Algebra: Difference between revisions
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** [[Rearrangement Inequality]] | ** [[Rearrangement Inequality]] | ||
** [[Schur's Inequality]] | ** [[Schur's Inequality]] | ||
** [[Smoothing]] | |||
** [[Triangle Inequality]] | ** [[Triangle Inequality]] | ||
** [[Trigonometric inequalities]] | ** [[Trigonometric inequalities]] | ||
** [[Trivial inequality]] | ** [[Trivial inequality]] | ||
== More Advanced Topics in Algebra == | == More Advanced Topics in Algebra == | ||
Revision as of 23:42, 4 July 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.
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
- Smoothing
- Triangle Inequality
- Trigonometric inequalities
- Trivial inequality
