Difference between revisions of "Algebra"
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(Added function stuff to Olympiad Topics) |
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| Line 49: | Line 49: | ||
** [[DeMoivre's Theorem]] | ** [[DeMoivre's Theorem]] | ||
** [[Roots of unity]] | ** [[Roots of unity]] | ||
| + | |||
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== Olympiad Topics== | == Olympiad Topics== | ||
| − | + | * [[Function | Functions]] | |
| + | ** [[Greatest integer function]]/[[Least integer function]] | ||
| + | ** [[Polynomial | Polynomials]] | ||
| + | ** [[Functional equation| Functional Equations]] | ||
*Inequalities | *Inequalities | ||
** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ||
| Line 69: | Line 74: | ||
** [[Trigonometric inequalities]] | ** [[Trigonometric inequalities]] | ||
** [[Trivial Inequality]] | ** [[Trivial Inequality]] | ||
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| + | |||
== More Advanced Topics in Algebra == | == More Advanced Topics in Algebra == | ||
| − | |||
* [[Group theory]] | * [[Group theory]] | ||
* [[Ring theory]] | * [[Ring theory]] | ||
Revision as of 15:28, 11 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. If this is not what you are looking for, you might try the page on abstract algebra.
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
- Trivial inequality
- Arithmetic Mean-Geometric Mean inequality for 2 variables
- Word problems
Intermediate Topics
Olympiad Topics
- Functions
- Inequalities
- Arithmetic Mean-Geometric Mean Inequality
- Cauchy-Schwarz Inequality
- Chebyshev's Inequality
- Geometric inequalities
- Hölder'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
