369548 | ISBN-13: 9780321369543
Net price: $25.00 (What's this?)More Info

For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006 | Pearson | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
Net price: $3.00 (What's this?)More Info

Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
Net price: $3.00 (What's this?)More Info

Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000 | Pearson | Unknown / Other | Instock
ISBN-10: 0201716275 | ISBN-13: 9780201716276
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Concept Videos: Algebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Pearson | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
Net price: $35.85 (What's this?)More Info

Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
Net price: $10.00 (What's this?)More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Pearson | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
Net price: $27.50 (What's this?)More Info

Prealgebra Review Workbook
Wheel
©2006 | Pearson | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
Net price: $27.50 (What's this?)More Info

Review of Algebra, A
Howard
©2002 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
Net price: $27.50 (What's this?)More Info

Spanish Basic Math Study Card
Leonarte
©2007 | Pearson | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
Net price: $3.00 (What's this?)More Info

TestGen All-in-One 2005 Package
Addison-Wesley
©2005 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321334469 | ISBN-13: 9780321334466
Suggested retail price: $0.00Net price: $0.00 (What's this?)More Info

Websites and Online Courses

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Mathematical Ideas a la Carte Plus, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Paper Package | Instock
ISBN-10: 032146110X | ISBN-13: 9780321461100
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Mathematical Ideas plus MyMathLab Student Access Kit, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Cloth Package | Instock
ISBN-10: 0321505751 | ISBN-13: 9780321505750
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Mathematical Ideas, Books a la Carte Edition, 11/E
Miller, Heeren & Hornsby
©2008 | Pearson | Unbound (Saleable); 1024 pp | Instock
ISBN-10: 0321461118 | ISBN-13: 9780321461117
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