# Algebra/Printable version

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Algebra

# Welcome To Algebra!

This Wikibook helps you to learn algebra. If you wish to read this book, click the link above.

# Authors
## Authors

The authors of Algebra include:
* Daniel Ehrenberg
* Anonymous Wikibook Contributors
* H Padleckas has written Algebra/Function Graphing and made contributions to other chapters. Plans to work on other chapters in Algebra about graphics.
* Jaden Mathos
* GoreyCat

# Contributors
## Completion Scale

* Sparse text 0-24%
* Developing text 25=49%
* Maturing text 50-74%
* Developed text 75-99%
* Comprehensive text 100%

## Ongoing merging work

TO DO
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 (completed by Wikigucoder)
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
* In this book
** Theory (A section pertaining to proofs can potentially can go under Elementary Arithmetic chapter)
** Iteration
** Talk:Algebra/ToInclude
** Arithmetic/Numerical Axioms (Was orphaned from the book, should keep an eye out for others)
** Equalities and Inequalities (Was orphaned from the book)
** Algebra
** Quadratic functions
** Solving equations
** Theory of Equations
* Redirect to another book (why?)
** Logarithms
ORPHANED PAGES
* Algebra/Absolute Value

# Chapter 0

Chapter 0: An Introduction to Mathematics
← Cover · Chapter 1 →
Introduction

## Sections

* 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

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary

# Chapter 1

Chapter 1: Elementary Arithmetic
← Chapter 0 · Chapter 2 →
Introduction

## Sections

* The Number Line - (Completed 12 October 2023)
* Operations in Arithmetic - 25% Done
* Operations with Decimals and Fractions - 5% Done
* Exponents and Roots
* Order of Operations
* Factoring and Divisibility
* Applications of Fractions and Decimals
* Units
* Rounding and Estimation
* Introduction to Statistics
* Problem Solving

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary

# Chapter 5

Chapter 5: The Cartesian Plane

## Sections

* The Coordinate (Cartesian) Plane
* Functions
* Data in Two Variables
* Bar Graphs and Histograms

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary

# Chapter 9
## Sections

* Polynomials
* Graphing Quadratic Functions
* Factoring Quadratics
* Completing the Square
* Complex Numbers
* Quadratic Formula
* Quadratic Inequalities

## Extra
# Chapter 11

* Composite Functions
* Inverses of Functions
* Operations with Functions
* Transformations

# Chapter 12
## Sections

* Exponential Growth and Decay
* Introduction to Logarithms
* The Number e

# Chapter 13
## Sections

* Dividing Polynomials

## Extra
# Chapter 14
## Sections

* Right Triangle Trigonometry
* The Law of Sines
* The Law of Cosines
* The Unit Circle
* Trigonometric Identities
* Sum and Difference Identities
* Double Angle, Half Angle, and Reduction Formulas
* Sum-to-Product and Product-to-Sum Formulas
* Graphs of Trigonometric Functions
* Inverse Trigonometric Functions
* Trigonometric Equations

## Extra
# Chapter 15

* Mathematical Induction
* Recursive Formulas
* Introduction to Sequences and Series
* Arithmetic Progression (AP)
* Geometric Progression (GP)
* Harmonic Progression (HP)

# Chapter 17
## Sections

* The Distance Formula
* Loci of Points
* Conic Sections
* Circles
* Ellipses
* Parabolas
* Hyperbolas
* Rotation of Axes
* Nonlinear Systems

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary

# Chapter 18
## Sections

* Parametric Equations

## Extra
# Chapter 20
## Introduction
## Sections

* Arithmetic with Complex Numbers
* Powers of Complex Numbers
* Complex Number Algebra
* More about the Quadratic Formula
* More about Polynomials

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary

# Chapter 21

* Algebraic Manipulation
* Polynomial Interpolation
* Symettric Polynomials
* Chebyshev Polynomials

# Chapter 22

* Expansion of Rational Numbers
* Diophantine Equations
* Expansion of Irrational Numbers
* Periodic Continued Fractions
* Hurwit's Theorem

# Chapter 23

* Symmetric Equations

# Chapter 24
## Introduction

* Derivatives

## Extra
# Chapter 25

* Symmetries
* Binary Operators
* Groups
* Lagrange's Theorem

# Glossary
## A

* Addition: The process of combining two numbers.

## D

* Division: The process of sharing an equal amount to a set group.

## E

* Expression: A mathematical sentence consisting of numbers, variables, and mathematical operators.

## M

* Multiplication: The process of repeated addition.

## S

* Subtraction: The process of taking away one number from another to find the difference between them.

# Formulas

Area of a rectangle: L x W

# Resources
## Further Reading

* Linear Algebra Done Right by Sheldon Axler (open access)

# Bibliography

* Carson, Tom (2006) PreAlgebra, Cengage Learning.
* Chrystal, George (1886) Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges
* Courant, Richard; Robbins, Herbert (1978), What is Mathematics?, Oxford University Press.
* Cummings, Jay (2021) Proofs: A Long-Form Mathematics Textbook
* Gonick, Larry (2015) The Cartoon Guide to Algebra
* Liu, Andy (2015) Arithmetical Wonderland, MAA Press.
* Lockhart, Paul (2017) Arithmetic, Harvard University Press.
* Millier, Julie (2011) PreAagebra, McGraw Hill.
* Monahan, Chris (2020) Must Know High School Pre-Calculus, McGraw Hill.
* Patrick, David; Rusczyk, Richard (2011) Prealgebra, Art of Problem Solving (AoPS)
* Tussy, Alan S. (2006) PreAlgebra, Cengage Learning.