Outline of algebra
The following outline is provided as an overview of and topical guide to algebra:
Algebra is one of the main branches of mathematics and is concerned with the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication are general operations, but their precise definitions lead to structures such as groups, rings, and fields.
Branches
Algebraic equations
See also: Equation
Algebraic equation – equation involving only algebraic expressions in the unknowns. These are further classified by degree.
- Linear equation – algebraic equation of degree one.
- Polynomial equation – equation in which a polynomial is set equal to another polynomial.
- Transcendental equation – equation involving a transcendental function of one of its variables.
- Functional equation – equation in which the unknowns are functions rather than simple quantities.
- Differential equation – equation involving derivatives.
- Integral equation – equation involving integrals.
- Diophantine equation – equation where the unknowns are required to be integers.
- Polynomials
- Variables
History
General algebra concepts
- Algebra –
- Cubic equation –
- Fundamental theorem of algebra – states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.
- Linear equation –
- Quadratic equation –
- Quartic equation –
- Quintic equation –
- Polynomial –
See also
External links
- '4000 Years of Algebra', lecture by Robin Wilson, at Gresham College, 17 October 2007 (available for MP3 and MP4 download, as well as a text file).
- ExampleProblems.com Example problems and solutions from basic and abstract algebra.
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