Outline of algebra

The following outline is provided as an overview of and topical guide to algebra:

Algebra – one of the main branches of mathematics, it concerns 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.

Overview

Main article: Algebra

• Arithmetic
• Equations
• An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
• A linear equation is algebraic equation of degree one.
• A polynomial equation is an equation in which a polynomial is set equal to another polynomial.
• A transcendental equation is an equation involving a transcendental function of one of its variables.
• A functional equation is an equation in which the unknowns are functions rather than simple quantities.
• A differential equation is an equation involving derivatives.
• An integral equation is an equation involving integrals.
• A Diophantine equation is an equation where the unknowns are required to be integers.
• Polynomials
• Variables

Branches

• Pre-algebra
• Elementary algebra
• Abstract algebra
• Linear algebra
• Universal algebra

History

Main article: History of algebra

General algebra concepts

• Algebra –
• Cubic equation –
• Fundamental theorem of algebra –
• Linear equation –
• Quadratic equation –
• Quartic equation –
• Quintic equation –
• Polynomial –

See also

• Table of mathematical symbols

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.