Table of Contents

(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
  • 6.5 Quadratic Equations 

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 

Answers to Selected Exercises
Credits
Subject Index