Tags
A tag is a keyword or label that categorizes your question with other, similar questions.
A property of an object is called invariant if, given some steps that alter the object, always remains, no matter what steps are used in what order.
392 questions
This a cohomology theory for smooth manifolds, where the (co)chain complex is defined by differential forms on a smooth manifold with differential given by exterior derivative. Then $n^{th}$ de Rham cohomology group is the quotient "closed $n$-forms/exact $n$-forms". Use in conjunction with other algebraic topology and differential geometry related tags if necessary.
391 questions
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space.
390 questions
Use this tag for questions related to absolute continuity, which is a smoothness property of functions stronger than that of continuity and uniform continuity.
389 questions
This tag is for questions regarding semidefinite programming (SDP) which is a subfield of convex optimization concerned with the optimization of a linear objective function (an objective function is a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.
388 questions
For questions related to the theory, applications, and computational aspects of optimal transport and related topics such as the Wasserstein (and other transportation cost) distances, the Monge-Ampere equation, metric gradient flows, martingale optimal transport, and optimal matching.
388 questions
This is the property shared by many binary operations including group operations. For a binary operation $\cdot$, associativity holds if $(x\cdot y)\cdot z = x \cdot(y\cdot z)$.
388 questions
A net is a generalization of a sequence where a directed set is used as the index set instead of positive integers.
Convergence of nets can be defined in a similar way as convergence of sequences.
Convergent nets in a topological space uniquely determine its topology.
387 questions
A module $I$ over a ring $R$ is injective if $\hom_{R}({-},I)$ is exact. The notion of injective modules is dual to the notion of a projective module. In homological algebra injective modules are used for computing right derived functors.
385 questions
A famous problem of probability, where a person samples a set with replacement until every element of the set (i.e. each coupon) has been obtained at least once. Questions deal with the associated probability distribution, proof techniques, etc.
383 questions
combinatorial properties of strings of symbols from a finite alphabet. Also includes
sequences such as the Thue-Morse and Rudin-Shapiro sequence.
383 questions
For questions about the topology of schemes and (classical) algebraic varieties.
379 questions
Matroids are a common generalization of linearly independent sets and independent sets in graphs. Among other applications, they are exactly the simplical complexes in which the greedy algorithm outputs the optimal solution. Matroids are also studied for their own sake.
378 questions
A simple Lie algebra is non-abelian Lie algebra with no nontrivial ideals. A *semisimple Lie algebra* is a Lie algebra which is the direct sum of simple Lie algebras. This tag is for questions about semisimple Lie algebras, including their classification and correspondent to root systems and Dynkin diagrams.
375 questions
For questions on determining whether a number is rational, and related problems. If applicable, use this tag instead of (rational-numbers) and (irrational-numbers). Consider adding a tag (radicals) or (logarithms), depending on what the question is about.
371 questions
For questions related to the vertex-connectivity or edge-connectivity of graphs or networks: the minimum number of vertices (respectively edges) that need to be deleted to disconnect the graph.
371 questions
A scalar field is a function of the type $X\to \Bbb R$, where $X$ may be an open set in $\mathbb R^n$ or more generally a smooth manifold.
370 questions
Question related to Lévy processes, i.e. stochastically continuous processes with independent, stationary increments.
369 questions
This tag is for questions regarding to "Inverse Laplace Transform" which is the transformation of a Laplace transform into a function of time.
369 questions
This tag is for questions relating to complex dynamics, study of dynamical systems defined by iteration of functions on complex number spaces. It was an area of research established by Fatou and Julia towards the beginning of the last century.
369 questions
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are two sequences of orthogonal polynomials which are related to de Moivre's formula. These polynomials are also known for their elegant Trigonometric properties, and can also be defined recursively. They are very helpful in Trigonometry, Complex Analysis, and other branches of Algebra.
369 questions
Model categories are categories with three distinguished classes of morphisms: the weak equivalences, the fibrations and the cofibrations. They provide a natural setting for (homotopy-theory) in an arbitrary category, by mimicking the usual properties of (co)fibrations and weak equivalences in topological spaces.
368 questions
A method of generating a polynomial that crosses through a set of data. The degree of this polynomial is equal to the size of the data.
368 questions
If the expression obtained after any substitution during limit analysis does not give enough information to determine the original limit, it is known as an indeterminate form.
368 questions
Functional calculus allows the evaluation of a function applied to a linear operator or a matrix. The function could be a polynomial, a holomorphic function, a continuous function or a measurable function defined on the spectrum of an operator or a Banach algebra. Functional calculus is a basic and powerful tool in the spectral theory of operators and operator algebras and is part of functional analysis.
368 questions
For questions about families of uniformly integrable random variables. Use the tags (measure-theory) or (probablity-theory).
364 questions
Questions on finding integer solutions to bivariate equations of the form $x^2-Dy^2=a$.
363 questions
Questions on problems that have yet to be completely solved by current mathematical methods.
363 questions
For questions about Combinatorial design theory, a part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. The theory has applications in the area of the design of experiments.
363 questions
Regularization, in mathematics and statistics and particularly in the fields of machine learning and inverse problems, refers to a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting. (Def: http://en.wikipedia.org/wiki/Regularization_(mathematics))
362 questions
This tag is for questions regarding to Ring Isomorphisms, a ring homomorphism having a $2$-sided inverse that is also a ring homomorphism. Isomorphic rings have all their ring-theoretic properties identical. One such ring can be regarded as "the same" as the other.
360 questions
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. (Def: http://en.m.wikipedia.org/wiki/Bifurcation_theory)
360 questions
In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.
359 questions
A group ring $R[G]$ is a ring constructed from a group $G$ and ring $R$. A special case of this construction is group algebra, which occurs naturally in representation theory.
358 questions