Algebra/Printable version

Algebra

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

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.

Cover

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%

Extra

• To Do List
• Book Order
• Problem Bank
• Templates

Chapter 0

Chapter 0: An Introduction to Mathematics

---

Introduction

Sections

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

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

Chapter 1

Chapter 1: Elementary Arithmetic

---

Introduction

Sections

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

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

Chapter 5

Chapter 5: The Cartesian Plane

---

Introduction

Sections

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

Extra

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

Chapter 9

Chapter 9: Quadratic Functions

---

Introduction

Sections

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

Extra

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

Chapter 11

Chapter 11: Properties of Functions

---

Introduction

Sections

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

Extra

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

Chapter 12

Chapter 12: Exponents and Logarithms

---

Introduction

Sections

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

Extra

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

Chapter 13

Chapter 13: Rational and Radical Functions

---

Introduction

Sections

1. Dividing Polynomials

Chapter 14

Chapter 14: Trigonometry

---

Introduction

Sections

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

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

Chapter 15

Chapter 15: Sequences and Series

---

Sections

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

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

Chapter 16

Chapter 16: Probability and Counting

---

Introduction

Sections

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

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

Chapter 17

Chapter 17: Conic Sections

---

Introduction

Sections

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

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

Chapter 18

Chapter 18: Parametric Equations and Polar Equations

---

Sections

1. Parametric Equations

Chapter 19

Chapter 19: Vectors

---

Sections

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

Chapter 20

Chapter 20: Complex Numbers

---

Sections

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

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

Chapter 21

Chapter 21: Approximation Theory

---

Introduction

Sections

1. Iteration
2. Polynomial Interpolation
3. Optimal Polynomials
4. Symmetric Equations
5. Chebyshev Polynomials

Extra

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

Chapter 22

Chapter 22: Continued Fractions

---

Introduction

Sections

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

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

Chapter 23

Chapter 23: Theory of Equations

---

Introduction

Sections

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

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

Chapter 24

Chapter 24: Graphs and Networks

---

Introduction

Sections

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

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

Chapter 25

Chapter 25: Limits of Functions

---

Introduction

Sections

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

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

Chapter 26

Chapter 26: Boolean Algebra

---

Introduction

Extra

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

Chapter 27

Chapter 27: Group Theory

---

Introduction

Sections

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

Extra

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

Glossary

A

• addition: The process of combining two numbers.

D

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

E

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

I

• integer:

M

• multiplication: The process of repeated addition.

N

• number:
• number system:

Q

• quantity:

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

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

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

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.