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Homogeneous equation Summary Homogeneous_system_of_linear_equations Very often, and in this article, the coefficients of the equations are real or complex numbers and the solutions are searched in the same set of numbers, but the theory and the algorithms apply for coefficients and solutions in any field. For solutions... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Underdetermined system Summary Underdetermined_system In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns). The terminology can be ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Underdetermined system Summary Underdetermined_system Therefore, the critical case (between overdetermined and underdetermined) occurs when the number of equations and the number of free variables are equal. For every variable giving a degree of freedom, there exists a corresponding constraint removing a degree of free... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
System of parameters Summary System_of_parameters In mathematics, a system of parameters for a local Noetherian ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: m is a minimal prime over (x1, ..., xd). The radical of (x1, ..., xd)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
T-norm Summary T-norm In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name tri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tall cardinal Summary Tall_cardinal In mathematics, a tall cardinal is a large cardinal κ that is θ-tall for all ordinals θ, where a cardinal is called θ-tall if there is an elementary embedding j: V → M with critical point κ such that j(κ) > θ and Mκ ⊆ M. Tall cardinals are equiconsistent with strong cardinals. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moderated Topology Summary Tame_topology In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programme under the French name topologie modérée (moderate topology). It is a topology in which the theory of dévissage can be applied to stratifi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tangent Lie group Summary Tangent_Lie_group In mathematics, a tangent Lie group is a Lie group whose underlying space is the tangent bundle TG of a Lie group G. As a Lie group, the tangent bundle is a semidirect product of a normal abelian subgroup with underlying space the Lie algebra of G, and G itself. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tangent vector Summary Tangent_vectors In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in Rn. More generally, tangent vectors are elements of a tangent space of a differenti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic tangle Summary Tangle_diagram In mathematics, a tangle is generally one of two related concepts: In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary. In link t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic tangle Summary Tangle_diagram The balance of this article discusses Conway's sense of tangles; for the link theory sense, see that article. Two n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considere... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tempered representation Summary Tempered_representation In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the Lp space L2+ε(G)for any ε > 0. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor order Summary Tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor order Summary Tensor Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tensor order Summary Tensor This leads to the concept of a tensor field. In some areas, tensor fields are so ubiquitous that they are often simply called "tensors". Tullio Levi-Civita and Gregorio Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard Riemann, Elwin Bruno Christoffel, and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ternary cubic form Summary Ternary_cubic In mathematics, a ternary cubic form is a homogeneous degree 3 polynomial in three variables. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ternary equivalence relation Summary Ternary_equivalence_relation In mathematics, a ternary equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric, reflexive, and transitive. The classic example is the relation of collinearity among thr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ternary operation Summary Ternary_operation In mathematics, a ternary operation is an n-ary operation with n = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A. In computer science, a ternary operator is an operator that takes three arguments as input... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ternary quartic Summary Ternary_quartic In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Triadic relation Summary Ternary_relation In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place. Just as a binary relation is formally defined as a set of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tertiary ideal Summary Tertiary_ideal In mathematics, a tertiary ideal is a two-sided ideal in a perhaps noncommutative ring that cannot be expressed as a nontrivial intersection of a right fractional ideal with another ideal. Tertiary ideals generalize primary ideals to the case of noncommutative rings. Although prima... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tertiary ideal Summary Tertiary_ideal Tertiary ideals and primary ideals coincide for commutative rings. To any (two-sided) ideal, a tertiary ideal can be associated called the tertiary radical, defined as t ( I ) = { r ∈ R | ∀ s ∉ I , ∃ x ∈ ( s ) x ∉ I and ( x ) ( r ) ⊂ I } . {\displaystyle t(I)=\{r\in R{\mbox{ }}|{\m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal theorem Summary Formal_theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal theorem Summary Formal_theorem Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal theorem Summary Formal_theorem A theory consists of some basis statements called axioms, and some deducing rules (sometimes included in the axioms). The theorems of the theory are the statements that can be derived from the axioms by using the deducing rules. This formalization led to proof theory, which allows ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Theta characteristic Summary Theta_characteristic In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle, he... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Theta constant Summary Theta_constant In mathematics, a theta constant or Thetanullwert' (German for theta zero value; plural Thetanullwerte) is the restriction θm(τ) = θm(τ,0) of a theta function θm(τ,z) with rational characteristic m to z = 0. The variable τ may be a complex number in the upper half-plane in which ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thick set Summary Thick_set In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set T {\displaystyle T} , for every p ∈ N {\displaystyle p\in \mathbb {N} } , there is some n ∈ N {\displaystyle n\in \mathbb {N} } such that { n , n + 1 , n + 2 , . . . , n + p ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thin set (Serre) Summary Hilbertian_field In mathematics, a thin set in the sense of Serre, named after Jean-Pierre Serre, is a certain kind of subset constructed in algebraic geometry over a given field K, by allowed operations that are in a definite sense 'unlikely'. The two fundamental ones are: solving a polynomial... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate time series Summary Time-series_regression In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate time series Summary Time-series_regression Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, si... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate time series Summary Time-series_regression Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate time series Summary Time-series_regression Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, whe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate time series Summary Time-series_regression A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Abelian topological group Summary Topological_abelian_group In mathematics, a topological abelian group, or TAG, is a topological group that is also an abelian group. That is, a TAG is both a group and a topological space, the group operations are continuous, and the group's binary operation is commutative. The theory ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stereotype algebra Summary Stereotype_algebra In mathematics, a topological algebra A {\displaystyle A} is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological game Summary Topological_game In mathematics, a topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the pla... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological game Summary Topological_game It turns out that some fundamental topological constructions have a natural counterpart in topological games; examples of these are the Baire property, Baire spaces, completeness and convergence properties, separation properties, covering and base properties, continuous images,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological game Summary Topological_game The term topological game was first introduced by Claude Berge, who defined the basic ideas and formalism in analogy with topological groups. A different meaning for topological game, the concept of “topological properties defined by games”, was introduced in the paper of Rasti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological game Summary Topological_game The survey paper of Telgársky emphasizes the origin of topological games from the Banach–Mazur game. There are two other meanings of topological games, but these are used less frequently. The term topological game introduced by Leon Petrosjan in the study of antagonistic pursui... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological game Summary Topological_game The trajectories in these topological games are continuous in time. The games of Nash (the Hex games), the Milnor games (Y games), the Shapley games (projective plane games), and Gale's games (Bridg-It games) were called topological games by David Gale in his invited address . ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological graph Summary Topological_graph In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and the edges by Jordan arcs (connected pieces of Jordan curves) joining the corresponding pairs of points. The points represent... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological graph Summary Topological_graph An important special class of topological graphs is the class of geometric graphs, where the edges are represented by line segments. (The term geometric graph is sometimes used in a broader, somewhat vague sense.) The theory of topological graphs is an area of graph theory, m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Discrete group Summary Discrete_subgroup In mathematics, a topological group G is called a discrete group if there is no limit point in it (i.e., for each element in G, there is a neighborhood which only contains that element). Equivalently, the group G is discrete if and only if its identity is isolated.A subgroup H o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Discrete group Summary Discrete_subgroup Hence, there is an isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying (non-topological) groups. There are some occasions when a topological group or Lie group is usefully endowed with ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Discrete group Summary Discrete_subgroup This happens for example in the theory of the Bohr compactification, and in group cohomology theory of Lie groups. A discrete isometry group is an isometry group such that for every point of the metric space the set of images of the point under the isometries is a discrete set. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Direct sum of topological groups Summary Direct_sum_of_topological_groups In mathematics, a topological group G {\displaystyle G} is called the topological direct sum of two subgroups H 1 {\displaystyle H_{1}} and H 2 {\displaystyle H_{2}} if the map is a topological isomorphism, meaning that it is a homeomorphism and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological half-exact functor Summary Topological_half-exact_functor In mathematics, a topological half-exact functor F is a functor from a fixed topological category (for example CW complexes or pointed spaces) to an abelian category (most frequently in applications, category of abelian groups or category of modules ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological module Summary Topological_module In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological ring Summary Topological_ring In mathematics, a topological ring is a ring R {\displaystyle R} that is also a topological space such that both the addition and the multiplication are continuous as maps: where R × R {\displaystyle R\times R} carries the product topology. That means R {\displaystyle R} is an ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological semigroup Summary Topological_semigroup In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous.Every topological group is a topological semigroup. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completely uniformizable space Summary Completely_uniformizable_space In mathematics, a topological space (X, T) is called completely uniformizable (or Dieudonné complete) if there exists at least one complete uniformity that induces the topology T. Some authors additionally require X to be Hausdorff. Some authors have... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Contractible space Summary Contractible_topological_space In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is one that can be continuously shrunk to a point within that space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sequentially compact Summary Sequentially_compact_space In mathematics, a topological space X is sequentially compact if every sequence of points in X has a convergent subsequence converging to a point in X {\displaystyle X} . Every metric space is naturally a topological space, and for metric spaces, the notions of co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fine uniformity Summary Fine_uniformity In mathematics, a topological space X is uniformizable if there exists a uniform structure on X that induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure). Any... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fine uniformity Summary Fine_uniformity However, it is true that the topology of a uniformizable space can always be induced by a family of pseudometrics; indeed, this is because any uniformity on a set X can be defined by a family of pseudometrics. Showing that a space is uniformizable is much simpler than showing it ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
D-space Summary D-space In mathematics, a topological space X {\displaystyle X} is a D-space if for any family { U x: x ∈ X } {\displaystyle \{U_{x}:x\in X\}} of open sets such that x ∈ U x {\displaystyle x\in U_{x}} for all points x ∈ X {\displaystyle x\in X} , there is a closed discrete subset D {\displaystyle D} of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Collectionwise normal space Summary Collectionwise_normal In mathematics, a topological space X {\displaystyle X} is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X {\displaystyle X} there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. Here a fa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countably generated space Summary Countably_generated_space In mathematics, a topological space X {\displaystyle X} is called countably generated if the topology of X {\displaystyle X} is determined by the countable sets in a similar way as the topology of a sequential space (or a Fréchet space) is determined by the co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baire space Summary Baire_space In mathematics, a topological space X {\displaystyle X} is said to be a Baire space if countable unions of closed sets with empty interior also have empty interior. According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Baire spaces. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Limit point compact Summary Limit_point_compact In mathematics, a topological space X {\displaystyle X} is said to be limit point compact or weakly countably compact if every infinite subset of X {\displaystyle X} has a limit point in X . {\displaystyle X.} This property generalizes a property of compact spaces. In a m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Separable space Summary Separable_space In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle \{x_{n}\}_{n=1}^{\infty }} of elements of the space such that every nonempty open subset of the space contains at leas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Feebly compact space Summary Feebly_compact_space In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite. The concept was introduced by S. Mardeĉić and P. Papić in 1955.Some facts: Every compact space is feebly compact. Every feebly compact paracompact space ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Feebly compact space Summary Feebly_compact_space For a completely regular Hausdorff space the properties of being feebly compact and pseudocompact are equivalent. Any maximal feebly compact space is submaximal. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ultraconnected space Summary Ultraconnected_space In mathematics, a topological space is said to be ultraconnected if no two nonempty closed sets are disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no T1 space with more th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weakly contractible Summary Weakly_contractible In mathematics, a topological space is said to be weakly contractible if all of its homotopy groups are trivial. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Σ-compact space Summary Countable_at_infinity In mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces.A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact. That terminology can be somewhat confusing as it does not fit the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological structure Summary Topological_structure In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological structure Summary Topological_structure Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spaces in their own ri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector topology Summary Topological_vector_space In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is also a topological space wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector topology Summary Topological_vector_space Some authors also require that the space is a Hausdorff space (although this article does not). One of the most widely studied categories of TVSs are locally convex topological vector spaces. This article focuses on TVSs that are not necessarily locally convex. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector topology Summary Topological_vector_space Banach spaces, Hilbert spaces and Sobolev spaces are other well-known examples of TVSs. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logical functor Summary Elementary_topoi In mathematics, a topos (US: , UK: ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toral Lie algebra Summary Toral_Lie_algebra In mathematics, a toral subalgebra is a Lie subalgebra of a general linear Lie algebra all of whose elements are semisimple (or diagonalizable over an algebraically closed field). Equivalently, a Lie algebra is toral if it contains no nonzero nilpotent elements. Over an algeb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toric manifold Summary Toric_manifold In mathematics, a toric manifold is a topological analogue of toric variety in algebraic geometry. It is an even-dimensional manifold with an effective smooth action of an n {\displaystyle n} -dimensional compact torus which is locally standard with the orbit space a simple convex ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toroid Summary Toroid_(geometry) In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toroid Summary Toroid_(geometry) The term toroid is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any number of holes. A g-holed toroid can be seen as approximating the surface of a torus having a topological genus, g, of 1 or greater. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toroid Summary Toroid_(geometry) The Euler characteristic χ of a g holed toroid is 2(1-g).The torus is an example of a toroid, which is the surface of a doughnut. Doughnuts are an example of a solid torus created by rotating a disk, and should not be confused with toroids. Toroidal structures occur in both natural and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Torsion sheaf Summary Torsion_sheaf In mathematics, a torsion sheaf is a sheaf of abelian groups F {\displaystyle {\mathcal {F}}} on a site for which, for every object U, the space of sections Γ ( U , F ) {\displaystyle \Gamma (U,{\mathcal {F}})} is a torsion abelian group. Similarly, for a prime number p, we say a she... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearly ordered set Summary Infinite_descending_chain In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies the following for all a , b {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearly ordered set Summary Infinite_descending_chain a ≤ b {\displaystyle a\leq b} or b ≤ a {\displaystyle b\leq a} (strongly connected, formerly called total).Reflexivity (1.) already follows from connectedness (4. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearly ordered set Summary Infinite_descending_chain ), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders. Total orders are sometimes also called simple, connex, or full orders.A set equipped with a total order is a totally ordered set; the terms simply ordered set, li... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Totally disconnected group Summary Totally_disconnected_group In mathematics, a totally disconnected group is a topological group that is totally disconnected. Such topological groups are necessarily Hausdorff. Interest centres on locally compact totally disconnected groups (variously referred to as groups of td-type, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Totally disconnected group Summary Totally_disconnected_group The compact case has been heavily studied – these are the profinite groups – but for a long time not much was known about the general case. A theorem of van Dantzig from the 1930s, stating that every such group contains a compact open subgroup, was all that ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Totally positive matrix Summary Totally_positive_matrix In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix is a positive number. A totally positive matrix has all entries positive, so it is also a positive matrix; and it ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite tower of fields Summary Infinite_tower_of_fields In mathematics, a tower of fields is a sequence of field extensions F0 ⊆ F1 ⊆ ... ⊆ Fn ⊆ ...The name comes from such sequences often being written in the form ⋮ | F 2 | F 1 | F 0 . {\displaystyle {\begin{array}{c}\vdots \\|\\F_{2}\\|\\F_{1}\\|\\\ F_{0}.\end{arra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toy theorem Summary Toy_theorem In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation of the general theorem, or a framework for proving the general theorem. One way of obtaining a toy theorem is by introducing some simpl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trace identity Summary Trace_identity In mathematics, a trace identity is any equation involving the trace of a matrix. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendence degree Summary Transcendental_extension In mathematics, a transcendental extension L / K {\displaystyle L/K} is a field extension such that there exists an element in the field L {\displaystyle L} that is transcendental over the field K {\displaystyle K} ; that is, an element that is not a root of any uni... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendence degree Summary Transcendental_extension A transcendence basis of a field extension L / K {\displaystyle L/K} (or a transcendence basis of L {\displaystyle L} over K {\displaystyle K} ) is a maximal algebraically independent subset of L {\displaystyle L} over K . {\displaystyle K.} Transcendence bases shar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendence degree Summary Transcendental_extension In particular, all transcendence bases of a field extension have the same cardinality, called the transcendence degree of the extension. Thus, a field extension is a transcendental extension if and only if its transcendence degree is positive. Transcendental extensi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendental functions Summary Transcendental_functions In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically using... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendental number Summary Transcendental_numbers In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are π and e.Though only a few classes of tran... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transcendental number Summary Transcendental_numbers Hence, the set of real numbers consists of non-overlapping rational, algebraic non-rational and transcendental real numbers. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical transformations Summary Transformation_(function) In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transf... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating function transformation Summary Generating_function_transformation In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating function transformation Summary Generating_function_transformation + f 1 1 ! z + f 2 2 ! z 2 + ⋯ . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating function transformation Summary Generating_function_transformation {\displaystyle {\widehat {F}}(z)=\sum _{n=0}^{\infty }{\frac {f_{n}}{n! }}z^{n}={\frac {f_{0}}{0! }}+{\frac {f_{1}}{1! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating function transformation Summary Generating_function_transformation }}z+{\frac {f_{2}}{2! }}z^{2}+\cdots .} In this article, we use the convention that the ordinary (exponential) generating function for a sequence { f n } {\displaystyle \{f_{n}\}} is denoted by the uppercase function F ( z ) {\displaystyle F(... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generating function transformation Summary Generating_function_transformation Additionally, we use the bracket notation for coefficient extraction from the Concrete Mathematics reference which is given by F ( z ) := f n {\displaystyle F(z):=f_{n}} . The main article gives examples of generating functions for many sequ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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