Difference between revisions of "Algebra"
(added complex numbers to intro) |
(Added Olympiad section, more links) |
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** [[Logarithm | Logarithms]] | ** [[Logarithm | Logarithms]] | ||
** [[Polynomial | Polynomials]] | ** [[Polynomial | Polynomials]] | ||
| + | ** [[Functional equation| Functional Equations]] | ||
* [[Inequality | Inequalities]] | * [[Inequality | Inequalities]] | ||
** [[Trivial inequality]] | ** [[Trivial inequality]] | ||
** [[Cauchy-Schwarz Inequality]] | ** [[Cauchy-Schwarz Inequality]] | ||
| + | ** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ||
| + | ** [[Triangle Inequality]] | ||
* [[Newton's Sums]] | * [[Newton's Sums]] | ||
* [[Trigonometry]] | * [[Trigonometry]] | ||
** [[DeMoivre's Theorem]] | ** [[DeMoivre's Theorem]] | ||
** [[Roots of unity]] | ** [[Roots of unity]] | ||
| + | |||
| + | |||
| + | == Olympiad Topics== | ||
| + | |||
| + | *Inequalities | ||
| + | ** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ||
| + | ** [[Cauchy-Schwarz Inequality]] | ||
| + | ** [[Chebyshevs 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]] | ||
Revision as of 13:34, 23 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 denoted by a letter. Many contest problems test one's fluency with algebraic manipulation.
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
