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