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Atoroidal Summary Atoroidal He then notes that for irreducible boundary-incompressible 3-manifolds this gives the algebraic definition. Jean-Pierre Otal (2001) uses the algebraic definition without additional restrictions. Bennett Chow (2007) uses the geometric definition, restricted to irreducible manifolds. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Atoroidal Summary Atoroidal Michael Kapovich (2009) requires the algebraic variant of atoroidal manifolds (which he calls simply atoroidal) to avoid being one of three kinds of fiber bundle. He makes the same restriction on geometrically atoroidal manifolds (which he calls topologically atoroidal) and in addition requi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automatic group Summary Biautomatic_group In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a "canonical form" and can tell i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automatic semigroup Summary Automatic_semigroup In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "canonical forms" for the elements of the semigroup, the other languages dete... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automorphic L-function Summary Automorphic_L-function In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automorphic factor Summary Automorphic_factor In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms. The general case, for general groups, is reviewed in the article 'factor of automorphy'. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automorphic function Summary Factor_of_automorphy In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Automorphic number Summary Automorphic_number In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose square "ends" in the same digits as the number itself. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial automorphism Summary Trivial_automorphism In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a gro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Autonomous category Summary Autonomous_category In mathematics, an autonomous category is a monoidal category where dual objects exist. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Autonomous convergence theorem Summary Autonomous_convergence_theorem In mathematics, an autonomous convergence theorem is one of a family of related theorems which specify conditions guaranteeing global asymptotic stability of a continuous autonomous dynamical system. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-autonomous system (mathematics) Summary Non-autonomous_system_(mathematics) In mathematics, an autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle Q → R {\displaystyle Q\to \mathbb {R} } over R {\displaystyle \mathbb {R} } . For instan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-autonomous system (mathematics) Summary Non-autonomous_system_(mathematics) A dynamic equation on Q → R {\displaystyle Q\to \mathbb {R} } is a differential equation which is algebraically solved for a higher-order derivatives. In particular, a first-order dynamic equation on a fiber bundle Q → R {\displaystyle Q\to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-autonomous system (mathematics) Summary Non-autonomous_system_(mathematics) {\displaystyle q_{t}^{i}=\Gamma (t,q^{i}).} For instance, this is the case of Hamiltonian non-autonomous mechanics. A second-order dynamic equation q t t i = ξ i ( t , q j , q t j ) {\displaystyle q_{tt}^{i}=\xi ^{i}(t,q^{j},q_{t}^{j})} on ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-autonomous system (mathematics) Summary Non-autonomous_system_(mathematics) This equation also is represented by a connection on an affine jet bundle J 1 Q → Q {\displaystyle J^{1}Q\to Q} . Due to the canonical embedding J 1 Q → T Q {\displaystyle J^{1}Q\to TQ} , it is equivalent to a geodesic equation on the tange... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Autonomous system (mathematics) Summary Autonomous_system_(mathematics) In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant sys... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countability axiom Summary Axioms_of_countability In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Edge cycle cover Summary Edge_cycle_cover In mathematics, an edge cycle cover (sometimes called simply cycle cover) of a graph is a family of cycles which are subgraphs of G and contain all edges of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Effaceable functor Summary Effaceable_functor In mathematics, an effaceable functor is an additive functor F between abelian categories C and D for which, for each object A in C, there exists a monomorphism u: A → M {\displaystyle u:A\to M} , for some M, such that F ( u ) = 0 {\displaystyle F(u)=0} . Similarly, a coeff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eigenform Summary Hecke_eigenform In mathematics, an eigenform (meaning simultaneous Hecke eigenform with modular group SL(2,Z)) is a modular form which is an eigenvector for all Hecke operators Tm, m = 1, 2, 3, .... Eigenforms fall into the realm of number theory, but can be found in other areas of math and science su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eigenfunction Summary Eigenfunction In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\displaystyle f} in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eigenoperator Summary Eigenoperator In mathematics, an eigenoperator, A, of a matrix H is a linear operator such that = λ A {\displaystyle =\lambda A\,} where λ {\displaystyle \lambda } is a corresponding scalar called an eigenvalue. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eigenplane Summary Eigenplane In mathematics, an eigenplane is a two-dimensional invariant subspace in a given vector space. By analogy with the term eigenvector for a vector which, when operated on by a linear operator is another vector which is a scalar multiple of itself, the term eigenplane can be used to describe ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eigenvalue perturbation Summary Eigenvalue_perturbation In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system A x = λ x {\displaystyle Ax=\lambda x} that is perturbed from one with known eigenvectors and eigenvalues A 0 x 0 = λ 0 x 0 {\displaystyle A_{0}x_{0}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Membership (set theory) Summary Element_(set_theory) In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primal ideal Summary Primal_ideal In mathematics, an element a of a commutative ring A is called (relatively) prime to an ideal Q if whenever ab is an element of Q then b is also an element of Q. A proper ideal Q of a commutative ring A is said to be primal if the elements that are not prime to it form an ideal. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Prime (order theory) Summary Prime_(order_theory) In mathematics, an element p of a partial order (P, ≤) is a meet prime element when p is the principal element of a principal prime ideal. Equivalently, if P is a lattice, p ≠ top, and for all a, b in P, a∧b ≤ p implies a ≤ p or b ≤ p. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal element Summary Normal_element In mathematics, an element x of a *-algebra is normal if it satisfies x x ∗ = x ∗ x . {\displaystyle xx^{*}=x^{*}x.} This definition stems from the definition of a normal linear operator in functional analysis, where a linear operator A from a Hilbert space into itself is called un... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unitary element Summary Unitary_element In mathematics, an element x of a *-algebra is unitary if it satisfies x ∗ = x − 1 . {\displaystyle x^{*}=x^{-1}.} In functional analysis, a linear operator A from a Hilbert space into itself is called unitary if it is invertible and its inverse is equal to its own adjoint A∗ and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Engel group Summary Engel_group In mathematics, an element x of a Lie group or a Lie algebra is called an n-Engel element, named after Friedrich Engel, if it satisfies the n-Engel condition that the repeated commutator ,y], ..., y] with n copies of y is trivial (where means xyx−1y−1 or the Lie bracket). It is called a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Engel group Summary Engel_group Every nilpotent group or Lie algebra is Engel. Engel's theorem states that every finite-dimensional Engel algebra is nilpotent. (Cohn 1955) gave examples of non-nilpotent Engel groups and algebras. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nilpotent Summary Nilpotent_element In mathematics, an element x {\displaystyle x} of a ring R {\displaystyle R} is called nilpotent if there exists some positive integer n {\displaystyle n} , called the index (or sometimes the degree), such that x n = 0 {\displaystyle x^{n}=0} . The term, along with its sister idempot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological divisor of zero Summary Topological_divisor_of_zero In mathematics, an element z {\displaystyle z} of a Banach algebra A {\displaystyle A} is called a topological divisor of zero if there exists a sequence x 1 , x 2 , x 3 , . . . {\displaystyle x_{1},x_{2},x_{3},...} of elements of A {\displaystyle A} such ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary functions Summary Elementary_function In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, including p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary row operation Summary Elementary_row_operations In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an el... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary proof Summary Elementary_proof In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime num... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary proof Summary Elementary_proof While there is generally no consensus as to what counts as elementary, the term is nevertheless a common part of the mathematical jargon. An elementary proof is not necessarily simple, in the sense of being easy to understand or trivial. In fact, some elementary proofs can be q... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gardener's ellipse Summary Gardener's_ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gardener's ellipse Summary Gardener's_ellipse Analytically, the equation of a standard ellipse centered at the origin with width 2 a {\displaystyle 2a} and height 2 b {\displaystyle 2b} is: Assuming a ≥ b {\displaystyle a\geq b} , the foci are ( ± c , 0 ) {\displaystyle (\pm c,0)} for c = a 2 − b 2 {\textstyle c={\sqrt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gardener's ellipse Summary Gardener's_ellipse An angled cross section of a cylinder is also an ellipse. An ellipse may also be defined in terms of one focal point and a line outside the ellipse called the directrix: for all points on the ellipse, the ratio between the distance to the focus and the distance to the direc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gardener's ellipse Summary Gardener's_ellipse For example, the orbit of each planet in the Solar System is approximately an ellipse with the Sun at one focus point (more precisely, the focus is the barycenter of the Sun–planet pair). The same is true for moons orbiting planets and all other systems of two astronomical ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gardener's ellipse Summary Gardener's_ellipse A circle viewed from a side angle looks like an ellipse: that is, the ellipse is the image of a circle under parallel or perspective projection. The ellipse is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same fre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic Gauss sum Summary Elliptic_Gauss_sum In mathematics, an elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic boundary value problem Summary Elliptic_boundary_value_problem In mathematics, an elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the stable state of an evolution problem. For example, the Dirichlet problem for the Laplacian gives the eventual distribution... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic boundary value problem Summary Elliptic_boundary_value_problem This is necessary because each category must be analyzed using different techniques. The present article deals with the category of boundary value problems known as linear elliptic problems. Boundary value problems and partial differential equation... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic boundary value problem Summary Elliptic_boundary_value_problem For instance, in the heat equation, the rate of change of temperature at a point is related to the difference of temperature between that point and the nearby points so that, over time, the heat flows from hotter points to cooler points. Boundary v... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K2, the Cartesian product of K with itself. If the field's characteristic is differen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve Many sources define an elliptic curve to be simply a curve given by an equation of this form. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non-singular cubic curves; see § Elliptic curves over a general field ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve If y2 = P(x), where P is any polynomial of degree three in x with no repeated roots, the solution set is a nonsingular plane curve of genus one, an elliptic curve. If P has degree four and is square-free this equation again describes a plane curve of genus one; however, it has no ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. The torus is also an abelian group, and this correspondence is also a group isomorphism. Elliptic ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve They also find applications in elliptic curve cryptography (ECC) and integer factorization. An elliptic curve is not an ellipse in the sense of a projective conic, which has genus zero: see elliptic integral for the origin of the term. However, there is a natural representation of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic curves Summary Elliptic_Curve Specifically, the intersections of the Minkowski hyperboloid with quadric surfaces characterized by a certain constant-angle property produce the Steiner ellipses in H 2 {\displaystyle \mathbb {H} ^{2}} (generated by orientation-preserving collineations). Further, the orthogonal t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic divisibility sequence Summary Elliptic_divisibility_sequence In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials on elliptic curves. EDS were first defined, and their arithmetic properties studied, by Morg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic hypergeometric series Summary Elliptic_hypergeometric_series In mathematics, an elliptic hypergeometric series is a series Σcn such that the ratio cn/cn−1 is an elliptic function of n, analogous to generalized hypergeometric series where the ratio is a rational function of n, and basic hypergeometric series wh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasi-elliptic surface Summary Elliptic_surfaces In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasi-elliptic surface Summary Elliptic_surfaces The surface and the base curve are assumed to be non-singular (complex manifolds or regular schemes, depending on the context). The fibers that are not elliptic curves are called the singular fibers and were classified by Kunihiko Kodaira. Both elliptic and singular fibe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isometric imbedding Summary Isometric_embedding In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\displaystyle X} is said to be embedded in another object Y {\displaystyle Y} , the embedd... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isometric imbedding Summary Isometric_embedding The fact that a map f: X → Y {\displaystyle f:X\rightarrow Y} is an embedding is often indicated by the use of a "hooked arrow" (U+21AA ↪ RIGHTWARDS ARROW WITH HOOK); thus: f: X ↪ Y . {\displaystyle f:X\hookrightarrow Y.} (On the other hand, this notation is sometimes res... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isometric imbedding Summary Isometric_embedding Given X {\displaystyle X} and Y {\displaystyle Y} , several different embeddings of X {\displaystyle X} in Y {\displaystyle Y} may be possible. In many cases of interest there is a standard (or "canonical") embedding, like those of the natural numbers in the integers, the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty product Summary 0! In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty sum Summary Empty_sum In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the additive identity. Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty sum Summary Empty_sum In other words, a "sum" s 1 {\displaystyle s_{1}} with only one term evaluates to that one term, while a "sum" s 0 {\displaystyle s_{0}} with no terms evaluates to 0. Allowing a "sum" with only 1 or 0 terms reduces the number of cases to be considered in many mathematical formulas. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty sum Summary Empty_sum Such "sums" are natural starting points in induction proofs, as well as in algorithms. For these reasons, the "empty sum is zero" extension is standard practice in mathematics and computer programming (assuming the domain has a zero element). For the same reason, the empty product is taken t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Endomorphism Summary Endomorphism In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space V is a linear map f: V → V, and an endomorphism of a group G is a group homomorphism f: G →... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equaliser (mathematics) Summary Equaliser_(mathematics) In mathematics, an equaliser is a set of arguments where two or more functions have equal values. An equaliser is the solution set of an equation. In certain contexts, a difference kernel is the equaliser of exactly two functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical equations Summary Mathematical_equations In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical equations Summary Mathematical_equations There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables.The "=" symbol, which appears in every equation, was invented in 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equidistant set Summary Equidistant_set In mathematics, an equidistant set (also called a midset, or a bisector) is a set whose elements have the same distance (measured using some appropriate distance function) from two or more sets. The equidistant set of two singleton sets in the Euclidean plane is the perpendicular... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equidistant set Summary Equidistant_set The concept of equidistant set is used to define frontiers in territorial domain controversies. For instance, the United Nations Convention on the Law of the Sea (Article 15) establishes that, in absence of any previous agreement, the delimitation of the territorial sea between c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equivalence relation Summary Equivalence_relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number a is equal to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equivalence relation Summary Equivalence_relation If a = b, then b = a (symmetric). If a = b and b = c, then a = c (transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ergodic sequence Summary Ergodic_sequence In mathematics, an ergodic sequence is a certain type of integer sequence, having certain equidistribution properties. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Essentially finite vector bundle Summary Essentially_finite_vector_bundle In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav V. Nori, as the main tool in the construction of the fundamental group scheme. Even if the definition is not intuitive there is a nice cha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Evasive Boolean function Summary Evasive_Boolean_function In mathematics, an evasive Boolean function ƒ (of n variables) is a Boolean function for which every decision tree algorithm has running time of exactly n. Consequently, every decision tree algorithm that represents the function has, at worst case, a running tim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
With high probability Summary With_high_probability In mathematics, an event that occurs with high probability (often shortened to w.h.p. or WHP) is one whose probability depends on a certain number n and goes to 1 as n goes to infinity, i.e. the probability of the event occurring can be made as close to 1 as desired b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exact category Summary Exact_category In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and cokernels, which is necessary for the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exact differential equation Summary Total_differential_equation In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in Physics and engineering. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exceptional Lie algebra Summary Exceptional_Lie_algebra In mathematics, an exceptional Lie algebra is a complex simple Lie algebra whose Dynkin diagram is of exceptional (nonclassical) type. There are exactly five of them: g 2 , f 4 , e 6 , e 7 , e 8 {\displaystyle {\mathfrak {g}}_{2},{\mathfrak {f}}_{4},{\mathfrak {e}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Accidental isomorphism Summary Accidental_isomorphism In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members ai and bj of two families, usually infinite, of mathematical objects, which is incidental, in that it is not an instance of a general pattern of such... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Purely existential proof Summary Purely_existential_proof In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose last quantifier is existential (e.g., "for all x,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Purely existential proof Summary Purely_existential_proof For example, the statement that the sine function is continuous everywhere, or any theorem written in big O notation, can be considered as theorems which are existential by nature—since the quantification can be found in the definitions of the concepts used. A c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Existence theorem 'Pure' existence results Existence_theorem > 'Pure' existence results In mathematics, an existence theorem is purely theoretical if the proof given for it does not indicate a construction of the object whose existence is asserted. Such a proof is non-constructive, since the whole approach may not lend... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Existence theorem 'Pure' existence results Existence_theorem > 'Pure' existence results Despite that, the purely theoretical existence results are nevertheless ubiquitous in contemporary mathematics. For example, John Nash's original proof of the existence of a Nash equilibrium in 1951 was such an existence theorem. An... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exp ring Summary Exp_ring In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R] with constant term 1. In other words the functor Exp from abelian groups to commutative r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial expansion Summary Polynomial_expansion In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial expansion Summary Polynomial_expansion It is customary to reintroduce powers in the final result when terms involve products of identical symbols. Simple examples of polynomial expansions are the well known rules ( x + y ) 2 = x 2 + 2 x y + y 2 {\displaystyle (x+y)^{2}=x^{2}+2xy+y^{2}} ( x + y ) ( x − y ) = ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Explicit reciprocity law Summary Explicit_reciprocity_law In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity law for the power residue symbol. Th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential ring Summary Exponential_field In mathematics, an exponential field is a field that has an extra operation on its elements which extends the usual idea of exponentiation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential sum Summary Exponential_sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function e ( x ) = exp ( 2 π i x ) . {\displaystyle e(x)=\exp(2\pi ix).\,} Therefore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exposed point Summary Exposed_point In mathematics, an exposed point of a convex set C {\displaystyle C} is a point x ∈ C {\displaystyle x\in C} at which some continuous linear functional attains its strict maximum over C {\displaystyle C} . Such a functional is then said to expose x {\displaystyle x} . There can be ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exposed point Summary Exposed_point A stronger notion is that of strongly exposed point of C {\displaystyle C} which is an exposed point x ∈ C {\displaystyle x\in C} such that some exposing functional f {\displaystyle f} of x {\displaystyle x} attains its strong maximum over C {\displaystyle C} at x {\displaystyle x} ,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solution in closed form Summary Analytical_solution In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, −, ×, ÷, and integer powers) and function composition. Commonly, the allowed functions are nth root, ex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Multiple solutions to an equation Narrowing_of_algebraic_value_sets > Introduction to value sets > Multiple solutions to an equation In mathematics, an expression must represent a single value. For example consider the equation, x 2 = 4 {\displaystyle x^{2}=4} which implies, x = 2 ∨ x ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Multiple solutions to an equation Narrowing_of_algebraic_value_sets > Introduction to value sets > Multiple solutions to an equation Each x must represent a single value in the expression. Either x is 2 or x = −2. This can be resolved by keeping track of the two values so that we make ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical expression Summary Mathematical_expression In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical expression Summary Mathematical_expression For example, 8 x − 5 {\displaystyle 8x-5} is an expression, while 8 x − 5 ≥ 5 x − 8 {\displaystyle 8x-5\geq 5x-8} is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extensive category Summary Extensive_category In mathematics, an extensive category is a category C with finite coproducts that are disjoint and well-behaved with respect to pullbacks. Equivalently, C is extensive if the coproduct functor from the product of the slice categories C/X × C/Y to the slice category C/(X + Y... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extraneous solution Summary Spurious_solution In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem. A missing solution is a solution that is a valid solution to the proble... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extremally disconnected space Summary Extremally_disconnected In mathematics, an extremally disconnected space is a topological space in which the closure of every open set is open. (The term "extremally disconnected" is correct, even though the word "extremally" does not appear in most dictionaries, and is sometimes m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extremally disconnected space Summary Extremally_disconnected Every Stonean space is a Stone space, but not vice versa. In the duality between Stone spaces and Boolean algebras, the Stonean spaces correspond to the complete Boolean algebras. An extremally disconnected first-countable collectionwise Hausdorff space must... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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