Algebra

Welcome to the Wikibook of

ALGEBRA

Preface

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.

You've been asked to buy peanuts for you and your friends at a football game. You've collected $12.50. One bag is $2.75. You want to know how many bags you can buy. This is an algebra problem! Related problems are how much money will be left over, and what should you buy or in what proportions should you return the extra money to your friends.

Algebra helps us to predict things that we don't yet know and to determine the relationships between the things we do. Algebra is a powerful and rich branch of mathematics that is useful in everyday life as well as business, engineering, and other technical fields.

Contents

Preface

Unit 1: Numbers, Variables and Relationships 

How can we use numbers and variables to find out unknown information?

Unit 2: An Introduction To Graphing

Math is a method of solving problems. You take information you know, and by manipulating it using mathematical principles, you can find information you don't know. Functions are the mathematical framework for solving problems. They have parameters, rules, and ways of being solved. This section will introduce you to functions and how to use them.

  1. The Cartesian Plane  
    1. The Coordinate (Cartesian) Plane
    2. Functions
    3. Data in Two Variables
    4. Bar Graphs and Histograms
  2. Linear Functions  
    1. Graphing Linear Functions  
    2. Linear Equations and Functions
    3. The X and Y Intercepts
    4. Slope
    5. Scatter Plots
    6. Standard Form and Solving Slope
    7. Graphing Inequalities
    8. Other Types of Graphs
  3. Systems and Matrices  
    1. Systems of Equations
    2. Graphing Systems of Inequalities
    3. Matrices
    4. Matrix Algebra
    5. Determinants
    6. Inveres of Matrices
    7. Solving Systems with Matrices
    8. Linear Programming
  4. Piecewise Functions  
    1. Piecewise Functions
    2. Absolute Value Functions
    3. Step Functions
    4. Floor and Ceiling Functions

Unit 3: Polynomials

  1. Quadratic Functions  
  2. Polynomials  
    1. Polynomials
    2. Factoring Polynomials
    3. Completing the Square
      1. Square Root is Positive (To be merged)
    4. Quadratic Formula
    5. Cubic Formula
    6. Binomial Theorem
    7. Graphing Polynomials
    8. Compound and Absolute Value Inequalities For Polynomials
    9. Graphing Systems of Inequalities For Polynomials

Unit 4: Other Functions

  1. Properties of Functions  
  2. Exponents and Logarithms  
  3. Rational and Radical Functions  
  4. Trigonometric Identities and Functions  

Unit 5: Algebra in Discrete Mathematics

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

Unit 6: Analytic Geometry

  1. Conic Sections  
    1. The Pythagorean Theorem and The Distance Formula
    2. Loci of Points
    3. Conic Sections
    4. Circle
    5. Ellipse
    6. Parabola
    7. Hyperbola
    8. Rotation of Axes
  2. Parametric Equations and Polar Coordinates  
  3. Vectors  

Unit 7: Advanced Algebra

Now that you have completed your mathematical journey, you may be wondering where to head over next. This unit provides six optional chapters that can be done in any order you please. The six chapters are meant to be independent from one another, and any of the chapters can be skipped entirely to put more focus on the topics that are of greater interest to you.

  1. Complex Numbers  
    1. Complex Numbers
    2. More about the Quadratic Formula
    3. More about Polynomials.
  2. Advanced Polynomials  
    1. Algebraic Manipulation
    2. Polynomial Interpolation
    3. Symettric Polynomials
    4. Chebyshev Polynomials
  3. Continued Fractions  
    1. Diophantine Equations
  4. Theory of Inequalities  
  5. Limits of Functions  
  6. Group Theory  
    1. Symmetries
    2. Binary Operators
    3. Groups
    4. Lagrange's Theorem

Appendix

Resources