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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.



Chapter 0: An Introduction to Mathematics75% developed

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.

Chapter 5: The Cartesian Plane25% developed

Chapter 6: Graphing Linear Functions25% developed
Chapter 7: Systems and Matrices25% developed

Chapter 8: Piecewise Functions0% developed

Unit 3: Polynomials

Chapter 9: Quadratic Functions0% developed
Chapter 10: Higher-Degree Polynomials0% developed

Unit 4: Other Functions

Chapter 11: Properties of Functions0% developed

Chapter 12: Exponents and Logarithms0% developed
Chapter 13: Rational and Radical Functions0% developed

Chapter 14: Trigonometry0% developed

Unit 5: Algebra in Discrete Mathematics

Chapter 15: Sequences and Series25% developed
Chapter 16: Probability and Statistics0% developed

Unit 6: Analytic Geometry

Chapter 17: Conic Sections25% developed
Chapter 18: Parametric Equations and Polar Coordinates25% developed
Chapter 19: Vectors25% 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.

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