From Wikipedia, the free encyclopedia
Overview of and topical guide to algebra
The following
outline is provided as an overview of and topical guide to algebra:
Algebra is one of the main branches of
mathematics , covering 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
An
algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by
degree .
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
See also
External links