1-1  Addition, Subtraction, Multiplication, and Division
1-2  Communicative Properties: The Order-Doesn't-Make-a-Difference
1-3  The Problem of the Unbalanced Ferry
1-4  Rules for Adding Odd and Even Numbers
1-5  Using Letters to Represent Numbers
1-6  The Gremlin
1-7  The Algebra Challenge
1-8  Undefined Terms: Axioms or Postulates
1-9  Postulates For The Natural Numbers
1-10  Precedence Rules For Arithmetic Expressions: Order of Operations
1-11  Worksheet: Precedence Rules
1-12  Properties: Closure and Distributive
1-13  Note to Chapter 1
1-14  Checkup Exercise

2-1  The Golden Rule of Equations
2-2  The Reflexive, Symmetric, and Transitive Properties
2-3  Conditional Equations
2-4  Expressions: The Implied Multiplication Rule
2-5  Worksheet: Equations
2-6  Expressions: Using Letters for Known and Unknown Quantities
2-7  Equations
2-8  Notes to Chapter 2
2-9  Checkup Exercise

3-1  Properties of Zero
3-2  The Distressing Case of Negative Numbers
3-3  Mutual Assured Destruction Rule/Additive Inverse Rule
3-4  Integers
3-5  The Absolute Value of a Number
3-6  Negative Numbers
3-7  Worksheet: Nagative Numbers
3-8  Checkup Exercise

4-1  Stanislavsky's Complete Guide to Everything Worth Knowing About Fractions
4-2  Proper / Equivalent Fractions
4-3  Reciprocals, Compound Fractions, and Division
4-4  Prohibition: No Zero Demoninators
4-5  Rational Numbers
4-6  Rules For Fractions
4-7  Chapter 2: Decimal Fractions
4-8  Worksheet: Equations with Fractions
4-9  Chapter 3: Percent
4-10  Note to Chapter 4
4-11  Checkup Exercise

5-1  The Square Tile Wall
5-2  Squared Numbers
5-3  Exponents
5-4  Powers of 10
5-5  Scientific Notation
5-6  Square Roots
5-7  Laws of Exponents
5-8  Negative Exponents and the Width of the Amoeba
5-9  Worksheet: Scientific Notation
5-10  Note to Chapter 5
5-11  Checkup Exercise

6-1  The Speed of the Fastball
6-2  The Pythagorean Theorem
6-3  The Square Root of 2
6-4  Irrational Numbers
6-5  Summary of Roots
6-6  Fractional Exponents
6-7  Worksheet: Expressions Involving Roots
6-8  Checkup Exercise

7-1  Monomials, Binomials, and Trinomials
7-2  Algebraic Expression Rule: Like Terms
7-3  Distributive Properties: Coefficients
7-4  The FOIL Method for Multiplying Binomials
7-5  General Rules Worth Remebering Worksheet: Multiplying Binomials
7-6  Note to Chapter 7
7-7  Checkup Exercise

8-1  Function Machines
8-2  Function notation
8-3  Calculating a Function Backwards: The Inverse of a Function
8-4  The Domain and Range of a Function
8-5  Independent and Dependent Variables
8-6  Function Notation
8-7  Notes to Chapter 8
8-8  Checkup Exercise

9-1  Locating Points in the Forest
9-2  The Distance Between Two Points
9-3  Graphing: x Axis and y Axis
9-4  Graphs of Linear Functions
9-5  To Calculate the Slope of a Line
9-6  Graphing Inequalities
9-7  Equations For Lines
9-8  Curves
9-9  Graphing Relationships
9-10  Vertical / Horizontal Line Test
9-11  Notes to Chapter 9
9-12  Checkup Exercise

10-1  The Desperate Race Against Time
10-2  The Solution to Two Simultaneous Equations
10-3  Supply/Demand Function?
10-4  Worksheet: Simultaneous Equations
10-5  Note to Chapter 10
10-6  Checkup Exercise

11-1  Polynomials
11-2  The Equation with Two Solutions
11-3  Solving Quadratic Equations by Fractoring
11-4  Competint the Square
11-5  The Quadratic Formula
11-6  Worksheet: Quadratic Equations
11-7  Checkup Exercise

12-1  The Stadium Scoreboard Lights
12-2  Definition of a Circle
12-3  Equation of Circle With Center at origin and Radius r
12-4  Formulas For Circles
12-5  The Special Number π
12-6  Coordinate Translation
12-7  Ellipses
12-8  The Equation of an Ellipse
12-9  Some Ellipses Are More Eccentric Than Others
12-10  Parabolas
12-11  Reflecting Telescopes
12-12  Hyperbolas
12-13  Notes to Chapter 12
12-14  Checkup Exercise

13-1  The Dragon's Swimming Hole
13-2  Curves That Co Up and Down
13-3  3rd and 4th Degree Curves
13-4  Algebraic Division
13-5  Worksheet: Polynomial Division
13-6  The Overly Thrilling Ride on the Discontinuous Curve
13-7  Notes to Chapter 13
13-8  Checkup Exercise

14-1  Recordis Family Tree
14-2  The Peril from the Exponentially Growing Bacteria
14-3  Exponential Functions
14-4  The Ping Pong Tournament
14-5  Logarithm Functions
14-6  Common Logarithms
14-7  Worksheet: Logarithms
14-8  Converting Curves to Lines
14-9  Solving the Planet Problem and Population Growth Problem
14-10  Notes to Chapter 14
14-11  Checkup Exercise

15-1  The Souvenir Pennant Factory
15-2  The Mystery of the Missing Hot Dogs
15-3  General Definition of Matrix Multiplication
15-4  Worksheet: Matrix Multiplication
15-5  Solving an Equation System with a Matrix Inverse
15-6  Recordis Precision Diet 9Version 3)
15-7  Determinants
15-8  The Height of the Balloon
15-9  Graphs in Three-Dimensional Space
15-10  Three-Equation, Three-Variable Systems: Summary
15-11  The Final Attack: 5-by-5 System
15-12  Notes to Chapter 15
15-13  Checkup Exercise

16-1  The Triangular Lookout Tower
16-2  The Sum 1 + 2 + 3 + ... + n
16-3  Summation Notation
16-4  Arithmetic Series
16-5  Recordis Not-Quite-Infinite Income
16-6  Geometric Series
16-7  Worksheet: Arithmetic and Geometric Series
16-8  Checkup Exercise

17-1  The Indecisive Baseball Manager
17-2  Factoring Function
17-3  The Card Game
17-4  Permutations
17-5  Combinations
17-6  Worksheet: Combinations Formula
17-7  Caculating (a+b)n
17-8  Pascal's Triangle
17-9  The Binomial Formula
17-10  Notes to Chapter 17
17-11  Checkup Exercise

18-1  Proving the Arithmetic Series Formula
18-2  The Method of Mathematical Induction
18-3  Proving the Geometric Series Formula
18-4  Proving the Binomial Formula
18-5  Checkup Exercise

19-1  The Square Root of -1
19-2  Complex Numbers
19-3  Multiplying complex Numbers
19-4  The Graph of a Complex numbers
19-5  Worksheet: Quadratic Equations with Complex Number Solutions
19-6  The Party
19-7  Notes to Chapter 19
19-8  Checkup Exercise