# Algebra

ALGEBRA

## Preface

**Algebra** is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.

You've been asked to buy peanuts for you and your friends at a football game. You've collected $12.50. One bag is $2.75. You want to know how many bags you can buy. This is an algebra problem! Related problems are how much money will be left over, and what should you buy or in what proportions should you return the extra money to your friends.

Algebra helps us to predict things that we don't yet know and to determine the relationships between the things we do. Algebra is a powerful and rich branch of mathematics that is useful in everyday life as well as business, engineering, and other technical fields.

## Contents

This book is part of a series on **Algebra:**

### Preface

- What is math, exactly? -
*And why should I care?* - Who should read this book -
*And what to expect* - Structure of This Book -
*And the order to read the book in*

### Unit 1: Numbers, Variables and Relationships

How can we use numbers and variables to find out unknown information?

**Chapter 1: Elementary Arithmetic**

Chapter 2: An Introduction to Algebra

Chapter 3: Solving Equations

### Unit 2: An Introduction To Graphing

Math is a method of solving problems. You take information you know, and by manipulating it using mathematical principles, you can find information you don't know. Functions are the mathematical framework for solving problems. They have parameters, rules, and ways of being solved. This section will introduce you to functions and how to use them.

**The Cartesian Plane****Linear Functions****Systems and Matrices****Piecewise Functions**

### Unit 3: Polynomials

**Quadratic Functions****Polynomials**

### Unit 4: Other Functions

**Properties of Functions****Exponents and Logarithms****Rational and Radical Functions****Trigonometric Identities and Functions**

### Unit 5: Algebra in Discrete Mathematics

**Sequences and Series****Probability and Statistics**

### Unit 6: Analytic Geometry

**Conic Sections****Parametric Equations and Polar Coordinates****Vectors**

### Unit 7: Advanced Algebra

Now that you have completed your mathematical journey, you may be wondering where to head over next. This unit provides six optional chapters that can be done in any order you please. The six chapters are meant to be independent from one another, and any of the chapters can be skipped entirely to put more focus on the topics that are of greater interest to you.

**Complex Numbers****Advanced Polynomials****Continued Fractions****Theory of Inequalities****Limits of Functions****Group Theory**