1,733 articles
Additive inverse
The additive inverse, also called the opposite number, of a is −a, the number added to a to give 0; subtraction is addition of the inverse.
Adele ring
The adele ring, or ring of adeles, is the locally compact topological ring built from all completions of a global field, central to class field theory.
Adjoint functors
Adjoint functors, also called an adjoint situation, are a pair of functors related by a natural bijection of morphisms, introduced by Daniel M. Kan in 1958.
Adjoint representation
The adjoint representation is the canonical representation of a Lie algebra on itself, with each element acting as the bracket map, and it encodes the Killing form and root system.
Adjugate matrix
The adjugate matrix, also called the classical adjoint, is the transpose of a square matrix's cofactor matrix; multiplying it by the matrix gives det(A) times the identity, which yields the inverse.
AF algebra
An AF algebra, or approximately finite-dimensional algebra, is a C-algebra built as an inductive limit of finite-dimensional C-algebras; Elliott classified them in 1976 by their ordered K0-groups.
Affine arithmetic
Affine arithmetic is a self-validated numerical computation model, proposed by Comba and Stolfi in 1993, that tracks correlations between uncertain quantities for tighter error bounds than interval arithmetic.
Affine Lie algebra
An affine Lie algebra, also called an affine Kac-Moody algebra, is an infinite-dimensional Lie algebra that is a central extension of the loop algebra of a semisimple Lie algebra.
Affine root system
An affine root system is an infinite root system whose quotient is a finite root system, underlying affine Kac–Moody Lie algebras and classified by Macdonald in 1972.
AKS primality test
The AKS primality test, or Agrawal-Kayal-Saxena primality test, is a deterministic polynomial-time algorithm deciding whether an integer is prime, announced in 2002 by three researchers at IIT Kanpur.
Al-Khwarizmi (محمد بن موسى الخوارزمي)
Al-Khwarizmi (Muhammad ibn Musa al-Khwarizmi, ca. 780–850) was a mathematician and astronomer at the House of Wisdom in Baghdad whose algebra treatise gave us "algebra", and whose Latinized name gave "algorithm".
Albert algebra
The Albert algebra, also called the exceptional Jordan algebra, is the 27-dimensional real Jordan algebra of 3×3 Hermitian matrices over the octonions, the only simple Jordan algebra that is not special.
Aleph number
Aleph numbers (ℵ₀, ℵ₁, …) are Cantor's indexed infinite cardinals; ℵ₀ counts the naturals, ℵ₁ the countable ordinals, and under the axiom of choice every infinite cardinal is an aleph.
Alex Chui
Alex Chui (Alex Chui Tsz Fung), born in Hong Kong in 2008, is a British mathematician who won seven medals, including five golds, in seven consecutive International Mathematical Olympiads from 2020 to 2026.
Alex Kontorovich
Alex Kontorovich is an American mathematician at Rutgers University known for work on thin orbits in number theory and for winning the AMS's 2014 Conant Prize.
Algebra
Algebra, historically called the cossic art, is a branch of mathematics studying operations and structures, from solving equations with unknowns to abstract algebra's groups, rings, and fields.
Algebra over a field
An algebra over a field, or K-algebra, is a vector space over a field k with a bilinear multiplication, making it both a ring and a vector space.
Algebraic closure
An algebraic closure of a field F is an algebraically closed algebraic extension of F; every field has one, unique up to isomorphism fixing F.
Algebraic cobordism
Algebraic cobordism, a cohomology theory for algebraic varieties built by Marc Levine and Fabien Morel, is the algebro-geometric analog of complex cobordism and the universal oriented cohomology theory on smooth varieties over fields of characteristic zero.
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics applying algebra, topology, and geometry to combinatorial problems, defined by method rather than subject matter and named in the late 1970s.
Algebraic curve
An algebraic curve, in the plane case also called a plane algebraic curve, is a one-dimensional variety defined by polynomial equations, central to algebraic geometry and used in cryptography.
Algebraic cycles and Chow groups
In algebraic geometry, an algebraic cycle is a finite integer combination of subvarieties, and the Chow groups are the groups of cycles modulo rational equivalence.
Algebraic equation
An algebraic equation is a polynomial set equal to zero, such as a0x^n + ... + an = 0; finding its roots is one of mathematics' oldest problems.
Algebraic expression
An algebraic expression, also called an expression in algebra, combines numbers, letters standing for numbers, and operation symbols without an equality sign, as in 2x^2 + 3x + 8.
Algebraic function
An algebraic function is a function defined by a polynomial equation over a field, such as y = √(x²+1); it is generally many-valued, with branches and algebraic branch points.
Algebraic geometry
Algebraic geometry is the branch of mathematics that studies geometric objects defined by polynomial equations, principally algebraic varieties and schemes, and it underlies elliptic-curve cryptography and algebraic-geometry codes.
Algebraic integer
An algebraic integer is a complex number that is a root of a monic polynomial with integer coefficients; examples include √2 and i, but not 1/2.
Algebraic K-theory
Algebraic K-theory is a branch of mathematics that assigns sequences of abelian K-groups to rings and schemes, with applications in number theory, topology, and algebraic geometry.
Algebraic logic
Algebraic logic, also called the algebra of logic, studies logical systems through algebras, so deduction and completeness become algebraic properties, a tradition begun by Boole in 1847.
Algebraic number
An algebraic number is a complex number that is a root of a polynomial with rational coefficients, such as √2 or the golden ratio; numbers like e and pi are transcendental.