Algebra/Printable version

Algebra

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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%

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

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

• Algebra/Absolute Value

Extra

• Problem Bank

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 - 25% Done
3. Exponents and Roots
4. Integers
5. Factoring and Divisibility
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
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. Polynomials
2. Graphing Quadratic Functions
3. Factoring Quadratics
4. Completing the Square
5. Complex Numbers
6. Quadratic Formula
7. Quadratic Inequalities

Extra

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

Chapter 11

Chapter 11: Properties of Functions

---

Introduction

Sections

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

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. 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

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

Chapter 15

Chapter 15: Sequences and Series

---

Sections

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

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

---

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. Expansion of Irrational Numbers
4. Periodic Continued Fractions
5. 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. Properties of Polynomial Roots
6. Higher-Degree Curves
7. Fermat's Last Theorem

Extra

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

Chapter 24

Chapter 24: 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 25

Chapter 25: 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

• 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

• 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