Algebra/Printable version


Algebra

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Cover

Chapter 0

ALGEBRA

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  
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  • Developing text 25=49%
  • Maturing text 50-74%
  • Developed text 75-99%
  • Comprehensive text 100%

Extra

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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   - 30% Done
  3. Exponents and Roots   - 25% Done
  4. Factoring and Divisibility  
  5. Integers  
  6. Fractions  
  7. Decimals  
  8. Order of Operations  
  9. Units  
  10. Rounding and Estimation  
  11. Introduction to Statistics  
  12. Problem Solving  

Extra

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  1. Review  
  2. Practice Problems   - (Completed 7 December 2024)
  3. Solutions to Practice Problems  
  4. Glossary  



Chapter 5

Chapter 5: The Cartesian Plane

Chapter 4 · Chapter 6

Chapter 4 · Algebra · Chapter 6

Introduction

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

Chapter 9: Quadratic Functions

Chapter 8 · Chapter 10

Chapter 8 · Algebra · Chapter 10

Introduction

Sections

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

Extra

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


Chapter 11

Chapter 11: Properties of Functions

Chapter 10 · Chapter 12

Chapter 10 · Algebra · Chapter 12

Introduction

Sections

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  1. Variation
  2. Extrema and Continuity
  3. Operations with Functions
  4. Composite Functions
  5. Inverses of Functions
  6. Parent Functions

Extra

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


Chapter 12

Chapter 12: Exponents and Logarithms

Chapter 11 · Chapter 13

Chapter 11 · Algebra · Chapter 13

Introduction

Sections

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

Extra

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


Chapter 13

Chapter 13: Rational and Radical Functions

Chapter 12 · Chapter 14

Chapter 12 · Algebra · Chapter 14

Introduction

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. Pythagoras' Theorem
  2. Right Triangle Trigonometry
  3. The Law of Sines
  4. The Law of Cosines
  5. Angles and their Measure
  6. The Unit Circle
  7. Trigonometric Identities
  8. Sum and Difference Identities
  9. Double Angle, Half Angle, and Reduction Formulas
  10. Sum-to-Product and Product-to-Sum Formulas
  11. Graphs of Trigonometric Functions
  12. Inverse Trigonometric Functions
  13. Solving Trigonometric Equations

Extra

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


Chapter 15

Chapter 15: Sequences and Series

Chapter 14 · Chapter 16

Chapter 14 · Algebra · Chapter 16

Sections

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  1. Discrete Functions
  2. Mathematical Induction
  3. Recursive Formulas
  4. Introduction to Sequences and Series
  5. Arithmetic Progression (AP)
  6. Geometric Progression (GP)
  7. Harmonic Progression (HP)
  8. Quadratic Progression (QP)
  9. Polynomial Fitting
  10. Generating Functions

Extra

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


Chapter 16

Chapter 16: Probability and Counting

Chapter 15 · Chapter 17

Chapter 15 · Algebra · Chapter 17

Introduction

Introduction

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Sections

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  1. Probability and Samples
  2. Counting Principles
  3. Binomial Coefficients
  4. Permutations and Combinations
  5. The Stars and Bars Method
  6. Two-Event Probability
  7. Independent and Dependent Events
  8. Conditional Probability
  9. Experimental Probability
  10. Binomial Distribution
  11. Normal Distribution
  12. The Central Limit Theorem
  13. Hypothesis Testing

Extra

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


Chapter 17

Chapter 17: Conic Sections

Chapter 16 · Chapter 18

Chapter 16 · Algebra · Chapter 18

Introduction

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

Chapter 18: Parametric Equations and Polar Equations

Chapter 17 · Chapter 19

Chapter 17 · Algebra · Chapter 19

Introduction

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Sections

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  1. Parametric Equations

Extra

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Chapter 19

Chapter 19: Vectors

Chapter 18 · Chapter 20

Chapter 18 · Algebra · Chapter 20

Sections

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  1. Vectors and Their Properties
  2. Vector Operations
  3. Vector and Parametric Equations
  4. Vectors in Three Dimensions
  5. Dot and Cross Products
  6. Vectors and Planes
  7. Determinants

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. Iteration
  2. Polynomial Interpolation
  3. Optimal Polynomials
  4. Symmetric Equations
  5. 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. Pell's Equation
  4. Expansion of Irrational Numbers
  5. Periodic Continued Fractions
  6. Hurwit's Theorem

Extra

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


Chapter 23

Chapter 23: Theory of Equations

Chapter 22 · Chapter 24

Chapter 22 · Algebra · Chapter 24

Introduction

Sections

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  1. Polynomial Roots
  2. Cubic Equations
  3. Quartic Equations
  4. Quintic Equations
  5. Sextic and Septic Equations
  6. Properties of Polynomial Roots
  7. Higher-Degree Curves
  8. Fermat's Last Theorem

Extra

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


Chapter 24

Chapter 24: Graphs and Networks

Chapter 23 · Chapter 25

Chapter 23 · Algebra · Chapter 25

Introduction

Sections

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  1. Graphs and Networks
  2. Euler Paths
  3. Hamiltonian Paths
  4. Chromatic Numbers
  5. Planar Graphs
  6. TSP Graphs
  7. The Shortest Route Algorithm
  8. Tree Graphs
  9. Minimum Spanning Trees

Extra

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


Chapter 25

Chapter 25: Limits of Functions

Chapter 24 · Chapter 26

Chapter 24 · Algebra · Chapter 26

Introduction

Sections

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  1. Limits
  2. One-Sided Limits
  3. Limit Properties
  4. Limits at Infinity
  5. Limits of Sequences
  6. Continuity
  7. The Definition of a Limit
  8. Derivatives
  9. Anti-Derivatives and Integrals

Extra

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


Chapter 26

Chapter 26: Boolean Algebra

Chapter 25 · Chapter 27

Chapter 25 · Algebra · Chapter 27

Introduction

Sections

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Extra

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


Chapter 27

Chapter 27: Group Theory

Chapter 26


Introduction

Sections

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

Extra

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


Glossary

  • addition: The process of combining two numbers.
  • digit:
  • division: The process of sharing an equal amount to a set group.
  • Expression: A mathematical sentence consisting of numbers, variables, and mathematical operators.
  • integer:
  • multiplication: The process of repeated addition.
  • number:
  • number system:
  • quantity:
  • subtraction: The process of taking away one number from another to find the difference between them.


Formulas

Area of a rectangle: L x W


Multiplication Table

× 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90
7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105
8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135
10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165
12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180
13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195
14 14 28 42 56 70 72 84 96 108 140 154 168 182 196 210
15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225


Resources

Further Reading

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Bibliography

  • Alexander, Daniel; Koeberlein, Geralyn (1999) "Elementary Geometry for College Students, 2nd Edition", Houghton Mifflin Company
  • 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)
  • Swokowski, Earl; Cole Jeffery (1997) ' Algebra and Trigonometry with Analytic Geometry, Ninth Edition, Brooks/Cole Publishing Company
  • Tussy, Alan S. (2006) PreAlgebra, Cengage Learning.


Index