Algebra/Printable version
This is the print version of Algebra You won't see this message or any elements not part of the book's content when you print or preview this page. |
The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Algebra
Cover
Welcome To Algebra!
editThis Wikibook helps you to learn algebra. If you wish to read this book, click the link above.
Authors
Authors
editThe 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
edit- Sparse text 0-24%
- Developing text 25=49%
- Maturing text 50-74%
- Developed text 75-99%
- Comprehensive text 100%
Extra
edit
Chapter 0
Chapter 0: An Introduction to Mathematics
Sections
edit- 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
edit
Chapter 1
Chapter 1: Elementary Arithmetic
Sections
edit- The Number Line - (Completed 12 October 2023)
- Operations in Arithmetic - 30% Done
- Exponents and Roots - 25% Done
- Factoring and Divisibility
- Integers
- Fractions
- Decimals
- Order of Operations
- Units
- Rounding and Estimation
- Introduction to Statistics
- Problem Solving
Extra
edit- Review
- Practice Problems - (Completed 7 December 2024)
- Solutions to Practice Problems
- Glossary
Chapter 5
Chapter 5: The Cartesian Plane
Sections
editExtra
edit
Chapter 9
Chapter 9: Quadratic Functions
Sections
edit- Graphing Quadratic Functions
- Factoring Quadratics
- Completing the Square
- Complex Numbers
- Quadratic Formula
- Quadratic Inequalities
- Quadratic Systems
Extra
edit
Chapter 11
Chapter 11: Properties of Functions
Sections
edit- Variation
- Extrema and Continuity
- Operations with Functions
- Composite Functions
- Inverses of Functions
- Parent Functions
Extra
edit
Chapter 12
Chapter 12: Exponents and Logarithms
Sections
editExtra
edit
Chapter 13
Chapter 13: Rational and Radical Functions
Sections
editExtra
edit
Chapter 14
Chapter 14: Trigonometry
Sections
edit- Pythagoras' Theorem
- Right Triangle Trigonometry
- The Law of Sines
- The Law of Cosines
- Angles and their Measure
- 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
- Solving Trigonometric Equations
Extra
edit
Chapter 15
Chapter 15: Sequences and Series
Sections
edit- Discrete Functions
- Mathematical Induction
- Recursive Formulas
- Introduction to Sequences and Series
- Arithmetic Progression (AP)
- Geometric Progression (GP)
- Harmonic Progression (HP)
- Quadratic Progression (QP)
- Polynomial Fitting
- Generating Functions
Extra
edit
Chapter 16
Chapter 16: Probability and Counting
Introduction
editSections
edit- Probability and Samples
- Counting Principles
- Binomial Coefficients
- Permutations and Combinations
- The Stars and Bars Method
- Two-Event Probability
- Independent and Dependent Events
- Conditional Probability
- Experimental Probability
- Binomial Distribution
- Normal Distribution
- The Central Limit Theorem
- Hypothesis Testing
Extra
edit
Chapter 17
Chapter 17: Conic Sections
Sections
edit- The Distance Formula
- Loci of Points
- Conic Sections
- Circles
- Ellipses
- Parabolas
- Hyperbolas
- Rotation of Axes
- Nonlinear Systems
Extra
edit
Chapter 18
Chapter 18: Parametric Equations and Polar Equations
Introduction
editSections
editExtra
edit
Chapter 19
Chapter 19: Vectors
Sections
edit- Vectors and Their Properties
- Vector Operations
- Vector and Parametric Equations
- Vectors in Three Dimensions
- Dot and Cross Products
- Vectors and Planes
- Determinants
Extra
edit
Chapter 20
Chapter 20: Complex Numbers
Sections
edit- Arithmetic with Complex Numbers
- Powers of Complex Numbers
- Complex Number Algebra
- More about the Quadratic Formula
- More about Polynomials
Extra
edit
Chapter 21
Chapter 21: Approximation Theory
Sections
editExtra
edit
Chapter 22
Chapter 22: Continued Fractions
Sections
edit- Expansion of Rational Numbers
- Diophantine Equations
- Pell's Equation
- Expansion of Irrational Numbers
- Periodic Continued Fractions
- Hurwit's Theorem
Extra
edit
Chapter 23
Chapter 23: Theory of Equations
Sections
edit- Polynomial Roots
- Cubic Equations
- Quartic Equations
- Quintic Equations
- Sextic and Septic Equations
- Properties of Polynomial Roots
- Higher-Degree Curves
- Fermat's Last Theorem
Extra
edit
Chapter 24
Chapter 24: Graphs and Networks
Sections
edit- Graphs and Networks
- Euler Paths
- Hamiltonian Paths
- Chromatic Numbers
- Planar Graphs
- TSP Graphs
- The Shortest Route Algorithm
- Tree Graphs
- Minimum Spanning Trees
Extra
edit
Chapter 25
Chapter 25: Limits of Functions
Sections
edit- Limits
- One-Sided Limits
- Limit Properties
- Limits at Infinity
- Limits of Sequences
- Continuity
- The Definition of a Limit
- Derivatives
- Anti-Derivatives and Integrals
Extra
edit
Chapter 26
Chapter 26: Boolean Algebra
Sections
editExtra
edit
Chapter 27
Chapter 27: Group Theory
Sections
editExtra
edit
Glossary
A
edit- addition: The process of combining two numbers.
D
edit- digit:
- division: The process of sharing an equal amount to a set group.
E
edit- Expression: A mathematical sentence consisting of numbers, variables, and mathematical operators.
I
edit- integer:
M
edit- multiplication: The process of repeated addition.
N
edit- number:
- number system:
Q
edit- quantity:
S
edit- 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
edit
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
A
editB
editC
editD
editE
editF
editG
editH
editI
editJ
editK
editL
editM
editN
editO
editP
editQ
editR
editS
editT
editU
editV
editW
editX
editY
editZ
edit