# Tags

A tag is a keyword or label that categorizes your question with other, similar questions.

This tag is for set theory topics typically studied at the advanced undergraduate or graduate level. These include cofinality, axioms of ZFC, axiom of choice, forcing, set-theoretic independence, large cardinals, models of set theory, ultrafilters, ultrapowers, constructible universe, inner model theory, definability, infinite combinatorics, transfinite hierarchies; etc. More elementary questions should use the "elementary-set-theory" tag instead.

Operator theory is the branch of functional analysis that focuses on bounded linear operators, but it includes closed operators and nonlinear operators.
Operator theory is also concerned with the study of algebras of operators.

For questions about modules over rings, concerning either their properties in general or regarding specific cases.

Convex analysis is the study of properties of convex sets and convex functions. For questions about optimization of convex functions over convex sets, please use the (convex-optimization) tag.

Questions involving asymptotic analysis, including growth of functions, Big-$O$ notation, Big-$\Omega$ and Big-$\Theta$ notations.

For questions about representations or any of the tools used to classify and analyze them. A representation linearizes a group, ring, or other object by mapping it to some set of linear transformations. A common goal of representation theory is classifying all representations of some type. Representation theory is a broad field, so questions not including the word "representation" may be appropriate.

For questions about mathematics competitions or the questions that typically appear in math competitions.

Questions regarding functions defined recursively, such as the Fibonacci sequence.

Geometry assuming the parallel postulate: in a plane, given a line and a point not on that line, there is exactly one line parallel to the given line through the given point.

For questions on manifolds of dimension $n$, a topological space that near each point resembles $n$-dimensional Euclidean space.

Questions regarding the Taylor series expansion of univariate and multivariate functions, including coefficients and bounds on remainders. A special case is also known as the Maclaurin series.

Questions about the properties of functions of the form $\sum_{n=0}^{\infty}a_n (x-c)^n$, where the $a_n$ are real or complex numbers, and $x$ is real or complex.

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

For question involving exponential functions and questions on exponential growth or decay.

For questions involving Hilbert spaces, that is, complete normed spaces whose norm comes from an inner product.

Galois theory allows one to reduce certain problems in field theory, especially those related to field extensions, to problems in group theory. For questions about field theory and not Galois theory, use the (field-theory) tag instead. For questions about abstractions of Galois theory, use (galois-connections).

Combinations are subsets of a given size of a given finite set.
All questions for this tag have to directly involve combinations; if instead the question is about binomial coefficients, use that tag.

Questions involving improper integrals, defined as the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or $\infty$ or $-\infty$, or as both endpoints approach limits.

Coefficients involved in the Binomial Theorem. $ \dbinom{n}{k}$ counts the subsets of size $k$ of a set of size $n$.

For requesting, clarifying, and comparing definitions of mathematical terms.

Questions related to the algebraic structure of algebraic integers

For questions about integration, where the theory is based on measures. It is almost always used together with the tag [measure-theory], and its aim is to specify questions about integrals, not only properties of the measure.

For questions about Riemann geometry, which is a branch of differential geometry dealing with Riemannian manifolds.

For questions about the Lebesgue measure, a measure defined on the Borel or Lebesgue subsets of the real line or $\mathbb R^d$ for some integer $d$. Use it with (tag: measure-theory) tag and (if necessary) with (tag:lebesgue-integral).

A Lie group is a group (in the sense of abstract algebra) that is also a differentiable manifold, such that the group operations (addition and inversion) are smooth, and so we can study them with differential calculus. They are a special type of topological group.
Consider using with the (group-theory) tag.

This tag is for questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution. The normal distribution is the most common type of distribution assumed in technical stock market analysis and in other types of statistical analyses.

A convex optimization problem consists of either minimizing a convex objective or maximizing a concave objective over a convex feasible region.

Differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.

For questions regarding partial derivatives. The partial derivative of a function of several variables is the derivative of the function with respect to one of those variables, with all others held constant.

In dynamical systems, the motion of a particle in some geometric space, governed by some time dependent rules, is studied. The process can be discrete (where the particle jumps from point to point) or continuous (where the particle follows a trajectory). Dynamical systems is used in mathematical models of diverse fields such as classical mechanics, economics, traffic modelling, population dynamics, and biological feedback.

Questions about determinants: their computation or their theory. If $E$ is a vector space of dimension $d$, then we can compute the determinant of a $d$-uple $(v_1,\ldots,v_d)$ with respect to a basis.

For questions about properties and applications of triangles.

Questions related to understanding line integrals, vector fields, surface integrals, the theorems of Gauss, Green and Stokes. Some related tags are (multivariable-calculus) and (differential-geometry).

Questions about the set of values at which a given function evaluates to zero. For questions about "square roots", "cube roots" and such, consider using the (radicals) and the (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

Questions on the use of algebraic techniques for proving geometric facts. Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. It is concerned with defining and representing geometrical shapes in a numerical way.