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In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods. == Secondary calculus == Secondary calculus a...	Wikipedia/Secondary_calculus_and_cohomological_physics
Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program. The basic difference between affine and Riemannian differential geometry is that affine differential geometry...	Wikipedia/Affine_differential_geometry
In mathematics the differential calculus over commutative algebras is a part of commutative algebra based on the observation that most concepts known from classical differential calculus can be formulated in purely algebraic terms. Instances of this are: The whole topological information of a smooth manifold ...	Wikipedia/Differential_calculus_over_commutative_algebras
In mathematics, a weak Lie algebra bundle ξ = ( ξ , p , X , θ ) {\displaystyle \xi =(\xi ,p,X,\theta )\,} is a vector bundle ξ {\displayst...	Wikipedia/Lie_algebra_bundle
In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and suffi...	Wikipedia/Frobenius_theorem_(differential_topology)
In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named ...	Wikipedia/Euler's_theorem_(differential_geometry)
In geometry, a geodesic () is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun g...	Wikipedia/Geodesic_equation
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in sym...	Wikipedia/Nijenhuis_tensor
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. == Usage in science and engineering == In formal expressions, the ordinal number used before the word order refers to the highest power in the series expan...	Wikipedia/First_order_of_approximation
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Earl...	Wikipedia/Mirror_symmetry_(string_theory)
In differential geometry, a discipline within mathematics, a distribution on a manifold M {\displaystyle M} is an assignment x ↦ Δ x ⊆ T ...	Wikipedia/Distribution_(differential_geometry)
There are many ways to derive the Lorentz transformations using a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory. This article provides ...	Wikipedia/Derivations_of_the_Lorentz_transformations
In physics, geometrothermodynamics (GTD) is a formalism developed in 2007 by Hernando Quevedo to describe the properties of thermodynamic systems in terms of concepts of differential geometry. Consider a thermodynamic system in the framework of classical equilibrium thermodynamics. The states of thermodynamic equilibr...	Wikipedia/Geometrothermodynamics
In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. An important case of vector-value...	Wikipedia/Vector-valued_differential_form
In mathematics, specifically linear algebra, a degenerate bilinear form f (x, y ) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V ) given by v ↦ (x ↦ f (x, v )) is not an isomorphism. An equivalent definition when V is finite-dimensional is that it has a non-trivial kernel: t...	Wikipedia/Non-degenerate
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a ten...	Wikipedia/Riemannian_curvature_tensor
Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU(n), or more generally any compact Lie group. A Yang–Mills theory se...	Wikipedia/Yang–Mills_theory
In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations of the projective group. This is a mixture of the approaches from Riemannian...	Wikipedia/Projective_differential_geometry
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects ...	Wikipedia/Spacetime_topology
In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundle...	Wikipedia/Atlas_(topology)
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also fo...	Wikipedia/Yang–Mills_equations
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-dimensional (solid figures), although many of its tools and principles can be applied to sets...	Wikipedia/Geometric_modeling
Computer-aided design (CAD) is the use of computers (or workstations) to aid in the creation, modification, analysis, or optimization of a design.: 3 This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database...	Wikipedia/Computer-aided_geometric_design
In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematicia...	Wikipedia/Euler–Lagrange_equations
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, throug...	Wikipedia/Standard_model_of_particle_physics
In algebra, a sextic (or hexic) polynomial is a polynomial of degree six. A sextic equation is a polynomial equation of degree six—that is, an equation whose left hand side is a sextic polynomial and whose right hand side is zero. More precisely, it has the form: a x ...	Wikipedia/Sextic_function
In the mathematical field of complex analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Those integrals are in turn named elliptic because they first were encountered for the calcu...	Wikipedia/Elliptic_function
In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) ...	Wikipedia/Hyperelliptic_function
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0...	Wikipedia/Solving_quadratic_equations_with_continued_fractions
In chemistry, a solution is defined by IUPAC as "A liquid or solid phase containing more than one substance, when for convenience one (or more) substance, which is called the solvent, is treated differently from the other substances, which are called solutes. When, as is often but not necessarily the case, the sum of t...	Wikipedia/Solution_(chemistry)
Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0. It was first presented by David E. Muller in 1956. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method. Whereas the secant ...	Wikipedia/Muller's_method
In mathematics, particularly in number theory, an indeterminate system has fewer equations than unknowns but an additional a set of constraints on the unknowns, such as restrictions that the values be integers. In modern times indeterminate equations are often called Diophantine equations.: iii == Examples == === ...	Wikipedia/Indeterminate_equation
In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups. In this picture, theories are classified in terms of their "chromatic le...	Wikipedia/Chromatic_homotopy_theory
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certain axioms relating them. These abstract from the category of topological spaces or of chain complexes (derived ca...	Wikipedia/Model_category
In mathematics, a simplicial set is a sequence of sets with internal order structure (abstract simplices) and maps between them. Simplicial sets are higher-dimensional generalizations of directed graphs. Every simplicial set gives rise to a "nice" topological space, known as its geometric realization. This realizatio...	Wikipedia/Simplicial_homotopy_theory
Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory. == B...	Wikipedia/Shape_theory_(mathematics)
In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It was originated by Whitehead in his 1950 paper "Simple homotopy types". == See also == Whitehead torsion == References == Cohen, M. M. (1973). A Course in Simple-Ho...	Wikipedia/Simple_homotopy_theory
In mathematics, the category of compactly generated weak Hausdorff spaces, CGWH, is a category used in algebraic topology as an alternative to the category of topological spaces, Top, as the latter lacks some properties that are common in practice and often convenient to use in proofs. There is also such a category for...	Wikipedia/Category_of_compactly_generated_weak_Hausdorff_spaces
In algebraic geometry and algebraic topology, branches of mathematics, A1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to Fabien Morel and Vladimir Voevodsky. The unde...	Wikipedia/A1_homotopy_theory
In algebraic topology, the cellular approximation theorem states that a map between CW-complexes can always be taken to be of a specific type. Concretely, if X and Y are CW-complexes, and f : X → Y is a continuous map, then f is said to be cellular, if f takes the n-skeleton of X to the n-skeleton of Y for all n, i.e. ...	Wikipedia/CW_approximation
In mathematics and specifically in topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored. It was founded by Dennis Sullivan (1977) and Daniel Quillen (1969). This simplification of homotopy theory makes certain calcul...	Wikipedia/Rational_homotopy_theory
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory ...	Wikipedia/Spectrum_(algebraic_topology)
In mathematics, the tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ⁡ ( X , − ) {\displaystyle \operatorname {Hom} (X,...	Wikipedia/Tensor-hom_adjunction
In mathematics, algebraic homotopy is a research program on homotopy theory proposed by J.H.C. Whitehead in his 1950 ICM talk, where he described it as: The ultimate object of algebraic homotopy is to construct a purely algebraic theory, which is equivalent to homotopy theory in the same sort of way that 'analytic' is...	Wikipedia/Algebraic_homotopy
In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space ...	Wikipedia/Stable_homotopy_theory
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, wh...	Wikipedia/Quantum_algorithm
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction i...	Wikipedia/Protein_structure_prediction
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The comp...	Wikipedia/Models_of_computation
Switching circuit theory is the mathematical study of the properties of networks of idealized switches. Such networks may be strictly combinational logic, in which their output state is only a function of the present state of their inputs; or may also contain sequential elements, where the present state depends on the ...	Wikipedia/Switching_theory
In computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather than computational complexity of individual problems and algorithms. It involves the research of both internal structures of various complexity classes and ...	Wikipedia/Structural_complexity_theory
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship betwee...	Wikipedia/Quantum_complexity_theory
The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in ...	Wikipedia/RSA_(algorithm)
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic needed to express the languages in them. For example, PH, the union of all complexity classes in the polynomial hierarchy, is precisely the class of languages expre...	Wikipedia/Descriptive_complexity_theory
In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. Thi...	Wikipedia/Feasible_solution
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (no...	Wikipedia/Shor's_algorithm
In computer science and computer programming, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. Different models of computation give rise to different reasons that an algorithm may be non-deterministic,...	Wikipedia/Non-deterministic_algorithm
In computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem. For function problems, the output is not simply 'yes' or 'no'. == Definition == A functional proble...	Wikipedia/Function_problem
In computer science, a deterministic algorithm is an algorithm that, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the m...	Wikipedia/Deterministic_algorithm
Introduction to Automata Theory, Languages, and Computation is an influential computer science textbook by John Hopcroft and Jeffrey Ullman on formal languages and the theory of computation. Rajeev Motwani contributed to later editions beginning in 2000. == Nickname == The Jargon File records the book's nickname, Ci...	Wikipedia/Introduction_to_Automata_Theory,_Languages,_and_Computation
Jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second(g0/s). == Expressions == As a vector, jerk j can be expr...	Wikipedia/Jerk_(physics)
The Charlot equation, named after Gaston Charlot, is used in analytical chemistry to relate the hydrogen ion concentration, and therefore the pH, with the formal analytical concentration of an acid and its conjugate base. It can be used for computing the pH of buffer solutions when the approximations of the Henderson–H...	Wikipedia/Charlot_equation
In algebra, Gauss's lemma, named after Carl Friedrich Gauss, is a theorem about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem of arithmetic). Gauss's lemma underlies all the theory of fa...	Wikipedia/Gauss's_lemma_(polynomial)
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the r...	Wikipedia/Discrete_Fourier_transform
Hippocrates of Chios (Ancient Greek: Ἱπποκράτης ὁ Χῖος; c. 470 – c. 421 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, po...	Wikipedia/Hippocrates_of_Chios
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide var...	Wikipedia/Buffer_solution
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ...	Wikipedia/Numerical_approximation
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and P...	Wikipedia/Horner_method
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equatio...	Wikipedia/Equation_of_state
In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. Simply, it is a method for transforming a polynomial equation of degree n ≥ 2 {\d...	Wikipedia/Tschirnhaus_transformation
In algebra, a quartic function is a function of the formα f ( x ) = a x 4 + b x 3 + c ...	Wikipedia/Quartic_equations
In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of its particularly simple equidimensional structure, the differential eq...	Wikipedia/Cauchy–Euler_equation
Cubic equations of state are a specific class of thermodynamic models for modeling the pressure of a gas as a function of temperature and density and which can be rewritten as a cubic function of the molar volume. Equations of state are generally applied in the fields of physical chemistry and chemical engineering, pa...	Wikipedia/Cubic_equations_of_state
In ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A that is simple, and for which the center is exactly K. (Note that not every simple algebra is a central simple algebra over its center: for instance, if K is a field of character...	Wikipedia/Central_simple_algebra
In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra. It is used in the Batalin–Vilkovisky formali...	Wikipedia/Gerstenhaber_algebra
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation V of a quiver assigns a vector space V(x) to each vertex x of th...	Wikipedia/Quiver_algebra
In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension. == Definition and first properties == A homomorphism of (unital, but not necessarily commutative) rings K → A ...	Wikipedia/Separable_algebra
In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the ring is a field, the most common application of such products is to describe the product of algebra representations. == Definition == Let R be a commutative ring and l...	Wikipedia/Tensor_product_of_rings
In mathematics, a subring of a ring R is a subset of R that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and that shares the same multiplicative identity as R. == Definition == A subring of a ring (R, +, *, 0, 1) is a subset S of R that preserves the struct...	Wikipedia/Algebra_of_dual_numbers
In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules...	Wikipedia/Sheaf_of_algebras
In abstract algebra, a quasi-free algebra is an associative algebra that satisfies the lifting property similar to that of a formally smooth algebra in commutative algebra. The notion was introduced by Cuntz and Quillen for the applications to cyclic homology. A quasi-free algebra generalizes a free algebra, as well as...	Wikipedia/Quasi-free_algebra
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms μ: M ⊗ M → M called multiplication, η: I → M called unit, such that the pentagon diagram and the unitor diagram commute. In th...	Wikipedia/Monoid_(category_theory)
In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of ...	Wikipedia/Enveloping_algebra_of_an_associative_algebra
In mathematics, a Brauer algebra is an associative algebra introduced by Richard Brauer in the context of the representation theory of the orthogonal group. It plays the same role that the symmetric group does for the representation theory of the general linear group in Schur–Weyl duality. == Structure == The Brauer ...	Wikipedia/Brauer_algebra
In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb. It is also related to integrable models, knot theory and the braid groups, quantum groups and subfactors of von Neumann algebras. == Structure == === Ge...	Wikipedia/Temperley-Lieb_algebra
In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra g {\displaystyle {\mathfrak {g}}} , the quantum enveloping algebra is typically denoted as ...	Wikipedia/Quantized_enveloping_algebra
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. Its subalgebras include diagram algebras such as the Brauer algebra, the Temperley–Lieb algebra, or the group algebra of the symmetric group. Representations of the partition algebra...	Wikipedia/Partition_algebra
In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used to capture information about a topological or geometric space. Explicitly, a differential graded algebra is a graded associative a...	Wikipedia/Differential_graded_algebra
In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used to capture information about a topological or geometric space. Explicitly, a differential graded algebra is a graded associative a...	Wikipedia/De_Rham_algebra
In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that A {\disp...	Wikipedia/Order_(ring_theory)
In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the c...	Wikipedia/Azumaya_algebra
In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism. In other words, if f : X → Y {\displaystyle f:X\to Y} and g : ...	Wikipedia/Retract_(category_theory)
Zermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory (NBG). It bears certain differences from its descendants, which are not always understood, an...	Wikipedia/Zermelo_set_theory
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y...	Wikipedia/Pushout_(category_theory)
In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism. In other words, if f : X → Y {\displaystyle f:X\to Y} and g : ...	Wikipedia/Section_(category_theory)
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which...	Wikipedia/Functional_programming
Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular quantum mechanics), natural language processing, control theory, probability theory and causality. The application of category theo...	Wikipedia/Applied_category_theory
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is written P = X ×f, Z, g Y. Usually the morphisms f and g are omi...	Wikipedia/Pullback_(category_theory)
In category theory, an end of a functor S : C o p × C → X {\displaystyle...	Wikipedia/End_(category_theory)
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the ...	Wikipedia/Descriptive_set_theory
In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f : X → Y is the "most general" morphism k : K → X that yields...	Wikipedia/Kernel_(category_theory)

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