**Chapter 1 - Introduction**

1-1 Why Anyone Needs This Math Book

1-2 What This Book Provides

1-3 The Layout of This Text

1-4 Who Would Benefit from This Book

1-5 Why Buy One Book that Contains 12 Years of Mathematics?

1-6 This Math is Really Used in Practice

1-7 What the Reader Should Already Know

**Chapter 2 - Numbers**

2-1 The Definition of a Number

2-2 Numbers are Universal

2-3 Counting

2-4 Naming Digits

2-5 Decimals

2-6 Common Symbols

2-7 Summary of Numbers

**Chapter 3 - Addition and Subtraction**

3-1 Explaining Addition

3-2 Addition of Single Digit Integers

3-3 Commutative Law of Addition

3-4 Understanding Variables

3-5 Associative Law of Addition

3-6 Explaining Subtraction

3-7 Subtraction of Single Digit Integers

3-8 Absolute Values

3-9 Addition and Subtraction are Complementary

3-10 Addition of Multi-Digit Integers

3-11 Separating Multi-Digit Numbers for Addition

3-12 Adding Decimals

3-13 Subtraction of Multi-Digit Integers

3-14 Subtraction Resulting in Negative Answers

3-15 Subtracting Decimals

3-16 Summary of Addition and Subtraction

**Chapter 4 - Multiplication and Division**

4-1 Explaining Multiplication

4-2 Operators for Multiplication

4-3 Multiplication of Single Digit Integers

4-4 Commutative Law of Multiplication

4-5 Associative Law of Multiplication

4-6 Distributive Law of Multiplication

4-7 Variations of the Distributive Law of Multiplication

4-8 Multiplication of Multi-Digit Integers

4-9 Separating Multi-Digit Numbers for Multiplication

4-10 Explaining Division

4-11 Division of Single Digit Integers

4-12 Division of Multi-Digit Numbers

4-13 Separating Multi-Digit Numbers for Division

4-14 Division with Remainders

4-15 Multiplying Decimals

4-16 Dividing Decimals

4-17 Rounding and Truncation

4-18 A Pause for Congrats!

**Chapter 5 - Fractions**

5-1 Defining Fractions

5-2 Reading Fractions

5-3 Types of Fractions

5-4 Converting Fractions to Decimals

5-5 Converting Decimals to Fractions

5-6 Multiplying Fractions

5-7 Making Different but Equal Fractions

5-8 Simplifying Fractions with Factorization and Cancellation

5-9 Prime Numbers

5-10 Prime Factorization

5-11 Reducing Fractions to Lowest Terms

5-12 Lowest Common Denominators (LCD)

5-13 Adding and Subtracting Fractions

5-14 Conversion of Mixed Numbers

5-15 Dividing Fractions

5-16 Summary of Fractions

**Chapter 6 - Percentages**

6-1 Defining Percentages

6-2 Operations using Percentages

6-3 Finding the Percentage of a Number

6-4 Percentages Shortcuts

6-5 Mean, Median, and Mode

6-6 Summary of Percentages

**Chapter 7 - Negative Numbers**

7-1 Defining Negative Numbers

7-2 Negative Numbers are Necessary

7-3 Addition and Subtraction with Negative Numbers

7-4 Multiplying and Dividing Negative Numbers

7-5 Performing Operations with More than 3 Numbers

7-6 Summary of Negative Number Operations

**Chapter 8 - Exponents**

8-1 Defining Exponents

8-2 Multiplying with Positive Exponents

8-3 Using Negative Exponents

8-4 More Rules for Using Exponents

8-5 Summary of Exponential Rules

8-6 Fractional Exponents

8-7 Scientific and Exponential Notation

8-8 Summary of Exponents

**Chapter 9 - Pre-Algebra**

9-1 Review of the Past and Goals for the Future

9-2 Definitions for Algebra

9-3 Operations with Variables

9-4 Order of Operations

9-5 Summary

**Chapter 10 - Solving One Algebraic Equation**

10-1 Introduction

10-2 Algebraic Definitions

10-3 Two Basic Methods for Solving An Algebraic Equation

10-4 Isolating the Variable

10-5 Factorization of Quadratic Equations by Inspection

10-6 Factorization Using the Quadratic Formula

10-7 Factorization of Higher Order Polynomials

10-8 Reducing an Algebraic Expression to Lowest Terms

10-9 Reducing Algebraic Equations Containing Absolute Values

10-10 Summary

**Chapter 11 - Solving a System of Equations**

11-1 Introduction

11-2 Substitution of Equations

11-3 Elimination of Variables

11-4 Using Matrices

11-5 Solving Systems with Matrix Reduction

11-6 Solving Systems with Cramer's Rule

11-7 Summary

**Chapter 12 - Word Problems**

12-1 Introduction

12-2 Steps to Solving Any Word Problem

12-3 Word Problem Examples

12-4 Summary

**Chapter 13 - Functions**

13-1 Introduction

13-2 Explaining Functions

13-3 Dependent and Independent Variables

13-4 Examples Using Functions

13-5 Inverse Functions

13-6 Summary

**Chapter 14 - Graphing**

14-1 Introduction

14-2 Plotting Points on the Cartesian Coordinate System

14-3 Plotting Linear Equations

14-4 Plotting Systems of Linear Equations

14-5 Plotting Quadratic Equations

14-6 Plotting Polynomials of Higher Degrees

14-7 Plotting Polynomials with Multiple Variables

14-8 Summary of Graphing

**Chapter 15 - Geometry**

15-1 Introduction

15-2 Lines and Angles

15-3 Triangles

15-4 Congruent Triangles

15-5 Polygons

15-6 Circles

15-7 Summary

**Chapter 16 - Measurement of Geometric Figures**

16-1 Introduction

16-2 Lengths, Perimeters and Areas of Polygons

16-3 Circle Measurements

16-4 Volumes and Surface Areas

16-5 Summary

**Chapter 17 - Trigonometry**

17-1 Introduction

17-2 Trigonometric Functions

17-3 Commonly Used Triangles

17-4 Oblique Triangle Relationships

17-5 Trigonometry and Graphing

17-6 Plotting Sine and Cosine Values

17-7 Using Radians

17-8 Summary

**Chapter 18 - Logarithms**

18-1 Introduction

18-2 Understanding Logarithms

18-3 Calculating Logarithms

18-4 Uses of Logarithms

18-5 Finding the Natural Logarithm

18-6 Summary

**Chapter 19 - Complex Numbers**

19-1 Introduction

19-2 Defining Imaginary Numbers

19-3 Adding and Subtracting Imaginary Numbers

19-4 Complex = Real + Imaginary

19-5 Graphing Complex Numbers

19-6 Summary

**Chapter 20 - Finding Geometry Using Algebra**

20-1 Introduction

20-2 Finding Geometry with Complex Exponents

20-3 Using Complex Exponents

20-4 Summary

**Chapter 21 - Introducing Calculus**

21-1 What More is There to Learn?

21-2 An Essential Introduction to Calculus

21-3 Summary of the Introduction

**Chapter 22 - The Derivative**

22-1 Introduction

22-2 Development of the Derivative Using Limits

22-3 Usefulness of the Derivative

22-4 Finding the Derivative of a Function

22-5 Derivatives of Special Functions

22-6 The Chain Rule

22-7 L'Hopital's Rule

22-8 Maxima and Minima

22-9 Newton's Method

22-10 Summary of Derivatives

**Chapter 23 - The Integral**

23-1 Introduction

23-2 Development of the Integral Using Limits

23-3 Finding the Integral from the Derivative

23-4 Solving Integrals

23-5 Summary of Integrals

**Chapter 24 - A Final Word on Mathematics **

24-1 How Computers and Calculators Understand Math

24-2 Continued Learning

24-3 Now What?

**Appendix A: Trigonometric Identities Appendix B: Table of Trigonometric Functions**