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Algebra

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

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Cover

Welcome To Algebra!

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


Authors

Authors

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The authors of Algebra include:


Contributors

Completion Scale

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Wikibook Development Stages
Sparse text   Developing text   Maturing text   Developed text   Comprehensive text  
  • Sparse text 0-24%
  • Developing text 25=49%
  • Maturing text 50-74%
  • Developed text 75-99%
  • Comprehensive text 100%

Ongoing merging work

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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

  1. In this book
    1. Theory (A section pertaining to proofs can potentially can go under Elementary Arithmetic chapter)
    2. Iteration
    3. Talk:Algebra/ToInclude
    4. Arithmetic/Numerical Axioms (Was orphaned from the book, should keep an eye out for others)
    5. Equalities and Inequalities (Was orphaned from the book)
    6. Algebra
    7. Quadratic functions
    8. Solving equations
    9. Theory of Equations
  2. Redirect to another book (why?)
    1. Logarithms

ORPHANED PAGES


Chapter 0

Chapter 0: An Introduction to Mathematics

← Cover · Chapter 1 →

← Cover · Algebra · Chapter 1 →

Introduction

Sections

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

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary



Chapter 1

Chapter 1: Elementary Arithmetic

← Chapter 0 · Chapter 2 →

← Chapter 0 · Algebra · Chapter 2 →

Introduction

Sections

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  1. The Number Line   - (Completed 12 October 2023)
  2. Operations in Arithmetic   - 25% Done
  3. Operations with Decimals and Fractions   - 5% Done
  4. Exponents and Roots  
  5. Order of Operations  
  6. Factoring and Divisibility  
  7. Applications of Fractions and Decimals  
  8. Units  
  9. Rounding and Estimation  
  10. Introduction to Statistics  
  11. Problem Solving  

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary



Chapter 5

Chapter 5: The Cartesian Plane

Introduction

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Sections

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  1. The Coordinate (Cartesian) Plane
  2. Functions
  3. Data in Two Variables
  4. Bar Graphs and Histograms

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 9

Introduction

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Sections

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  1. Polynomials
  2. Graphing Quadratic Functions
  3. Factoring Quadratics
  4. Completing the Square
  5. Complex Numbers
  6. Quadratic Formula
  7. Quadratic Inequalities

Extra

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Chapter 11

  1. Composite Functions
  2. Inverses of Functions
  3. Operations with Functions
  4. Transformations


Chapter 12

Introduction

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Sections

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  1. Exponential Growth and Decay
  2. Introduction to Logarithms
  3. The Number e


Chapter 13

Introduction

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Sections

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  1. Dividing Polynomials

Extra

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Chapter 14

Chapter 14: Trigonometry

← Chapter 13 · Chapter 15 →

← Chapter 13 · Algebra · Chapter 15 →

Introduction

Sections

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  1. Right Triangle Trigonometry
  2. The Law of Sines
  3. The Law of Cosines
  4. The Unit Circle
  5. Trigonometric Identities
  6. Sum and Difference Identities
  7. Double Angle, Half Angle, and Reduction Formulas
  8. Sum-to-Product and Product-to-Sum Formulas
  9. Graphs of Trigonometric Functions
  10. Inverse Trigonometric Functions
  11. Trigonometric Equations

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 15

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


Chapter 17

Introduction

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Sections

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  1. The Distance Formula
  2. Loci of Points
  3. Conic Sections
  4. Circles
  5. Ellipses
  6. Parabolas
  7. Hyperbolas
  8. Rotation of Axes
  9. Nonlinear Systems

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 18

Introduction

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Sections

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  1. Parametric Equations

Extra

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Chapter 19

Introduction

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Sections

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Extra

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Chapter 20

Chapter 20: Complex Numbers

← Chapter 19 · Chapter 21 →

← Chapter 19 · Algebra · Chapter 21 →

Sections

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  1. Arithmetic with Complex Numbers
  2. Powers of Complex Numbers
  3. Complex Number Algebra
  4. More about the Quadratic Formula
  5. More about Polynomials

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 21

Chapter 21: Approximation Theory

← Chapter 20 · Chapter 22 →

← Chapter 20 · Algebra · Chapter 22 →

Introduction

Sections

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  1. Polynomial Interpolation
  2. Symmetric Equations
  3. Chebyshev Polynomials

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 22

Chapter 22: Continued Fractions

← Chapter 21 · Chapter 23 →

← Chapter 21 · Algebra · Chapter 23 →

Introduction

Sections

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  1. Expansion of Rational Numbers
  2. Diophantine Equations
  3. Expansion of Irrational Numbers
  4. Periodic Continued Fractions
  5. Hurwit's Theorem

Extra

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  1. Review
  2. Practice Problems
  3. Solutions to Practice Problems
  4. Glossary


Chapter 23

  1. Cardano Method
  2. Ferrari Method


Chapter 24

Introduction

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  1. Derivatives

Sections

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Extra

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Chapter 25

  1. Symmetries
  2. Binary Operators
  3. Groups
  4. Lagrange's Theorem


Glossary

A

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  • Addition: The process of combining two numbers.

D

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

E

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

M

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  • Multiplication: The process of repeated addition.

S

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  • 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

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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.


Index

A

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B

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C

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D

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E

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F

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G

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H

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I

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J

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K

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L

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M

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N

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O

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P

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Q

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R

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S

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T

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U

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V

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W

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X

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Y

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Z

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