Mathematical Ideas, 14th edition

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 (Annotated Instructor’s Edition only)

Answers to Selected Exercises (Student Edition Only)

Credits

Index of Applications

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.