Algebra

Welcome to the Wikibook of

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:

Basic Algebra
Algebra
Intermediate Algebra
Vectors
Introductory Linear Algebra
Linear Algebra
Abstract Algebra
Intro to Rings and Algebras
Associative Composition Algebra

• Cover
• Authors
• For Contributors

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

Chapter 4: Inequalities

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.

5. The Cartesian Plane
   1. The Coordinate (Cartesian) Plane
   2. Functions
   3. Data in Two Variables
   4. Bar Graphs and Histograms
6. Linear Functions
   1. Graphing Linear Functions
   2. Linear Equations and Functions
   3. The X and Y Intercepts
   4. Slope
   5. Scatter Plots
   6. Standard Form and Solving Slope
   7. Graphing Inequalities
   8. Other Types of Graphs
7. Systems and Matrices
   1. Systems of Equations
   2. Graphing Systems of Inequalities
   3. Matrices
   4. Matrix Algebra
   5. Determinants
   6. Inveres of Matrices
   7. Solving Systems with Matrices
   8. Linear Programming
8. Piecewise Functions
   1. Piecewise Functions
   2. Absolute Value Functions
   3. Step Functions
   4. Floor and Ceiling Functions

Unit 3: Polynomials

9. Quadratic Functions
10. Higher-Degree Polynomials
    1. Polynomials
    2. Factoring Polynomials
    3. Completing the Square
       1. Square Root is Positive (To be merged)
    4. Quadratic Formula
    5. Cubic Formula
    6. Binomial Theorem
    7. Graphing Polynomials
    8. Compound and Absolute Value Inequalities For Polynomials
    9. Graphing Systems of Inequalities For Polynomials

Unit 4: Other Functions

11. Properties of Functions
12. Exponents and Logarithms
13. Rational and Radical Functions
14. Trigonometric Identities and Functions

Unit 5: Algebra in Discrete Mathematics

15. Sequences and Series
    1. Mathematical Induction
    2. Recursive Formulas
    3. Introduction to Sequences and Series
    4. Arithmetic Progression (AP)
    5. Geometric Progression (GP)
    6. Harmonic Progression (HP)
16. Probability and Statistics

Unit 6: Analytic Geometry

17. Conic Sections
    1. The Pythagorean Theorem and The Distance Formula
    2. Loci of Points
    3. Conic Sections
    4. Circle
    5. Ellipse
    6. Parabola
    7. Hyperbola
    8. Rotation of Axes
18. Parametric Equations and Polar Coordinates
19. 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.

20. Complex Numbers
    1. Complex Numbers
    2. More about the Quadratic Formula
    3. More about Polynomials.
21. Advanced Polynomials
    1. Algebraic Manipulation
    2. Polynomial Interpolation
    3. Symettric Polynomials
    4. Chebyshev Polynomials
22. Continued Fractions
    1. Diophantine Equations
23. Theory of Equations and Inequalities
24. Limits of Functions
25. Group Theory
    1. Symmetries
    2. Binary Operators
    3. Groups
    4. Lagrange's Theorem

Resources

• Resources
• Bibliography
• Glossary
• Index