# Difference between revisions of "Algebra"

ComplexZeta (talk | contribs) |
Mysmartmouth (talk | contribs) (corrected "Newton sums" link) |
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** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ||

** [[Triangle Inequality]] | ** [[Triangle Inequality]] | ||

− | * [[Newton | + | * [[Newton sums]] |

* [[Trigonometry]] | * [[Trigonometry]] | ||

** [[DeMoivre's Theorem]] | ** [[DeMoivre's Theorem]] | ||

** [[Roots of unity]] | ** [[Roots of unity]] | ||

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== Olympiad Topics== | == Olympiad Topics== |

## Revision as of 13:01, 27 June 2006

In mathematics, **algebra** is the study of examining, manipulating, and solving equations, inequalities, and other mathematical expressions. Algebra revolves around the concept of the variable, an unknown quantity given a name and usually denoted by a letter or symbol. Many contest problems test one's fluency with algebraic manipulation.

## Contents

## Introductory Topics

- Algebraic expressions
- Complex numbers
- Equations
- Linear equations (1 and 2 variables)
- Systems of equations

- Factoring
- Functions
- Exponentials
- Graphing
- Lines
- Quadratics
- Basic Transformations

- Logarithms
- Square root function
- Polynomials

- Inequalities
- Word problems

## Intermediate Topics

## Olympiad Topics

- Inequalities
- Arithmetic Mean-Geometric Mean Inequality
- Cauchy-Schwarz Inequality
- Chebyshev's Inequality
- Geometric inequalities
- Holder's Inequality
- Isoperimetric inequalities
- Jensen's Inequality
- Minkowski Inequality
- Muirhead's Inequality
- Power mean inequality
- Rearrangement Inequality
- Schur's Inequality
- Triangle Inequality
- Trigonometric inequalities
- Trivial inequality