Difference between revisions of "Algebra"
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** [[Trigonometric inequalities]] | ** [[Trigonometric inequalities]] | ||
** [[Trivial inequality]] | ** [[Trivial inequality]] | ||
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| + | == More Advanced Topics in Algebra == | ||
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| + | * [[Group theory]] | ||
| + | * [[Ring theory]] | ||
| + | * [[Field theory]] | ||
| + | * [[Galois theory]] | ||
| + | * [[Homological algebra]] | ||
| + | * [[Lie theory]] | ||
| + | * [[Algebraic geometry]] | ||
Revision as of 19:38, 24 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
