Algebra - Topics Containing The Word "algebra"

Topics Containing The Word "algebra"

• Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied. This is usually taught at school under the title algebra (or intermediate algebra and college algebra in subsequent years). University-level courses in group theory may also be called elementary algebra.
• Abstract algebra, sometimes also called modern algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.
• Linear algebra, in which the specific properties of vector spaces are studied (including matrices). Linear algebra developed from the study of linear equations.
• Universal algebra, in which properties common to all algebraic structures are studied.
• Algebraic number theory, in which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
• Algebraic geometry, a branch of geometry, in its primitive form specifying curves and surfaces by solutions of polynomials equations.
• Algebraic combinatorics, in which abstract algebraic methods are used to study combinatorial questions.

Many mathematical structures are called algebras.

• Algebra over a field or more generally Algebra over a ring.
  Algebra over a field is not only the concern in abstract algebra, but its analytic structure is also important in the field of functional analysis.
• In measure theory,
  • Sigma-algebra
  • Algebra over a set
• In category theory
  • F-algebra and F-coalgebra
  • T-algebra
• In logic,
  • Relational algebra, in which a set of finitary relations that is closed under certain operators.
  • Boolean algebra, a structure which consists of only two value, 0 and 1. See also Boolean algebra (structure).
  • Heyting algebra