Table of Contents

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