# Algebra

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