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Mathematical Ideas, 15th edition

Published by Pearson (October 10, 2023) © 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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Mathematical Ideas connects math to your current and future life and career, with timely and relevant applications. It is designed for non-STEM majors and focuses on math in the workplace, supported by broad coverage, clear organization, abundant examples and well-planned exercise sets. Features like “When Will I Ever Use This?” in each chapter connect topics to career or workplace situations. Problem-solving strategies help increase your problem-solving skills, and “For Further Thought” encourages you to share your reasoning with other students for deeper understanding. Graphing calculators are optional. Among other enhancements, the 15th Edition adds a wealth of updated applications such as Approximating Average Number of Points per Game, Evaluating COVID-19 Risks, and more.

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

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