Algebra

This book is part of a series on Algebra:

Basic Algebra
Algebra
Intermediate Algebra
Linear Algebra
Abstract Algebra
Intro to Rings and Algebras

Welcome to the Wikibooks Algebra textbook! Take a moment to skim over the chapters and sections to get a better idea if this is the right text for you. This textbook is currently undergoing an expansion and reorganization, so keep checking back for new content. Eventually it will become a comprehensive, well-organized textbook capable of being used for personal or academic use.

• Algebra is the study of symbolic mathematics and mathematical structures.
• It is a major branch of mathematics.
• You can perform a Google Search in this book.

Contents

Chapter 1: Introduction to Mathematics

1. Algebra will begin with an introduction into the world of Mathematics, starting with an explanation of what this book is about, whom it is for, and what you can expect to find within it. There will also be a variety of information and resources regarding math.
2. About This Book
   1. What is math, exactly? - And why should I care?
   2. Who should read this book - And what to expect

Chapter 2: Numbers, Variables and Relationships

Algebra As a Problem Solving Technique

• 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. In this chapter you will begin learning how to use numbers and variables to find out unknown information. This starts off with a closer look at numbers and operations, then covers variables and equations.

1. Review
   1. Elementary Arithmetic
   2. Order of Operations
2. Numbers and Variables
   1. Algebra and Properties Of Real Numbers
   2. Division is not commutative
   3. Rules of Exponents
   4. Roots and Radicals
   5. Variables
   6. Sets
3. Equations With One Variable
   1. What are Equations?
   2. Solving Equations With One Variable
   3. Word Problems
4. Inequalities
   1. Different Types of Relationships
   2. Interval notation and Graphing Intervals
   3. Solving Inequalities

• 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 common functions and how to use them.

Chapter 3: Linear Functions An Introduction To Graphing

1. Introduction to Linear Functions
   1. Functions
   2. Graphing Linear Functions
      1. The Coordinate (Cartesian) Plane
      2. Linear Equations and Functions
      3. The X and Y Intercepts
      4. Slope
      5. Standard Form and Solving Slope
   3. Graphing Inequalities
   4. The Pythagorean Theorem and The Distance Formula
   5. Absolute Value
   6. Systems of Equations
   7. Compound and Absolute Value Inequalities
   8. Graphing Systems of Inequalities
   9. Other Types of Graphs

Chapter 4: Polynomials

1. Polynomials
   1. Factoring Polynomials
   2. Completing the Square
      1. Square Root is Positive (To be merged)
   3. Quadratic Formula
   4. Binomial Theorem

Chapter 5: Graphing Polynomials

1. More about Graphing
   1. Graphing Polynomials
   2. Inverses of Functions
   3. Compound and Absolute Value Inequalities For Polynomials
   4. Graphing Systems of Inequalities For Polynomials

Chapter 6: Conic Sections

1. Conic Sections
   1. Circle
   2. Ellipse
   3. Parabola
   4. Hyperbola

Chapter 7: Complex Numbers

1. Complex Numbers
   1. More about the Quadratic Formula
   2. Yet more about Polynomials and the "Fundamental Theorem of Algebra"

Chapter 8: Elementary Probability and Statistics

1. Introduction to Probability and Statistics
   1. Probability
   2. Statistics
   3. Scatter Plots

Chapter ∞:Ongoing merging work

TO DO

Fix algebra for Q & R in Proportions or Ratios section

Add word problems to multiplication

Add word problems to division

Add word problems to exponents

Add word problems to roots

Add word problems for possible relationships part of inequalities

Add graphics for multiplying by 1 and -1 to description of special case multiply by -1

Add description for special case Going back to equality

Fill in example of half area function

Fix contents, Clarify Explanation

Move Todos here ... or fill 'em in

Why use standard form vs. Slope Intercept form? Need more context.

Continue Creating Links between pages.

Continue Creating Standard Algebra Heading ... Continue through Table of Contents

Leap in sophistication ... End of the conversational tone. Need to make friendlier, simpler

To be merged/unsorted

1. In this book
   1. Theory
   2. Iteration
   3. Stemplots (Do we want this?)
   4. Talk:Algebra/ToInclude
   5. Arithmetic/Numerical Axioms (Was orphaned from the book, should keep an eye out for others)
   6. Equalities and Inequalities (Was orphaned from the book)
   7. Algebra
   8. Proofs/Exercises Don't forget to merge this page out of this book.
   9. Quadratic functions
   10. Solving equations
   11. Theory of Equations
2. Redirect to another book (why?)
   1. Logarithms
3. Closure
   1. Algebra/Closure/Answers