Outline of algebra

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

Branches

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

Algebraic equations

An algebraic equation is an 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 only solutions of interest of the unknowns are the integer ones.

History

• History of algebra

General algebra concepts

• 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.
• Equations – equality of two mathematical expressions
• Linear equation – an algebraic equation with a degree of one
• Quadratic equation – an algebraic equation with a degree of two
• Cubic equation – an algebraic equation with a degree of three
• Quartic equation – an algebraic equation with a degree of four
• Quintic equation – an algebraic equation with a degree of five
• Polynomial – an algebraic expression consisting of variables and coefficients
• Inequalities – a comparison between values
• Functions – mapping that associates a single output value with each input value
• Sequences – ordered list of elements either finite or infinite
• Systems of equations – finite set of equations
• Vectors – element of a vector space
• Matrix – two dimensional array of numbers
• Vector space – basic algebraic structure of linear algebra
• Field – algebraic structure with addition, multiplication and division
• Groups – algebraic structure with a single binary operation
• Rings – algebraic structure with addition and multiplication

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.