Thinking Mathematically

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