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Generalized hypergeometric series Summary Hypergeometric_sum In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized maps Summary Generalized_maps In mathematics, a generalized map is a topological model which allows one to represent and to handle subdivided objects. This model was defined starting from combinatorial maps in order to represent non-orientable and open subdivisions, which is not possible with combinatorial ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monomial matrix Summary Monomial_matrices In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a gen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized n-gon Summary Generalized_n-gon In mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective planes (generalized triangles, n = 3) and generalized quadrangles (n = 4). Many generalized polygons arise from groups ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential generating series Summary Exponential_generating_function In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential generating series Summary Exponential_generating_function One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers. There are various types of generating functions, including ordinary generating functions, exponential ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential generating series Summary Exponential_generating_function The particular generating function, if any, that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed. Generating functions are often expressed in closed form (rather than as a s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential generating series Summary Exponential_generating_function However such interpretation is not required to be possible, because formal series are not required to give a convergent series when a nonzero numeric value is substituted for x. Also, not all expressions that are meaningful as functions of x are mean... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal In mathematics, a generating set Γ of a module M over a ring R is a subset of M such that the smallest submodule of M containing Γ is M itself (the smallest submodule containing a subset is the intersection of all submodules containing the set). The set Γ is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal In particular, a principal ideal is an ideal that has a generating set consisting of a single element. Explicitly, if Γ is a generating set of a module M, then every element of M is a (finite) R-linear combination of some elements of Γ; i.e., for each x in M... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal Put in another way, there is a surjection ⨁ g ∈ Γ R → M , r g ↦ r g g , {\displaystyle \bigoplus _{g\in \Gamma }R\to M,\,r_{g}\mapsto r_{g}g,} where we wrote rg for an element in the g-th component of the direct sum. (Coincidentally, since a generating set a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal If R is a field, then a minimal generating set is the same thing as a basis. Unless the module is finitely generated, there may exist no minimal generating set.The cardinality of a minimal generating set need not be an invariant of the module; Z is generated... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal Let R be a local ring with maximal ideal m and residue field k and M finitely generated module. Then Nakayama's lemma says that M has a minimal generating set whose cardinality is dim k M / m M = dim k M ⊗ R k {\displaystyle \dim _{k}M/mM=\dim _{k}M\otim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating set of a module Summary Generating_set_of_an_ideal If M is flat, then this minimal generating set is linearly independent (so M is free). See also: Minimal resolution. A more refined information is obtained if one considers the relations between the generators; see Free presentation of a module. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generic polynomial Summary Generic_polynomial In mathematics, a generic polynomial refers usually to a polynomial whose coefficients are indeterminates. For example, if a, b, and c are indeterminates, the generic polynomial of degree two in x is a x 2 + b x + c . {\displaystyle ax^{2}+bx+c.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generic polynomial Summary Generic_polynomial However in Galois theory, a branch of algebra, and in this article, the term generic polynomial has a different, although related, meaning: a generic polynomial for a finite group G and a field F is a monic polynomial P with coefficients in the field of rational functions L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Double torus Summary Genus_g_surface In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g many tori: the interior of a disk is removed from each of g many tori and the boundaries of the g many disks are identified (glued together), forming a g-torus.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hirzebruch polynomial Summary Elliptic_genus In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra In mathematics, a geometric algebra (also known as a real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra The geometric product was first briefly mentioned by Hermann Grassmann, who was chiefly interested in developing the closely related exterior algebra. In 1878, William Kingdon Clifford greatly expanded on Grassmann's work to form what are now usually called Clifford algebras ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra Adding the dual of the Grassmann exterior product (the "meet") allows the use of the Grassmann–Cayley algebra, and a conformal version of the latter together with a conformal Clifford algebra yields a conformal geometric algebra (CGA) providing a framework for classical geome... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra The term "geometric algebra" was repopularized in the 1960s by Hestenes, who advocated its importance to relativistic physics.The scalars and vectors have their usual interpretation, and make up distinct subspaces of a geometric algebra. Bivectors provide a more natural repre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra A trivector can represent an oriented volume, and so on. An element called a blade may be used to represent a subspace of V {\displaystyle V} and orthogonal projections onto that subspace. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra Rotations and reflections are represented as elements. Unlike a vector algebra, a geometric algebra naturally accommodates any number of dimensions and any quadratic form such as in relativity. Examples of geometric algebras applied in physics include the spacetime algebra (a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric algebra Summary Geometric_algebra Geometric calculus, an extension of GA that incorporates differentiation and integration, can be used to formulate other theories such as complex analysis and differential geometry, e.g. by using the Clifford algebra instead of differential forms. Geometric algebra has been a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometrical progression Summary Geometric_sequence In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometrical progression Summary Geometric_sequence Examples of a geometric sequence are powers rk of a fixed non-zero number r, such as 2k and 3k. The general form of a geometric sequence is a , a r , a r 2 , a r 3 , a r 4 , … {\displaystyle a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots } where r ≠ 0 is the common ratio a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric series Summary Geometric_sum In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series 1 2 + 1 4 + 1 8 + 1 16 + ⋯ {\displaystyle {\frac {1}{2}}\,+\,{\frac {1}{4}}\,+\,{\frac {1}{8}}\,+\,{\frac {1}{16}}\,+\,\cdots }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric series Summary Geometric_sum . {\displaystyle a+ar+ar^{2}+ar^{3}+...} , where a {\displaystyle a} is the coefficient of each term and r {\displaystyle r} is the common ratio between adjacent terms. The geometric series had an important role in the early development of calculus, is used throughout mathematics,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transformation (geometry) Summary Partial_transformation In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both R 2 {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gerbe Summary Gerbe In mathematics, a gerbe (; French: ) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2. They can be seen as an analogue of fibre bundles where the fibr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gerbe Summary Gerbe Gerbes provide a convenient, if highly abstract, language for dealing with many types of deformation questions especially in modern algebraic geometry. In addition, special cases of gerbes have been used more recently in differential topology and differential geometry to give alternative description... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Global field Summary Global_field In mathematics, a global field is one of two types of fields (the other one is local field) which are characterized using valuations. There are two kinds of global fields: Algebraic number field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graded Lie algebra Summary Graded_Lie_algebra In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket operation. A choice of Cartan decom... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graded Lie algebra Summary Graded_Lie_algebra A graded Lie superalgebra extends the notion of a graded Lie algebra in such a way that the Lie bracket is no longer assumed to be necessarily anticommutative. These arise in the study of derivations on graded algebras, in the deformation theory of Murray Gerstenhaber, Kuni... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graded Lie algebra Summary Graded_Lie_algebra A supergraded Lie superalgebra is a further generalization of this notion to the category of superalgebras in which a graded Lie superalgebra is endowed with an additional super Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } -gradation. These arise when one forms a grad... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graded dimension Summary Direct_sum_of_graded_vector_spaces In mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gradually varied surface Summary Gradually_varied_surface In mathematics, a gradually varied surface is a special type of digital surfaces. It is a function from a 2D digital space (see digital geometry) to an ordered set or a chain. A gradually varied function is a function from a digital space Σ {\displaystyle \Sigma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph C*-algebra Summary Graph_C*-algebras In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz algebras and Cuntz-Krieger algebras, but the class of graph C*-algebras has been shown to also include several other widely... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph C*-algebra Summary Graph_C*-algebras Although graph C*-algebras include numerous examples, they provide a class of C*-algebras that are surprisingly amenable to study and much more manageable than general C*-algebras. The graph not only determines the associated C*-algebra by specifying relations for generators, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph partitioning Summary Graph_partition In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph partitioning Summary Graph_partition Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see Buluc et al. (2013). Two comm... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph polynomial Summary Graph_polynomial In mathematics, a graph polynomial is a graph invariant whose values are polynomials. Invariants of this type are studied in algebraic graph theory. Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graph polynomial Summary Graph_polynomial The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial The flow polynomial, a polynomial whose values at intege... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Great circle Summary Great_circles In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Eu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Great circle Summary Great_circles Its arc length is the great-circle distance between the points (the intrinsic distance on a sphere), and is proportional to the measure of the central angle formed by the two points and the center of the sphere. A great circle is the largest circle that can be drawn on any given spher... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Great circle Summary Great_circles Any other circle of the sphere is called a small circle, and is the intersection of the sphere with a plane not passing through its center. Small circles are the spherical-geometry analog of circles in Euclidean space. Every circle in Euclidean 3-space is a great circle of exactly one... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
GCD matrix Summary GCD_matrix In mathematics, a greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ground field Summary Ground_field In mathematics, a ground field is a field K fixed at the beginning of the discussion. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Direct sum of groups Summary Direct_sum_of_groups In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete group Summary Complete_group In mathematics, a group G is said to be complete if every automorphism of G is inner, and it is centerless; that is, it has a trivial outer automorphism group and trivial center. Equivalently, a group is complete if the conjugation map, G → Aut(G) (sending an element g to conjugati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group action Summary Regular_group_action In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group action Summary Regular_group_action For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it. For example, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group action Summary Regular_group_action A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of GL(n, K), the group of the invertible matrices of dimension n over a field K. The symmetric group ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extension (algebra) Summary Group_extension In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q {\displaystyle Q} and N {\displaystyle N} are two groups, then G {\displaystyle G} is an extension of Q {\displaystyle Q} by N {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extension (algebra) Summary Group_extension Group extensions arise in the context of the extension problem, where the groups Q {\displaystyle Q} and N {\displaystyle N} are known and the properties of G {\displaystyle G} are to be determined. Note that the phrasing " G {\displaystyle G} is an extension of N {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group sheaf Summary Group_sheaf In mathematics, a group functor is a group-valued functor on the category of commutative rings. Although it is typically viewed as a generalization of a group scheme, the notion itself involves no scheme theory. Because of this feature, some authors, notably Waterhouse and Milne (who fol... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary group theory Summary Elementary_group_theory In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary group theory Summary Elementary_group_theory Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics.In geometry, groups arise naturally in the study of symmetries and geometric t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary group theory Summary Elementary_group_theory Point groups describe symmetry in molecular chemistry. The concept of a group arose in the study of polynomial equations, starting with Évariste Galois in the 1830s, who introduced the term group (French: groupe) for the symmetry group of the roots of an equation,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary group theory Summary Elementary_group_theory After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right. To explore groups, mathematician... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary group theory Summary Elementary_group_theory In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iwasawa group Summary Iwasawa_group In mathematics, a group is called an Iwasawa group, M-group or modular group if its lattice of subgroups is modular. Alternatively, a group G is called an Iwasawa group when every subgroup of G is permutable in G (Ballester-Bolinches, Esteban-Romero & Asaad 2010, pp. 24–25). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iwasawa group Summary Iwasawa_group Kenkichi Iwasawa (1941) proved that a p-group G is an Iwasawa group if and only if one of the following cases happens: G is a Dedekind group, or G contains an abelian normal subgroup N such that the quotient group G/N is a cyclic group and if q denotes a generator of G/N, then for al... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iwasawa group Summary Iwasawa_group As part of Schmidt's proof, he proves that a finite p-group is a modular group if and only if every subgroup is permutable, by (Schmidt 1994, Lemma 2.3.2, p. 55). Every subgroup of a finite p-group is subnormal, and those finite groups in which subnormality and permutability coincide... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boundedly generated group Summary Boundedly_generated_group In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see Lubotzky & Segal 2003). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary amenable group Summary Elementary_amenable_group In mathematics, a group is called elementary amenable if it can be built up from finite groups and abelian groups by a sequence of simple operations that result in amenable groups when applied to amenable groups. Since finite groups and abelian groups are amen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Almost simple group Summary Almost_simple_group In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group – that is, if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group A i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite conjugacy class property Summary Infinite_conjugacy_class_property In mathematics, a group is said to have the infinite conjugacy class property, or to be an ICC group, if the conjugacy class of every group element but the identity is infinite.The von Neumann group algebra of a group is a factor if and only if... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Supersoluble group Summary Supersoluble_group In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability is stronger than the notion of solvability. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplicative group scheme Summary Affine_group_scheme In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme struc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Half range Fourier series Summary Half_range_Fourier_series In mathematics, a half range Fourier series is a Fourier series defined on an interval {\displaystyle } instead of the more common {\displaystyle } , with the implication that the analyzed function f ( x ) , x ∈ {\displaystyle f(x),x\in } should be extended... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Half-exponential function Summary Half-exponential_function In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f {\displaystyle f} such that f {\displaystyle f} composed with itself results in an exponential function: for some constants a {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Half-integer Summary Half-integer In mathematics, a half-integer is a number of the form where n {\displaystyle n} is a whole number. For example, are all half-integers. The name "half-integer" is perhaps misleading, as the set may be misunderstood to include numbers such as 1 (being half the integer 2). A name such as... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Half-integer Summary Half-integer Half-integers occur frequently enough in mathematics and in quantum mechanics that a distinct term is convenient. Note that halving an integer does not always produce a half-integer; this is only true for odd integers. For this reason, half-integers are also sometimes called half-odd-i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Handle decompositions of 3-manifolds Summary Handle_decompositions_of_3-manifolds In mathematics, a handle decomposition of a 3-manifold allows simplification of the original 3-manifold into pieces which are easier to study. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Handle decomposition Summary Handle_decomposition In mathematics, a handle decomposition of an m-manifold M is a union where each M i {\displaystyle M_{i}} is obtained from M i − 1 {\displaystyle M_{i-1}} by the attaching of i {\displaystyle i} -handles. A handle decomposition is to a manifold what a CW-decomposition i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ore's harmonic number Summary Harmonic_divisor_number In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: 1, 6, 28, 140, 270, 496, 672, 1638, 2... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harmonic progression (mathematics) Summary Harmonic_progression_(mathematics) In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harmonious set Summary Harmonious_set In mathematics, a harmonious set is a subset of a locally compact abelian group on which every weak character may be uniformly approximated by strong characters. Equivalently, a suitably defined dual set is relatively dense in the Pontryagin dual of the group. This notion was intro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harshad numbers Summary Harshad_number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-harshad (or n-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hedgehog space Summary Hedgehog_space In mathematics, a hedgehog space is a topological space consisting of a set of spines joined at a point. For any cardinal number κ {\displaystyle \kappa } , the κ {\displaystyle \kappa } -hedgehog space is formed by taking the disjoint union of κ {\displaystyle \kappa } real unit i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hedgehog space Summary Hedgehog_space The hedgehog space is a metric space, when endowed with the hedgehog metric d ( x , y ) = | x − y | {\displaystyle d(x,y)=\left|x-y\right|} if x {\displaystyle x} and y {\displaystyle y} lie in the same spine, and by d ( x , y ) = | x | + | y | {\displaystyle d(x,y)=\left|x\right|+... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Helix Mathematical description Helical_chain > Mathematical description In mathematics, a helix is a curve in 3-dimensional space. The following parametrisation in Cartesian coordinates defines a particular helix; perhaps the simplest equations for one is x ( t ) = cos ( t ) , {\displaystyle x(t)=\cos(t),\,} y ( t ) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Helix Mathematical description Helical_chain > Mathematical description {\displaystyle h(t)=t.\,} A circular helix of radius a and slope a/b (or pitch 2πb) is described by the following parametrisation: x ( t ) = a cos ( t ) , {\displaystyle x(t)=a\cos(t),\,} y ( t ) = a sin ( t ) , {\displaystyle y(t)=a\sin(t),\,}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Induced-hereditary property Summary Hereditary_property In mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly considered in topology and graph theory, but also in set theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heteroclinic cycle Summary Heteroclinic_cycle In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system. It is a topological circle of equilibrium points and connecting heteroclinic orbits. If a heteroclinic cycle is asymptotically stable, approaching trajectories spend longer an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heteroclinic network Summary Heteroclinic_network In mathematics, a heteroclinic network is an invariant set in the phase space of a dynamical system. It can be thought of loosely as the union of more than one heteroclinic cycle. Heteroclinic networks arise naturally in a number of different types of applications, incl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary relations Heterogeneous relation Mathematical_relation > Heterogeneous relation In mathematics, a heterogeneous relation is a binary relation, a subset of a Cartesian product A × B , {\displaystyle A\times B,} where A and B are possibly distinct sets. The prefix hetero is from the Greek ἕτερος (heteros, "other, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hexadecagon Summary Hexadecagon In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hierarchy (mathematics) Summary Hierarchy_(mathematics) In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hierarchy (mathematics) Summary Hierarchy_(mathematics) Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where n ≤ n ′ {\displaystyle n\leq n'} whenever we can find some other number m {\displaystyle m} so th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hierarchy (mathematics) Summary Hierarchy_(mathematics) This idea can be applied to any commutative monoid. On the other hand, the set of integers Z requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation n + m = n ′ {\displaystyle n+m=n'} by writing m = ( n ′ − n )... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hierarchy (mathematics) Summary Hierarchy_(mathematics) This is not just a pedantic claim; there are also mathematical hierarchies, in the general sense, that are not describable using set theory.Other natural hierarchies arise in computer science, where the word refers to partially ordered sets whose elements are clas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Higher local field Summary Higher_local_field In mathematics, a higher (-dimensional) local field is an important example of a complete discrete valuation field. Such fields are also sometimes called multi-dimensional local fields. On the usual local fields (typically completions of number fields or the quotient fields... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Higher local field Summary Higher_local_field In contrast to one-dimensional local fields, higher local fields have a sequence of residue fields. There are different integral structures on higher local fields, depending how many residue fields information one wants to take into account.Geometrically, higher local field... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Higher spin alternating sign matrix Summary Higher_spin_alternating_sign_matrix In mathematics, a higher spin alternating sign matrix is a generalisation of the alternating sign matrix (ASM), where the columns and rows sum to an integer r (the spin) rather than simply summing to 1 as in the usual alternating sign matri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Higher spin alternating sign matrix Summary Higher_spin_alternating_sign_matrix {\displaystyle {\begin{pmatrix}0&0&2&0\\0&2&-1&1\\2&-1&2&-1\\0&1&-1&2\end{pmatrix}};\quad {\begin{pmatrix}0&0&2&0&0\\0&1&-1&2&0\\2&-1&-1&0&2\\0&0&2&0&0\\0&2&0&0&0\end{pmatrix}};\quad {\begin{pmatrix}0&0&0&2\\0&2&0&0\\2&-2&2&0\\0&2&0&0\end{p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Highly abundant number Summary Highly_abundant_number In mathematics, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum of the divisors of any smaller natural number. Highly abundant numbers and several similar classes of numbers were ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Highly structured ring spectrum Summary Highly_structured_ring_spectrum In mathematics, a highly structured ring spectrum or A ∞ {\displaystyle A_{\infty }} -ring is an object in homotopy theory encoding a refinement of a multiplicative structure on a cohomology theory. A commutative version of an A ∞ {\displaystyle A_... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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