Mathematical Ideas

For courses in Liberal Arts Mathematics.

Engages non-STEM students with a practical presentation that connects mathematics to their current and future lives 

Mathematical Ideas is a versatile text that has evolved to meet changing curricular needs and trends, but remains steadfast to its primary objectives – comprehensive coverage, appropriate organization, clear exposition, abundant examples, and well-planned exercise sets with numerous applications. 

With a fresh focus on math in the workplace, this program shows students in liberal arts and survey courses how math will play an important role in their futures, while helping them to develop a solid understanding of mathematical concepts. The 14th Edition updates and enhances the text’s hallmark features, and expands its robust MyLab™ Math course to include StatCrunch^® applets, animations, corequisite course material, new section lecture videos, and much more.

Also available with MyLab Math 

MyLab Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

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 fourteenth edition, along with long-time coauthor John Hornsby, and 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 at and 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 6th 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.

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 Systems 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-Euclidian 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

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 IA-1 (Annotated Instructor’s Edition only)

ANSWERS TO SELECTED EXERCISES A-1 (Student Edition Only)

CREDITS C-1

INDEX OF APPLICATIONS I-1

INDEX

*The online section on Magic Squares as well as a Trigonometry chapter, a Metrics chapter, and Extension topics can all be found in the MyLab™ Math course or at www.pearsonhighered.com/mathstatsresources

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