(NOTE: Each chapter concludes with a Chapter Summary, Review, and Test, and a comprehensive Chapter Test.)

1. Problem Solving and Critical Thinking

• 1.1 Inductive and Deductive Reasoning
• 1.2 Estimation, Graphs, and Mathematical Models
• 1.3 Problem Solving

2. Set Theory

• 2.1 Basic Set Concepts
• 2.2 Subsets
• 2.3 Venn Diagrams and Set Operations
• 2.4 Set Operations and Venn Diagrams with Three Sets
• 2.5 Survey Problems

3. Logic

• 3.1 Statements, Negations, and Quantified Statements
• 3.2 Compound Statements and Connectives
• 3.3 Truth Tables for Negation, Conjunction, and Disjunction
• 3.4 Truth Tables for the Conditional and the Biconditional
• 3.5 Equivalent Statements and Variations of Conditional Statements
• 3.6 Negations of Conditional Statements and De Morgan’s Laws
• 3.7 Arguments and Truth Tables
• 3.8 Arguments and Euler Diagrams

4. Number Representation and Calculation

• 4.1 Our Hindu-Arabic System and Early Positional Systems
• 4.2 Number Bases in Positional Systems
• 4.3 Computation in Positional Systems
• 4.4 Looking Back at Early Numeration Systems

5. Number Theory and the Real Number System

• 5.1 Number Theory: Prime and Composite Numbers
• 5.2 The Integers; Order of Operations
• 5.3 The Rational Numbers
• 5.4 The Irrational Numbers
• 5.5 Real Numbers and Their Properties; Clock Addition
• 5.6 Exponents and Scientific Notation
• 5.7 Arithmetic and Geometric Sequences

6. Algebra: Equations and Inequalities

• 6.1 Algebraic Expressions and Formulas
• 6.2 Linear Equations in One Variable and Proportions
• 6.3 Applications of Linear Equations
• 6.4 Linear Inequalities in One Variable

7. Algebra: Graphs, Functions, and Linear Systems

• 7.1 Graphing and Functions
• 7.2 Linear Functions and Their Graphs
• 7.3 Systems of Linear Equations in Two Variables
• 7.4 Linear Inequalities in Two Variables
• 7.5 Linear Programming
• 7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions

8. Personal Finance

• 8.1 Percent, Sales Tax, and Discounts
• 8.2 Income Tax
• 8.3 Simple Interest
• 8.4 Compound Interest
• 8.5 Annuities, Methods of Saving, and Investments
• 8.6 Cars
• 8.7 The Cost of Home Ownership
• 8.8 Credit Cards

9. Measurement

• 9.1 Measuring Length; The Metric System
• 9.2 Measuring Area and Volume
• 9.3 Measuring Weight and Temperature

10. Geometry

• 10.1 Points, Lines, Planes, and Angles
• 10.2 Triangles
• 10.3 Polygons, Perimeter, and Tessellations
• 10.4 Area and Circumference
• 10.5 Volume and Surface Area
• 10.6 Right Triangle Trigonometry
• 10.7 Beyond Euclidean Geometry

11. Counting Methods and Probability Theory

• 11.1 The Fundamental Counting Principle
• 11.2 Permutations
• 11.3 Combinations
• 11.4 Fundamentals of Probability
• 11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations
• 11.6 Events Involving Not and Or; Odds
• 11.7 Events Involving And; Conditional Probability
• 11.8 Expected Value

12. Statistics

• 12.1 Sampling, Frequency Distributions, and Graphs
• 12.2 Measures of Central Tendency
• 12.3 Measures of Dispersion
• 12.4 The Normal Distribution
• 12.5 Problem Solving with the Normal Distribution
• 12.6 Scatter Plots, Correlation, and Regression Lines

13. Voting and Apportionment

• 13.1 Voting Methods
• 13.2 Flaws of Voting Methods
• 13.3 Apportionment Methods
• 13.4 Flaws of Apportionment Methods

14. Graph Theory

• 14.1 Graphs, Paths, and Circuits
• 14.2 Euler Paths and Euler Circuits
• 14.3 Hamilton Paths and Hamilton Circuits
• 14.4 Trees