Algebra
Topics in mathematicsStatisticsCalculus and analysisGeometryDiscrete mathematicsFoundationsBasicsAlgebraStatistics and probabilityApplied mathematicsFunctionsMathematicsTheoretical computer scienceFrom Lably lessonsNumber theoryOtherCounting and numbersGeometry and topologyApplied MathematicsGeneralAnalysisArithmeticProbability and statistics
A
- Abelian groupCommutative group (mathematics)
- Abstract algebraBranch of mathematics
- Affine spaceEuclidean space without distance and angles
- AlgebraBranch of mathematics
- Algebra over a fieldVector space equipped with a bilinear product
- Algebraic equationPolynomial equation, generally univariate
- Algebraic expressionMathematical expression using basic operations
- Algebraic geometryBranch of mathematics
- Algebraic structureSet with operations obeying given axioms
- Algebraic topologyBranch of mathematics
- Algebraic varietyMathematical object studied in the field of algebraic geometry
- Alternating groupGroup of even permutations of a finite set
- Alternating multilinear mapIn mathematics, more specifically in multilinear algebra, an alternating multilinear map i
- AntihomomorphismIn mathematics, an antihomomorphism is a type of function defined on sets with multiplicat
- Associative propertyProperty of a mathematical operation
B
C
- Category of ringsCategory whose objects are rings and whose morphisms are ring homomorphisms
- Cauchy–Schwarz inequalityMathematical inequality relating inner products and norms
- Classification of finite simple groupsTheorem classifying finite simple groups
- Commutative algebraBranch of algebra that studies commutative rings
- Commutative propertyProperty of some mathematical operations
- Commutative ringAlgebraic structure
- Complemented latticeBound lattice in which every element has a complement
- Conjugacy classIn group theory, equivalence class under the relation of conjugation
- Coordinate vectorConcept in linear algebra
- Cramer's ruleFormula for systems of linear equations
- Cross productMathematical operation on vectors in 3D space
- Cubic equationPolynomial equation of degree 3
- Cyclic groupMathematical group that can be generated as the set of powers of a single element
D
E
- Eigenvalues and eigenvectorsConcepts from linear algebra
- Einstein notationShorthand notation for tensor operations
- Elementary algebraBasic concepts of algebra
- EquationMathematical formula expressing equality
- Euclidean vectorGeometric object that has length and direction
- Exterior algebraAlgebra associated to any vector space
F
- Factorization(Mathematical) decomposition into a product
- Field (mathematics)Algebraic structure with addition, multiplication, and division
- Field extensionConstruction of a larger algebraic field by "adding elements" to a smaller field
- Finite fieldAlgebraic structure
- Free algebraFree object in the category of associative algebras
- Free product of associative algebrasIn algebra, the free product (coproduct) of a family of associative algebras over a commut
- Frobenius characteristic mapIn mathematics, especially representation theory and combinatorics, a Frobenius characteri
- Frobenius endomorphismMap raising elements to the pth power, in characteristic p
- Fundamental groupMathematical group of the homotopy classes of loops in a topological space
- Fundamental theorem of algebraEvery polynomial has a real or complex root
G
- Galois groupMathematical group
- Galois theoryMathematical connection between field theory and group theory
- Gauss–Seidel methodIterative method used to solve a linear system of equations
- Gaussian eliminationAlgorithm for solving systems of linear equations
- Geometric algebraAlgebraic structure designed for geometry
- Graded Lie algebraIn mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is co
- Graded ringType of algebraic structure
- Graded vector spaceIn mathematics, a graded vector space is a vector space that has the extra structure of a
- Group (mathematics)Set with associative invertible operation
- Group representationGroup homomorphism into the general linear group over a vector space
- Group theoryBranch of mathematics that studies the properties of groups
- Group with operatorsConcept in mathematics regarding sets operating on groups
H
- Heyting algebraAlgebraic structure used in logic
- Hilbert's basis theoremPolynomial ideals are finitely generated
- Hilbert's NullstellensatzRelation between algebraic varieties and polynomial ideals
- History monoidIn mathematics and computer science, a history monoid is a way of representing the histori
- Homogeneous polynomialPolynomial whose nonzero terms all have the same degree
- Homological algebraBranch of mathematics
- HomomorphismStructure-preserving map between two algebraic structures of the same type
- Hopf algebraConstruction in algebra
- Horner's methodAlgorithm for polynomial evaluation
I
- Ideal (ring theory)Submodule of a mathematical ring
- Identity elementSpecific element of an algebraic structure
- Identity matrixSquare matrix with ones on the main diagonal and zeros elsewhere
- Inner product spaceVector space with generalized dot product
- Integer factorizationDecomposition of a number into a product
- Inverse elementGeneralization of additive and multiplicative inverses
- IsomorphismIn mathematics, invertible homomorphism
- Isomorphism theoremsGroup of mathematical theorems
J
K
L
- Lagrange's theorem (group theory)Theorem on the orders of subgroups
- Laplace expansionExpression of a determinant in terms of minors
- Lie algebraAlgebraic structure used in analysis
- Lie groupGroup that is also a differentiable manifold with group operations that are smooth
- Lie's third theoremIn the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional
- Linear algebraBranch of mathematics
- Linear combinationSum of terms, each multiplied with a scalar
- Linear equationEquation that does not involve powers or products of variables
- Linear independenceVectors whose linear combinations are nonzero
- Linear mapMathematical function, in linear algebra
- Linear Operators (book)Linear Operators is a three-volume textbook on the theory of linear operators, written by
- LU decompositionType of matrix factorization
M
- Magma (algebra)Algebraic structure with a binary operation
- Magnitude (mathematics)Property determining comparison and ordering
- Main diagonalEntries of a matrix for which the row and column indices are equal
- Map of latticesConcept in mathematics
- Matrix (mathematics)Array of numbers
- Matrix multiplicationMathematical operation in linear algebra
- Matrix unitIn linear algebra, a matrix unit is a matrix with only one nonzero entry with value 1. The
- Metric tensorStructure defining distance on a manifold
- Modular groupOrientation-preserving mapping class group of the torus
- Modularity theoremRelates rational elliptic curves to modular forms
- Module (mathematics)Generalization of vector spaces from fields to rings
- Moduli spaceGeometric space whose points represent algebro-geometric objects of some fixed kind
- MonoidAlgebraic structure with an associative operation and an identity element
N
- Near-ringAlgebraic structure in mathematics
- Non-associative algebraAlgebra over a field where binary multiplication is not necessarily associative
- Norm (mathematics)Length in a vector space
- Normal subgroupSubgroup invariant under conjugation
- Normed vector spaceVector space on which a distance is defined
- Numerical linear algebraField of mathematics
O
P
- Polynomial evaluationIn mathematics and computer science, polynomial evaluation refers to computation of the va
- Polynomial identity ringIn ring theory, a branch of mathematics, a ring R is a polynomial identity ring if there i
- Polynomial ringAlgebraic structure
- Prime decomposition of 3-manifoldsIn mathematics, the prime decomposition theorem for 3-manifolds states that every compact,
- Product of ringsRing built from other rings (mathematics)
- Projection (linear algebra)Idempotent linear transformation from a vector space to itself
- Prüfer groupIn mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic grou
Q
- Quadratic equationPolynomial equation of degree two
- Quadratic formPolynomial with all terms of degree two
- Quadratic form (statistics)In multivariate statistics, if is a vector of random variables, and is an -dimensional sym
- Quadratic formulaFormula that provides the solutions to a quadratic equation
- Quartic equationPolynomial equation of degree 4
- QuasigroupMagma obeying the Latin square property
- QuaternionFour-dimensional number system
- Quintic equationPolynomial equation of degree 5
R
- Racks and quandlesSets with binary operations analogous to the Reidemeister moves used on knot diagrams
- Rank (linear algebra)Dimension of the column space of a matrix
- Rank–nullity theoremIn linear algebra, relation between 3 dimensions
- Representation theoryBranch of mathematics that studies abstract algebraic structures
- ResultantMathematical concept in polynomial theory
- Richard V. SouthwellSir Richard Vynne Southwell, FRS (2 July 1888 – 9 December 1970) was a British mathematici
- Ring (mathematics)Algebraic structure with addition and multiplication
- Ring of polynomial functionsIn mathematics, the ring of polynomial functions on a vector space V over a field k gives
- Ring of setsIn mathematics, there are two different notions of a ring of sets, both referring to certa
- Ring theoryBranch of algebra
- Rng (algebra)Algebraic ring without a multiplicative identity
- Robert RecordeWelsh mathematician and inventor of the equals sign
- Rotations and reflections in two dimensionsIn Euclidean geometry, two-dimensional rotations and reflections are two kinds of Euclidea
- Rubik's Cube groupMathematical group
S
- Scalar (mathematics)Elements of a field, e.g. real numbers, in the context of linear algebra
- Scalar multiplicationAlgebraic operation
- SemifieldAlgebraic structure
- SemigroupAlgebraic structure
- SemilatticePartial order with joins
- Semiprimitive ringIn algebra, a semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a rin
- SemiringAlgebraic ring that need not have additive negative elements
- Sheaf (mathematics)Tool to track locally defined data attached to the open sets of a topological space
- Simple groupGroup without normal subgroups other than the trivial group and itself
- Sporadic groupFinite simple group type not classified as Lie, cyclic or alternating
- Stan FrankelStanley Phillips Frankel (1919 – May, 1978) was an American computer scientist. He worked
- SubobjectIn category theory, a branch of mathematics, a subobject is, roughly speaking, an object t
- Subobject classifierIn category theory, a subobject classifier is a special object Ω of a category such that,
- SubringSubset of a ring that forms a ring itself
- Successive over-relaxationMethod of solving a linear system of equations
- Symbolic integrationComputation of an antiderivatives
- System of linear equationsSeveral equations of degree 1 to be solved simultaneously
- System of polynomial equationsA system of polynomial equations (sometimes simply a polynomial system) is a set of simult
T
- Tensor productMathematical operation on vector spaces
- Tensor product of algebrasTensor product of algebras over a field; itself another algebra
- Total ring of fractionsConstruction within abstract algebra
- Trace monoidIn computer science, a trace is an equivalence class of strings, wherein certain letters i
- TransposeMatrix operation which flips a matrix over its diagonal
- Transpose of a linear mapIn linear algebra, the transpose of a linear map between two vector spaces, defined over t
- Trial divisionInteger factorization algorithm
- Triangle inequalityProperty of geometry, also used to generalize the notion of "distance" in metric spaces
- Triangular matrixSpecial kind of square matrix