Mathematical Ideas

Mathematical Ideas 13/e,  captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in everyday life. With a fresh, new focus on math in the workplace, this program shows students how math will play an important role in their future, while encouraging them to understand and embrace the mathematical concepts.

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Charles Miller

Vern Heeren grew up in the Sacramento Valley of California. After earning a Bachelor of Arts degree in mathematics, with a minor in physics, at Occidental College, and completing his Master of Arts degree in mathematics at the University of California, Davis, he began a 38-year teaching career at American River College, teaching math and a little physics. He coauthored Mathematical Ideas in 1968 with office mate Charles Miller, and he has enjoyed researching and revising it over the years. It has been a joy for him to complete the thirteenth edition, along with long time coauthor John Hornsby, and now also with son Christopher. These days, besides pursuing his mathematical interests, Vern enjoys spending time with his wife Carole and their family, exploring the wonders of nature near their home in central Oregon.

John Hornsby joined the author team of Margaret Lial, Charles Miller, and Vern Heeren in 1988. In 1990, the sixth edition of Mathematical Ideas became the first of nearly 150 titles he has coauthored for Scott Foresman, HarperCollins, Addison-Wesley, and Pearson in the years that have followed. His books cover the areas of developmental and college algebra, precalculus, trigonometry, and mathematics for the liberal arts. He is a native and resident of New Roads, Louisiana.

Christopher Heeren is a native of Sacramento, California. While studying engineering in college, he had an opportunity to teach a math class at a local high school, and this sparked both a passion for teaching and a change of major. He received a Bachelor of Arts degree and a Master of Arts degree, both in mathematics, from California State University¿—Sacramento. Chris has taught mathematics at the middle school, high school, and college levels, and he currently teaches at American River College in Sacramento. He has a continuing interest in using technology to bring mathematics to life. When not writing, teaching, or preparing to teach, Chris enjoys spending time with his lovely wife Heather and their three children (and two dogs and a guinea pig).

Preface

Acknowledgments

About the Authors

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 Numeracy in Today’s World

            Chapter 1 Summary

            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 

2.4 Surveys and Cardinal Numbers 

            Chapter 2 Summary

            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 The Conditional and Related Statements 

3.5 Analyzing Arguments with Euler Diagrams 

3.6 Analyzing Arguments with Truth Tables 

            Chapter 3 Summary

            Chapter 3 Test 

4. Numeration Systems

4.1 Historical Numeration Systems 

4.2 More Historical Numeration Systems 

4.3 Arithmetic in the Hindu-Arabic System

4.4 Conversion between Number Bases 

            Chapter 4 Summary

            Chapter 4 Test 

5. Number Theory

5.1 Prime and Composite Numbers 

5.2 Large Prime Numbers 

5.3 Selected Topics from Number Theory

5.4 Greatest Common Factor and Least Common Multiple

5.5 The Fibonacci Sequence and the Golden Ratio

5.6 Magic Squares (online)

            Chapter 5 Summary

            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 

            Chapter 6 Summary

            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 

            Chapter 7 Summary

            Chapter 7 Test 

8. Graphs, Functions, and Systems of Equations and Inequalities

8.1 The Rectangular Coordinate System and Circles 

8.2 Lines, Slope, and Average Rate of Change

8.3 Equations of Lines 

8.4 Linear Functions, Graphs, and Models 

8.5 Quadratic Functions, Graphs, and Models 

8.6 Exponential and Logarithmic Functions, Graphs, and Models 

8.7 Systems of Linear Equations 

8.8 Applications of Linear Systems 

8.9 Linear Inequalities, Systems, and Linear Programming

            Chapter 8 Summary

            Chapter 8 Test 

9. Geometry

9.1 Points, Lines, Planes, and Angles 

9.2 Curves, Polygons, Circles, and Geometric Constructions 

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

9.4 Perimeter, Area, and Circumference

9.5 Volume and Surface Area

9.6 Transformational Geometry

9.7 Non-Euclidean Geometry and Topology

9.8 Chaos and Fractal Geometry

            Chapter 9 Summary

            Chapter 9 Test 

10. Counting Methods

10.1 Counting by Systematic Listing

10.2 Using the Fundamental Counting Principle

10.3 Using Permutations and Combinations 

10.4 Using Pascal’s Triangle

10.5 Counting Problems Involving “Not” and “Or”

            Chapter 10 Summary

            Chapter 10 Test 

11. Probability

11.1 Basic Concepts 

11.2 Events Involving “Not” and “Or”

11.3 Conditional Probability and Events Involving “And”

11.4 Binomial Probability

11.5 Expected Value and Simulation

            Chapter 11 Summary

            Chapter 11 Test 

12. Statistics

12.1 Visual Displays of Data

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 Measures of Position

12.5 The Normal Distribution

            Chapter 12 Summary

            Chapter 12 Test 

13. Personal Financial Management

13.1 The Time Value of Money

13.2 Consumer Credit 

13.3 Truth in Lending

13.4 The Costs and Advantages of Home Ownership 

13.5 Financial Investments 

            Chapter 13 Summary

            Chapter 13 Test 

14. Graph Theory

14.1 Basic Concepts 

14.2 Euler Circuits and Route Planning

14.3 Hamilton Circuits and Algorithms 

14.4 Trees and Minimum Spanning Trees 

            Chapter 14 Summary

            Chapter 14 Test 

15. Voting and Apportionment

15.1 The Possibilities of Voting

15.2 The Impossibilities of Voting

15.3 The Possibilities of Apportionment 

15.4 The Impossibilities of Apportionment 

            Chapter 15 Summary 

            Chapter 15 Test 

Answers to Selected Exercises

Credits

Index of Applications

Index

NOTE: Trigonometry module and Metrics module available in MyMathLab or online at www.pearsonhighered.com/mathstatsresources.

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