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 Calculating, Estimating, and Reading Graphs

Extension: Using Writing to Learn about Mathematics

Collaborative Investigation: Discovering Patterns in Pascal's Triangle

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 and Cartesian Products

2.4 Surveys and Cardinal Numbers

Extension: Infinite Sets and Their Cardinalities

Collaborative Investigation: Surveying the Members of Your Class

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

Extension: Logic Problems and Sudoku

3.6 Analyzing Arguments with Truth Tables

Collaborative Investigation: Logic Problems and Sudoku Revisited

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

Extension: Modular Systems

Collaborative Investigation: A Perpetual Calendar Algorithm

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

Extension: Modern Cryptography

5.5 The Fibonacci Sequence and the Golden Ratio

Collaborative Investigation: Investigating an Interesting Property of Number Squares

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

Extension: Complex Numbers

Collaborative Investigation: Budgeting to Buy a Car

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

Extension: Complex Solutions of Quadratic Equations

Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?

Chapter 7 Test

8. Graphs, Functions, and Systems of Equations and Inequalities

8.1 The Rectangular Coordinate System and Circles

8.2 Lines, Slope, and Average Rate of Change

8.3 Equations of Lines and Linear Models

8.4 An Introduction to Functions: Linear Functions, Applications, and Models

8.5 Quadratic Functions, Graphs, and Models

8.6 Exponential and Logarithmic Functions, Applications, and Models

8.7 Systems of Equations

8.8 Applications of Systems

Extension: Using Matrix Row Operations to Solve Systems

8.9 Linear Inequalities, Systems, and Linear Programming

Collaborative Investigation: Tracking an Epidemic

Chapter 8 Test

9. Geometry

9.1 Points, Lines, Planes, and Angles

9.2 Curves, Polygons, and Circles

Extension: Geometric Constructions

9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem

9.4 Perimeter, Area, and Circumference

9.5