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Mathematical Ideas, 15th edition

Published by Pearson (December 31, 2022) © 2024

  • Charles D. Miller American River College
  • Vern E. Heeren American River College
  • John Hornsby University of New Orleans
  • Christopher Heeren American River College

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For courses in Liberal Arts Mathematics or Survey of Mathematics.

Connects math to students' lives with relevant, updated applications

Mathematical Ideas captures the interest of non-STEM students with an applications-oriented approach that links mathematics to their current and future lives. It meets changing curricular needs and trends but maintains its coverage, organization, clear exposition, abundant examples and well-planned exercise sets. The authors demonstrate how math will play an important role in students' futures and careers while helping them to develop a solid understanding of concepts. The 15th Edition adds many new and updated applications, and more resources for corequisite courses.

Hallmark features of this title

  • Numerous examples with annotations illustrate concepts and skills, providing step-by-step directions for solving similar problems.
  • When Will I Ever Use This? in each chapter aims to answer that age-old question by connecting topics to career or workplace situations.
  • For Further Thought encourages students to share their reasoning processes among themselves to gain a deeper understanding of key concepts.
  • Optional Graphing Technology: Graphing calculator screens show how technology can help support results found analytically, but students do not need a graphing calculator to use the text.
  • Margin Notes interspersed throughout the text touch on the lives of mathematicians, research in math, newspaper and magazine articles, and other note-worthy interesting sources.

New and updated features of this title

  • NEW / UPDATED: Chapter Openers: Some have been added or updated for this revision. To support the text's career theme, chapter openers address a situation related to a particular career. Some include a problem that the reader is asked to solve.
  • REVISED: Over 1000 new or modified exercises in a broad variety of exercises that integrate drill, conceptual and applied problems.
    • Exercises that focus on real-life data have been updated, and new applications are offered in several chapters (particularly chapters 6, 7, 8, 11, 12, and 13).
  • UPDATED: Real data in the form of graphs, charts and tables: The authors continue to use up-to-date information from magazines, newspapers and the Internet to create real applications that are relevant and meaningful.
  • UPDATED: For Further Thought entries, following the exercise sets of many sections, encourage students to share their reasoning processes among themselves to gain a deeper understanding of key mathematical concepts.

Features of MyLab Math for the 15th Edition

  • UPDATED: Revised Section Lecture Videos cover objectives with a clear and engaging approach. They incorporate the use of animations, applets and StatCrunch to demonstrate concepts.
  • NEW: Many new Interactive Figures (in editable GeoGebra format) have been added and can be assigned in MyLab Math. These bring mathematical concepts to life, helping students see the concepts through directed explorations and purposeful manipulation.
  • UPDATED: Integrated Review in MyLab Math is updated with prerequisite content tailor-made for a corequisite liberal arts math course. Integrated Review includes prerequisite review within each chapter in the MyLab, giving students who need it just the right amount of review.
    • Corequisite resources include assignable exercises for additional objectives beyond those included in the Integrated Review assignments and corequisite worksheets including activities.
  • NEW: Enhanced Assignments for each section are designed to optimize students' learning. They are prebuilt but editable for easy course set-up, and contain personalized prerequisite skills exercises for gaps identified in the chapter-level Skills Check Quiz.
    • For some exercises, learning aids are strategically turned off to ensure that students understand how to work the exercises independently.

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
  • Summary
  • 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
  • Summary
  • 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
  • Summary
  • 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
  • 4.5 Arithmetic in Other Bases
  • Summary
  • 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)* 
  • Summary
  • 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 
  • Summary
  • 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 
  • Summary
  • 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 
  • Summary
  • 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 
  • Summary
  • 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”
  • Summary
  • 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
  • Summary
  • 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
  • Summary
  • 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
  • 13.6 Income Tax Liability
  • 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
  • Summary
  • 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 
  • Summary
  • Test

Answers to Selected Exercises

Credits

Index of Applications

Index

About our authors

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 14th 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 3 children.

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