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Connection one-form Summary Connection_1-form In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form as a tensorial object. On the other hand, the connection form has the advantage that it is a differential form defined on the differentiable manifold, rather th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Connection one-form Summary Connection_1-form In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative. A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial because under a chan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Connection one-form Summary Connection_1-form The main tensorial invariant of a connection form is its curvature form. In the presence of a solder form identifying the vector bundle with the tangent bundle, there is an additional invariant: the torsion form. In many cases, connection forms are considered on vector bund... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Density bundle Summary Density_on_a_manifold In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain line bundle, called the density bundle. An element of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lp sum Summary Lp_sum In mathematics, and specifically in functional analysis, the Lp sum of a family of Banach spaces is a way of turning a subset of the product set of the members of the family into a Banach space in its own right. The construction is motivated by the classical Lp spaces. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian group Summary Non-Abelian_group In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at least one pair of elements a and b of G, such that a ∗ b ≠ b ∗ a. This class of groups contrasts with the abelian groups.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian group Summary Non-Abelian_group It is the smallest finite non-abelian group. A common example from physics is the rotation group SO(3) in three dimensions (for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order). Bot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equivalent measures Summary Equivalence_of_measures In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have measure zero. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sum-of-divisors function Summary Sum_of_divisors In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer (including 1 and the number itself). It appears... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive-definite function on a group Summary Positive_definite_function_on_a_group In mathematics, and specifically in operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive-de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poisson kernel Summary Poisson_integral In mathematics, and specifically in potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel can be understood as the derivative of the Green's function for ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Freudenthal suspension theorem Summary Freudenthal_suspension_theorem In mathematics, and specifically in the field of homotopy theory, the Freudenthal suspension theorem is the fundamental result leading to the concept of stabilization of homotopy groups and ultimately to stable homotopy theory. It explains the behavi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Accessible pointed graph Summary Accessible_pointed_graph In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow mul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real-root isolation Summary Real-root_isolation In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together, contain all t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real-root isolation Summary Real-root_isolation Moreover, it may be difficult to distinguish the real roots from the non-real roots with small imaginary part (see the example of Wilkinson's polynomial in next section). The first complete real-root isolation algorithm results from Sturm's theorem (1829). However, when r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Anti-commutative property Summary Anti-commutative_property In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments. The noti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Antiholomorphic function Summary Antiholomorphic_function In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions. A function of the complex variable z defined on an open set in the complex plane is said to be an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Antiholomorphic function Summary Antiholomorphic_function This implies that a function is antiholomorphic if and only if it can be expanded in a power series in z in a neighborhood of each point in its domain. Also, a function f(z) is antiholomorphic on an open set D if and only if the function f(z) is holomorphic on D... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauge symmetry (mathematics) Summary Gauge_symmetry_(mathematics) In mathematics, any Lagrangian system generally admits gauge symmetries, though it may happen that they are trivial. In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory. A ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauge symmetry (mathematics) Summary Gauge_symmetry_(mathematics) For instance, this is the case of gauge symmetries in classical field theory. Yang–Mills gauge theory and gauge gravitation theory exemplify classical field theories with gauge symmetries.Gauge symmetries possess the following two peculiarities. Being La... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Periodic summation Summary Periodic_summation In mathematics, any integrable function s ( t ) {\displaystyle s(t)} can be made into a periodic function s P ( t ) {\displaystyle s_{P}(t)} with period P by summing the translations of the function s ( t ) {\displaystyle s(t)} by integer multiples of P. This is called peri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological dual space Summary Dual_(linear_algebra) In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V , {\displaystyle V,} together with the vector space structure of pointwise addition and scalar multiplication... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological dual space Summary Dual_(linear_algebra) When applied to vector spaces of functions (which are typically infinite-dimensional), dual spaces are used to describe measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. Early terms for dual incl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev approximation Summary Chebyshev_approximation In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application. A closely ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev approximation Summary Chebyshev_approximation This is typically done with polynomial or rational (ratio of polynomials) approximations. The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arithmetic combinatorics Summary Additive_Combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arithmetic Geometry Summary Arithmetic_Geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.In more abstract terms, arit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arithmetico–geometric series Summary Arithmetico-geometric_sequence In mathematics, arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. Put plainly, the nth term of an arithmetico-geometric sequence is the prod... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arithmetico–geometric series Summary Arithmetico-geometric_sequence For instance, the sequence 0 1 , 1 2 , 2 4 , 3 8 , 4 16 , 5 32 , ⋯ {\displaystyle {\dfrac {\color {blue}{0}}{\color {green}{1}}},\ {\dfrac {\color {blue}{1}}{\color {green}{2}}},\ {\dfrac {\color {blue}{2}}{\color {green}{4}}},\ {\dfrac {\color {blue}{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Assembly map Summary Assembly_map In mathematics, assembly maps are an important concept in geometric topology. From the homotopy-theoretical viewpoint, an assembly map is a universal approximation of a homotopy invariant functor by a homology theory from the left. From the geometric viewpoint, assembly maps correspond... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymmetry In mathematics Asymmetry > In mathematics In mathematics, asymmetry can arise in various ways. Examples include asymmetric relations, asymmetry of shapes in geometry, asymmetric graphs et cetera. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Comodule over a Hopf algebroid Summary Comodule_over_a_Hopf_algebroid In mathematics, at the intersection of algebraic topology and algebraic geometry, there is the notion of a Hopf algebroid which encodes the information of a presheaf of groupoids whose object sheaf and arrow sheaf are represented by algebras. Because... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cerf theory Summary Cerf_theory In mathematics, at the junction of singularity theory and differential topology, Cerf theory is the study of families of smooth real-valued functions f: M → R {\displaystyle f\colon M\to \mathbb {R} } on a smooth manifold M {\displaystyle M} , their generic singularities and the topology... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Auxiliary function Summary Auxiliary_function In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions that appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value zero for many arguments, or ha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Axiomatic proof Axiomatization Axiomatic_logic > Axiomatic method > Axiomatization In mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. It is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms — in order that a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Base change lifting Summary Base_change_lifting In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galois group to a subgroup. The Doi–Naganuma lifting from 1967 was a precurs... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Basic hypergeometric series Summary Basic_hypergeometric_function In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Biangular coordinates Summary Biangular_coordinates In mathematics, biangular coordinates are a coordinate system for the plane where C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} are two fixed points, and the position of a point P not on the line C 1 C 2 ¯ {\displaystyle {\overline {C_{1}C_{2}}}} is determin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bicubic interpolation Summary Bi-cubic_interpolation In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid. The interpolated surface (meaning the kernel shape, not the i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bicubic interpolation Summary Bi-cubic_interpolation In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue. In contrast to bilinear interpolation, which only takes 4 pixels (2×2) into account, bicubic interpolation cons... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bilinear filtering Summary Bilinear_filtering In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary splitting Summary Binary_splitting In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Biracks and biquandles Summary Biracks_and_biquandles In mathematics, biquandles and biracks are sets with binary operations that generalize quandles and racks. Biquandles take, in the theory of virtual knots, the place that quandles occupy in the theory of classical knots. Biracks and racks have the same relation, whi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Birational automorphism Summary Birational_geometry In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than pol... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bracket (mathematics) Summary Bracket_(mathematics) In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets , braces { } and angle brackets ⟨ ⟩, are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calculus on Euclidean space Summary Calculus_on_Euclidean_space In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space R n {\displaystyle \mathbb {R} ^{n}} as well as a finite-dimensional real vector space. This ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calculus on finite weighted graphs Summary Calculus_on_finite_weighted_graphs In mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights associated to the edges. This involves formulating discrete operato... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calculus on finite weighted graphs Summary Calculus_on_finite_weighted_graphs Differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation (where the vertices represent pixels and the weighted edges encode pixel similarity based on ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Canonical singularity Summary Log_canonical_singularity In mathematics, canonical singularities appear as singularities of the canonical model of a projective variety, and terminal singularities are special cases that appear as singularities of minimal models. They were introduced by Reid (1980). Terminal singularities... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catastrophe theory Summary Catastrophe_theory In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catastrophe theory Summary Catastrophe_theory It considers the special case where the long-run stable equilibrium can be identified as the minimum of a smooth, well-defined potential function (Lyapunov function). Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catastrophe theory Summary Catastrophe_theory However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures. In the late 1970s, applications of catastrophe theory to areas outside its scope began to be crit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Categorification Summary Categorification In mathematics, categorification is the process of replacing set-theoretic theorems with category-theoretic analogues. Categorification, when done successfully, replaces sets with categories, functions with functors, and equations with natural isomorphisms of functors satisfyin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Categorification Summary Categorification The reverse of categorification is the process of decategorification. Decategorification is a systematic process by which isomorphic objects in a category are identified as equal. Whereas decategorification is a straightforward process, categorification is usually much less str... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cellular homology Summary Cellular_homology In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Derived functors Summary Derived_functor In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical fallacies Summary False_proof In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical fallacies Summary False_proof Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and are not a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical fallacies Summary False_proof The latter usually applies to a form of argument that does not comply with the valid inference rules of logic, whereas the problematic mathematical step is typically a correct rule applied with a tacit wrong assumption. Beyond pedagogy, the resolution of a fallacy can lead to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical fallacies Summary False_proof Pseudaria, an ancient lost book of false proofs, is attributed to Euclid.Mathematical fallacies exist in many branches of mathematics. In elementary algebra, typical examples may involve a step where division by zero is performed, where a root is incorrectly extracted or, more... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integral manifold Summary Integrability_conditions_for_differential_systems In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integral manifold Summary Integrability_conditions_for_differential_systems A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system is a set of 1-forms on a smooth manifold (which one sets equal to 0 to find solutions to the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integral manifold Summary Integrability_conditions_for_differential_systems A maximal integral manifold is an immersed (not necessarily embedded) submanifold i: N ⊂ M {\displaystyle i:N\subset M} such that the kernel of the restriction map on forms i ∗: Ω p 1 ( M ) → Ω p 1 ( N ) {\displaystyle i^{*}:\Omega _{p}^{1}(M)\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chiral homology Summary Topological_chiral_homology In mathematics, chiral homology, introduced by Alexander Beilinson and Vladimir Drinfeld, is, in their words, "a “quantum” version of (the algebra of functions on) the space of global horizontal sections of an affine D X {\displaystyle {\mathcal {D}}_{X}} -scheme (i.e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chromatic tower Summary Chromatic_homotopy_theory 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, theor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circle-valued Morse theory Summary Circle-valued_Morse_theory In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology. It is an important special case of Sergei Novikov's Mors... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Global class field theory Summary Higher_class_field_theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.Hilbert is credited as one of pion... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Global class field theory Summary Higher_class_field_theory The existence theorem states that the reciprocity map can be used to give a bijection between the set of abelian extensions of F and the set of closed subgroups of finite index of C F . {\displaystyle C_{F}.} A standard method for developing global class field... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Global class field theory Summary Higher_class_field_theory This was first done by Emil Artin and Tate using the theory of group cohomology, and in particular by developing the notion of class formations. Later, Neukirch found a proof of the main statements of global class field theory without using cohomological ideas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Global class field theory Summary Higher_class_field_theory Inside class field theory one can distinguish special class field theory and general class field theory. Explicit class field theory provides an explicit construction of maximal abelian extensions of a number field in various situations. This portion of the th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Timeline of class field theory Summary Timeline_of_class_field_theory In mathematics, class field theory is the study of abelian extensions of local and global fields. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical Wiener space Summary Wiener_space In mathematics, classical Wiener space is the collection of all continuous functions on a given domain (usually a subinterval of the real line), taking values in a metric space (usually n-dimensional Euclidean space). Classical Wiener space is useful in the study of stochasti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sweedler notation Summary Incidence_coalgebra In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all arrows around,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sweedler notation Summary Incidence_coalgebra In finite dimensions, this duality goes in both directions (see below). Coalgebras occur naturally in a number of contexts (for example, representation theory, universal enveloping algebras and group schemes). There are also F-coalgebras, with important applications in comp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coarse function Summary Coarse_function In mathematics, coarse functions are functions that may appear to be continuous at a distance, but in reality are not necessarily continuous. Although continuous functions are usually observed on a small scale, coarse functions are usually observed on a large scale. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oriented cobordant Summary Cobordism_theory In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oriented cobordant Summary Cobordism_theory The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions for piecewise linear and topological manifolds. A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oriented cobordant Summary Cobordism_theory Cobordisms are studied both for the equivalence relation that they generate, and as objects in their own right. Cobordism is a much coarser equivalence relation than diffeomorphism or homeomorphism of manifolds, and is significantly easier to study and compute. It is not poss... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oriented cobordant Summary Cobordism_theory Cobordisms are central objects of study in geometric topology and algebraic topology. In geometric topology, cobordisms are intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cocompact embedding Summary Cocompact_embedding In mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness has been in use in mathematical analysis since the 1980s, without being referred to by any name (Lemma 6),(Lemma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dimension counting Summary Dimension_counting In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties. For affine and projective algebraic varieties, the codimension equals the height of the defining idea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coherent duality Summary Coherent_duality In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory. The historical roots of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coherent duality Summary Coherent_duality The resulting theory is now sometimes called Serre–Grothendieck–Verdier duality, and is a basic tool in algebraic geometry. A treatment of this theory, Residues and Duality (1966) by Robin Hartshorne, became a reference. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coherent duality Summary Coherent_duality One concrete spin-off was the Grothendieck residue. To go beyond proper morphisms, as for the versions of Poincaré duality that are not for closed manifolds, requires some version of the compact support concept. This was addressed in SGA2 in terms of local cohomology, and Groth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohomology with compact support Summary Cohomology_with_compact_support In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combinatorial group theory Summary Combinatorial_group_theory In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and ge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combinatorial topology Summary Combinatorial_topology In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combinatorial topology Summary Combinatorial_topology The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology.A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topolog... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combinatorial topology Summary Combinatorial_topology Azriel Rosenfeld (1973) proposed digital topology for a type of image processing that can be considered as a new development of combinatorial topology. The digital forms of the Euler characteristic theorem and the Gauss–Bonnet theorem were obtained by Li Chen and Yo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compact object (category theory) Summary Compact_object_(mathematics) In mathematics, compact objects, also referred to as finitely presented objects, or objects of finite presentation, are objects in a category satisfying a certain finiteness condition. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compactly generated Summary Compactly_generated In mathematics, compactly generated can refer to: Compactly generated group, a topological group which is algebraically generated by one of its compact subsets Compactly generated space, a topological space whose topology is coherent with the family of all compact subspac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Comparison theorem Summary Comparison_theorem In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often occur in fields such as calculus, differential equations and Riemannian geometry. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stein complementary series representation Summary Complementary_series_representation In mathematics, complementary series representations of a reductive real or p-adic Lie groups are certain irreducible unitary representations that are not tempered and do not appear in the decomposition of the regular representation i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stein complementary series representation Summary Complementary_series_representation Several conjectures in mathematics, such as the Selberg conjecture, are equivalent to saying that certain representations are not complementary. For examples see the representation theory of SL2(R). Elias M. Stein (1972) constructed s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex cobordism ring Summary Complex_cobordism_ring In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real dimension Summary Complex_dimension In mathematics, complex dimension usually refers to the dimension of a complex manifold or a complex algebraic variety. These are spaces in which the local neighborhoods of points (or of non-singular points in the case of a variety) are modeled on a Cartesian product of the form... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real dimension Summary Complex_dimension However, for a real algebraic variety (that is a variety defined by equations with real coefficients), its dimension refers commonly to its complex dimension, and its real dimension refers to the maximum of the dimensions of the manifolds contained in the set of its real points.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real dimension Summary Complex_dimension For example a smooth complex hypersurface in complex projective space of dimension n will be a manifold of dimension 2(n − 1). A complex hyperplane does not separate a complex projective space into two components, because it has real codimension 2. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex geometry Summary Complex_algebraic_geometry In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varietie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex geometry Summary Complex_algebraic_geometry Because of the blend of techniques and ideas from various areas, problems in complex geometry are often more tractable or concrete than in general. For example, the classification of complex manifolds and complex algebraic varieties through the minimal model program a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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