25% developed

Algebra

From Wikibooks, open books for an open world
Jump to navigation Jump to search
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 Relationships0% developed

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

Chapter 1: Elementary Arithmetic25% developed

Chapter 2: An Introduction to Algebra25% developed
Chapter 3: Solving Equations25% developed

Chapter 4: Inequalities0% developed

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 25% developed
    1. The Coordinate (Cartesian) Plane
    2. Functions
    3. Data in Two Variables
    4. Bar Graphs and Histograms
  2. Linear Functions 25% developed
    1. Graphing Linear Functions 25% developed
    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 25% developed
    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 0% developed
    1. Piecewise Functions
    2. Absolute Value Functions
    3. Step Functions
    4. Floor and Ceiling Functions

Unit 3: Polynomials

  1. Quadratic Functions 25% developed
  2. Higher-Degree Polynomials 25% developed
    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 25% developed
  2. Exponents and Logarithms 25% developed
  3. Rational and Radical Functions 25% developed
  4. Trigonometric Identities and Functions 25% developed

Unit 5: Algebra in Discrete Mathematics

  1. Sequences and Series 25% developed
    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 0% developed

Unit 6: Analytic Geometry

  1. Conic Sections 25% developed
    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 25% developed
  3. Vectors 25% developed

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 25% developed
    1. Complex Numbers
    2. More about the Quadratic Formula
    3. More about Polynomials.
  2. Advanced Polynomials 25% developed
    1. Algebraic Manipulation
    2. Polynomial Interpolation
    3. Symettric Polynomials
    4. Chebyshev Polynomials
  3. Continued Fractions 0% developed
    1. Diophantine Equations
  4. Theory of Equations and Inequalities 25% developed
  5. Limits of Functions 25% developed
  6. Group Theory 25% developed
    1. Symmetries
    2. Binary Operators
    3. Groups
    4. Lagrange's Theorem

Appendix

Resources