text stringlengths 42 3.65k | source stringclasses 1
value |
|---|---|
Braid length Summary Braid_symmetry In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see § Introduction... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Real Analysis Summary Real_Analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Branching theorem Summary Branching_theorem In mathematics, the branching theorem is a theorem about Riemann surfaces. Intuitively, it states that every non-constant holomorphic function is locally a polynomial. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butterfly lemma Summary Butterfly_lemma In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice. Lemma. Suppose G {\displaystyle G} is a group wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butterfly lemma Summary Butterfly_lemma Then there is an isomorphism of quotient groups: ( A ∩ C ) B ( A ∩ D ) B ≅ ( A ∩ C ) D ( B ∩ C ) D . {\displaystyle {\frac {(A\cap C)B}{(A\cap D)B}}\cong {\frac {(A\cap C)D}{(B\cap C)D}}.} This can be generalized to the case of a group with operators ( G , Ω ) {\displaystyle (G,\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butterfly lemma Summary Butterfly_lemma Zassenhaus proved this lemma specifically to give the most direct proof of the Schreier refinement theorem. The 'butterfly' becomes apparent when trying to draw the Hasse diagram of the various groups involved. Zassenhaus' lemma for groups can be derived from a more general resul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cake number Summary Cake_number In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly n planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Caliber (mathematics) Summary Caliber_(mathematics) In mathematics, the caliber or calibre of a topological space X is a cardinal κ such that for every set of κ nonempty open subsets of X there is some point of X contained in κ of these subsets. This concept was introduced by Shanin (1948). There is a similar concept f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Canonical class Summary Anticanonical_bundle In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle \,\!\Omega ^{n}=\omega } , which is the nth exterior power of the cotangent bundle Ω {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Canonical class Summary Anticanonical_bundle It may equally well be considered as an invertible sheaf. The canonical class is the divisor class of a Cartier divisor K {\displaystyle K} on V {\displaystyle V} giving rise to the canonical bundle — it is an equivalence class for linear equivalence on V {\displaystyle V} ,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Capacitated arc routing problem Summary Capacitated_arc_routing_problem In mathematics, the capacitated arc routing problem (CARP) is that of finding the shortest tour with a minimum graph/travel distance of a mixed graph with undirected edges and directed arcs given capacity constraints for objects that move along the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Capacitated arc routing problem Summary Capacitated_arc_routing_problem The CARP can be solved with combinatorial optimization including convex hulls. The large-scale capacitated arc routing problem (LSCARP) is a variant of the capacitated arc routing problem that applies to hundreds of edges and nodes to realistically... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harmonic capacity Summary Harmonic_capacity In mathematics, the capacity of a set in Euclidean space is a measure of the "size" of that set. Unlike, say, Lebesgue measure, which measures a set's volume or physical extent, capacity is a mathematical analogue of a set's ability to hold electrical charge. More precisely, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cardinality Summary Cardinality In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = { 2 , 4 , 6 } {\displaystyle A=\{2,4,6\}} contains 3 elements, and therefore A {\displaystyle A} has a cardinality of 3. Beginning in the late 19th century, this concept w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cardinality Summary Cardinality The cardinality of a set is also called its size, when no confusion with other notions of size is possible. The cardinality of a set A {\displaystyle A} is usually denoted | A | {\displaystyle |A|} , with a vertical bar on each side; this is the same notation as absolute value, and the m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Caret (punctuation) Surrogate symbol for superscript and exponentiation Caret_(punctuation) > Uses > Surrogate symbol for superscript and exponentiation In mathematics, the caret can signify exponentiation (e.g. 3^5 for 35) where the usual superscript is not readily usable (as on some graphing calculators). It is also ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of abelian groups Summary Category_of_abelian_groups In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: indeed, every small abelian category can be embedded in Ab. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of finite dimensional Hilbert spaces Summary Category_of_finite_dimensional_Hilbert_spaces In mathematics, the category FdHilb has all finite-dimensional Hilbert spaces for objects and the linear transformations between them as morphisms. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grp (category theory) Summary Grp_(category_theory) In mathematics, the category Grp (or Gp) has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of preordered sets Summary Category_of_preordered_sets In mathematics, the category Ord has preordered sets as objects and order-preserving functions as morphisms. This is a category because the composition of two order-preserving functions is order preserving and the identity map is order preserving. The mono... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of preordered sets Summary Category_of_preordered_sets There are thus no zero objects in Ord. The categorical product in Ord is given by the product order on the cartesian product. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of preordered sets Summary Category_of_preordered_sets We have a forgetful functor Ord → Set that assigns to each preordered set the underlying set, and to each order-preserving function the underlying function. This functor is faithful, and therefore Ord is a concrete category. This functor has a left adjoint... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of relations Summary Category_of_relations In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R: A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
N-category number Summary N-category_number In mathematics, the category number of a mathematician is a humorous construct invented by Dan Freed, intended to measure the capacity of that mathematician to stomach the use of higher categories. It is defined as the largest number n such that they can think about n-categor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of compactly generated weak Hausdorff spaces Summary Mapping_space In mathematics, the category of compactly generated weak Hausdorff spaces CGWH is one of typically used categories in algebraic topology as a substitute for the category of topological spaces, as the latter lacks some of the pleasant properties... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of manifolds Summary Category_of_manifolds In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two Cp maps is again conti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of medial magmas Summary Category_of_medial_magmas In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas (that is, sets with a medial binary operation), and whose morphisms are magma homomorphisms (which are equivalent... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of commutative algebras Summary Category_of_rings In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is large, meaning... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Categorical topology Summary Categorical_topology In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the identity f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of topological vector spaces Summary Category_of_topological_vector_spaces In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characteristic equation (calculus) Summary Characteristic_equation_(calculus) In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or difference equation. The characteristic equation can only b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characteristic equation (calculus) Summary Characteristic_equation_(calculus) The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation. For a differential equation parameterized on time, t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characteristic equation (calculus) Summary Characteristic_equation_(calculus) For both types of equation, persistent fluctuations occur if there is at least one pair of complex roots. The method of integrating linear ordinary differential equations with constant coefficients was discovered by Leonhard Euler, who found ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characteristic subring Summary Characteristic_(algebra) In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chromatic spectral sequence Summary Chromatic_spectral_sequence In mathematics, the chromatic spectral sequence is a spectral sequence, introduced by Ravenel (1978), used for calculating the initial term of the Adams spectral sequence for Brown–Peterson cohomology, which is in turn used for calculating the stable homot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circle action Summary Circle_action In mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle \mathbb {S} ^{1}} , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circle action Summary Circle_action The circle group plays a central role in Pontryagin duality and in the theory of Lie groups. The notation T {\displaystyle \mathbb {T} } for the circle group stems from the fact that, with the standard topology (see below), the circle group is a 1-torus. More generally, T n {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circumflex accent Mathematics Circumflex_accent > Uses > Mathematics In mathematics, the circumflex is used to modify variable names; it is usually read "hat", e.g., î is "i hat". The Fourier transform of a function ƒ is often denoted by f ^ {\displaystyle {\hat {f}}} . In the notation of sets, a hat above an element s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circumflex accent Mathematics Circumflex_accent > Uses > Mathematics In geometry, a hat is sometimes used for an angle. For instance, the angles A ^ {\displaystyle {\hat {A}}} or A B ^ C {\displaystyle A{\hat {B}}C} . In vector notation, a hat above a letter indicates a unit vector (a dimensionless vector with a magnit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circumflex accent Mathematics Circumflex_accent > Uses > Mathematics For instance, ı ^ {\displaystyle {\hat {\mathbf {\imath } }}} , x ^ {\displaystyle {\hat {\mathbf {x} }}} , or e ^ 1 {\displaystyle {\hat {\mathbf {e} }}_{1}} stands for a unit vector in the direction of the x-axis of a Cartesian coordinate system. In... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
L-matrix Summary L-matrix In mathematics, the class of L-matrices are those matrices whose off-diagonal entries are less than or equal to zero and whose diagonal entries are positive; that is, an L-matrix L satisfies L = ( ℓ i j ) ; ℓ i i > 0 ; ℓ i j ≤ 0 , i ≠ j . {\displaystyle L=(\ell _{ij});\quad \ell _{ii}>0;\quad ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z-matrix (mathematics) Summary Z-matrix_(mathematics) In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, the matrices of the form: Z = ( z i j ) ; z i j ≤ 0 , i ≠ j . {\displaystyle Z=(z_{ij});\quad z_{ij}\leq 0,\quad i\neq j.} Note that this d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z-matrix (mathematics) Summary Z-matrix_(mathematics) The Jacobian of a competitive dynamical system is a Z-matrix by definition. Likewise, if the Jacobian of a cooperative dynamical system is J, then (−J) is a Z-matrix. Related classes are L-matrices, M-matrices, P-matrices, Hurwitz matrices and Metzler matrices. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z-matrix (mathematics) Summary Z-matrix_(mathematics) L-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular and its inverse is nonnegative. All matrices that are ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moebius inversion Summary Möbius_inversion In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius.A large generalization of this formula applies t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker limit formula Summary Kronecker_limit_formula In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more complicated Eisenstein se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric Langlands correspondence History Geometric_Langlands_correspondence > History In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory and representation theory. Formulated by Robert Langlands in the late 1960s, the Langlands correspondence is re... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
S-duality Relation to the Langlands program S-duality > In quantum field theory > Relation to the Langlands program In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory to the branch of mathematics known as representation theory. Formulated by Robert L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
S-duality Relation to the Langlands program S-duality > In quantum field theory > Relation to the Langlands program Starting with two Yang–Mills theories related by S-duality, Kapustin and Witten showed that one can construct a pair of quantum field theories in two-dimensional spacetime. By analyzing what this dimensio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moebius plane Summary Moebius_plane In mathematics, the classical Möbius plane (named after August Ferdinand Möbius) is the Euclidean plane supplemented by a single point at infinity. It is also called the inversive plane because it is closed under inversion with respect to any generalized circle, and thus a natural se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moebius plane Summary Moebius_plane In inversive geometry a straight line is considered to be a generalized circle containing the point at infinity; inversion of the plane with respect to a line is a Euclidean reflection. More generally, a Möbius plane is an incidence structure with the same incidence relationships as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical groups Summary Classical_Lie_groups In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical groups Summary Classical_Lie_groups The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups.The classical groups form the deepest and most useful part of the subject of linear Lie groups. Most types of classical groups find application in classical ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical groups Summary Classical_Lie_groups A few examples are the following. The rotation group SO(3) is a symmetry of Euclidean space and all fundamental laws of physics, the Lorentz group O(3,1) is a symmetry group of spacetime of special relativity. The special unitary group SU(3) is the symmetry group of quantum... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical orthogonal polynomials Summary Classical_orthogonal_polynomials In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical orthogonal polynomials Summary Classical_orthogonal_polynomials Markov and T.J. Stieltjes led to the general notion of orthogonal polynomials. For given polynomials Q , L: R → R {\displaystyle Q,L:\mathbb {R} \to \mathbb {R} } and ∀ n ∈ N 0 {\displaystyle \forall \,n\in \mathbb {N} _{0}} the classical orthogo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classification of finite simple groups Summary Classification_of_finite_simple_groups In mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classification of finite simple groups Summary Classification_of_finite_simple_groups The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
List of finite simple groups Summary Finite_simple_groups In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple groups, together with... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classifying space for O(n) Summary Classifying_space_for_O(n) In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space R ∞ {\displaystyle \mathbb {R} ^{\infty }} . It is analogous to the classifying space for U(n). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classifying space for U(n) Summary Classifying_space_for_U(n) In mathematics, the classifying space for the unitary group U(n) is a space BU(n) together with a universal bundle EU(n) such that any hermitian bundle on a paracompact space X is the pull-back of EU(n) by a map X → BU(n) unique up to homotopy. This space wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Closed graph theorem Summary Closed_graph_theorem In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions when functions with closed graphs are necessarily continuous. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Closed subgroup theorem Summary Closed-subgroup_theorem In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the smooth structure (and hence the gr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coadjoint representation Summary Coadjoint_action In mathematics, the coadjoint representation K {\displaystyle K} of a Lie group G {\displaystyle G} is the dual of the adjoint representation. If g {\displaystyle {\mathfrak {g}}} denotes the Lie algebra of G {\displaystyle G} , the corresponding action of G {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coadjoint representation Summary Coadjoint_action The importance of the coadjoint representation was emphasised by work of Alexandre Kirillov, who showed that for nilpotent Lie groups G {\displaystyle G} a basic role in their representation theory is played by coadjoint orbits. In the Kirillov method of orbits, represe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tangle hypothesis Summary Cobordism_hypothesis In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lurie outlined a proof of the cobordism hypothesis, though the details of his approach have yet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coclass conjectures Summary Coclass_conjectures In mathematics, the coclass of a finite p-group of order pn is n − c, where c is the class. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Codomain Summary Codomain In mathematics, the codomain or set of destination of a function is the set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or image of a function. A codo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Codomain Summary Codomain Namely, a function that is not surjective has elements y in its codomain for which the equation f(x) = y does not have a solution. A codomain is not part of a function f if f is defined as just a graph. For example in set theory it is desirable to permit the domain of a function to be a proper... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohomology operation Summary Cohomology_operation In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a cohomology operation should be ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohomology operation Summary Cohomology_operation In the Adams spectral sequence the bicommutant aspect is implicit in the use of Ext functors, the derived functors of Hom-functors; if there is a bicommutant aspect, taken over the Steenrod algebra acting, it is only at a derived level. The convergence is to groups in s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Collage theorem Summary Collage_theorem In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Base-10 logarithm Summary Logarithm_table In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard loga... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Base-10 logarithm Summary Logarithm_table On calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log". To mitigate this ambiguity, the ISO 80000 specification recommends that log10 (x) should be written lg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Base-10 logarithm Summary Logarithm_table Instead, tables of base-10 logarithms were used in science, engineering and navigation—when calculations required greater accuracy than could be achieved with a slide rule. By turning multiplication and division to addition and subtraction, use of logarithms avoided laborious a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutator (ring theory) Summary Commutator_bracket In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutator subspace Summary Commutator_subspace In mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators of operators in the ideal with bounded operators. Modern characterisation of the commutator subspace is thro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compact complement topology Summary Compact_complement_topology In mathematics, the compact complement topology is a topology defined on the set R {\displaystyle \scriptstyle \mathbb {R} } of real numbers, defined by declaring a subset X ⊆ R {\displaystyle \scriptstyle X\subseteq \mathbb {R} } open if and only if it is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compact open topology Summary Compact_open_topology In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory and functional analysis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Direct comparison test Summary Direct_comparison_test In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing the convergence or divergence of an infinite series or an improper integr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete Fermi–Dirac integral Summary Complete_Fermi–Dirac_integral In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is defined by F j ( x ) = 1 Γ ( j + 1 ) ∫ 0 ∞ t j e t − x + 1 d t , ( j > − 1 ) {\displaystyle F_{j}(x)={\frac {1}{\Gamma (j+1)}}\int _{0}^{\inft... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Witt algebra Summary Witt_algebra In mathematics, the complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are holomorphic except at two fixed points. It is also the complexification of the Lie algebra of polynomial vector fields on a circle, a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conjugate pair Summary Complex_conjugation In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers then the complex conjugate of a + b i {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conjugate pair Summary Complex_conjugation In polar form, if r {\displaystyle r} and φ {\displaystyle \varphi } are real numbers then the conjugate of r e i φ {\displaystyle re^{i\varphi }} is r e − i φ . {\displaystyle re^{-i\varphi }.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conjugate pair Summary Complex_conjugation This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a 2 + b 2 {\displaystyle a^{2}+b^{2}} (or r 2 {\displaystyle r^{2}} in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex conjugate of a vector space Summary Complex_conjugate_of_a_vector_space In mathematics, the complex conjugate of a complex vector space V {\displaystyle V\,} is a complex vector space V ¯ {\displaystyle {\overline {V}}} , which has the same elements and additive group structure as V , {\displaystyle V,} but who... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex conjugate of a vector space Summary Complex_conjugate_of_a_vector_space The letter v {\displaystyle v} stands for a vector in V , {\displaystyle V,} α {\displaystyle \alpha } is a complex number, and α ¯ {\displaystyle {\overline {\alpha }}} denotes the complex conjugate of α . {\displaystyle \alpha .} More con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex conjugate root theorem Summary Complex_conjugate_root_theorem In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.It follows from thi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauss plane Summary Complex_plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauss plane Summary Complex_plane The multiplication of two complex numbers can be expressed more easily in polar coordinates—the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex projective plane Summary Complex_projective_plane In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space. It is a complex manifold of complex dimension 2, described by three complex coordinates ( Z 1 , Z 2 , Z 3 ) ∈ C 3 , ( Z 1 , Z 2 , Z 3 ) ≠ ( 0 , ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex squaring map Summary Complex_squaring_map In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It can be constructed by performing the following steps: Choose any complex number on the unit circle whose argument (an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complexification Summary Complexification In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplicatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complexification (Lie group) Summary Complexification_(Lie_group) In mathematics, the complexification or universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property that every continuous homomorphism of the original group into a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complexification (Lie group) Summary Complexification_(Lie_group) They are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear. For compact Lie groups, the complexification, sometimes called the Chevalley complexification after Claude Chevalley, can be defined as the group of c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Composition operator Summary Composition_operator In mathematics, the composition operator C ϕ {\displaystyle C_{\phi }} with symbol ϕ {\displaystyle \phi } is a linear operator defined by the rule where f ∘ ϕ {\displaystyle f\circ \phi } denotes function composition. The study of composition operators is covered by AM... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compound of three octahedra Summary Compound_of_three_octahedra In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other. Although appearing earlier in the mathematical litera... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalised metric Summary Generalised_metric In mathematics, the concept of a generalised metric is a generalisation of that of a metric, in which the distance is not a real number but taken from an arbitrary ordered field. In general, when we define metric space the distance function is taken to be a real-valued func... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive measure Summary Positive_measure In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive measure Summary Positive_measure Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.