# Tags

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

For questions about real analysis, a branch of mathematics dealing with limits, convergence of sequences, construction of the real numbers, the least upper bound property; and related analysis topics, such as continuity, differentiation, and integration through the Fundamental Theorem of Calculus. This tag can also be used for more advanced topics, like measure theory.

For basic questions about limits, continuity, derivatives, integrals, and their applications, mainly of one-variable functions. For questions about convergence of sequences and series, this tag can be use with more specialized tags.

For questions about vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically concerning matrices, use the (matrices) tag. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

For basic questions about probability and the questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities. For questions about the theoretical footing of probability (especially using [tag:measure-theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

For questions about monoids, groups, rings, modules, fields, vector spaces, algebras over fields, various types of lattices, and other such algebraic objects. Associate with related tags like [group-theory], [ring-theory], [modules], etc as necessary. To clarify which topic of abstract algebra is most related to your question and help other users when searching.

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of the integrals being considered. This tag often goes along with the (calculus) tag.

For questions concerning sequences and series. Typical questions concern, but are not limited to: identifying sequences, identifying terms, recurrence relations, $\epsilon-N$ proofs of convergence, convergence tests, finding closed forms for sums. For questions on finite sums, use the (summation) tag instead.

For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness; compactness; separation axioms; bases; convergence: sequences, nets and filters; continuous functions; compactifications; function spaces; etc. Please use the more specific tags, (algebraic-topology), (differential-topology), (metric-spaces), (functional-analysis) whenever appropriate.

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

For questions mainly about theory of complex analytic/holomorphic functions of one complex variable. Use [tag:complex-numbers] instead for questions about complex numbers. Use [tag:several-complex-variables] instead for questions about holomorphic functions of more than one complex variables.

Functional analysis, the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces and other topics. For basic questions about functions use more suitable tags like (functions), (functional-equations) or (elementary-set-theory).

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.

For questions about the study of algebraic structures consisting of a set of elements together with an operation that satisfies four conditions: closure, associativity, identity and invertibility.

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

For questions about ordinary differential equations, which are differential equations involving ordinary derivatives of one or more dependent variables with respect to a single independent variables.
For questions specifically concerning partial differential equations, use the [tag:pde] instead.

Questions on the evaluation and properties of limits in the sense of analysis and related fields. For limits in the sense of category theory, use (limits-colimits) instead.

For questions solely about the modern theoretical footing for probability, for example, probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-distributions] for specific distribution functions, and consider [tag:stochastic-processes] when appropriate.

Questions on advanced topics - beyond those in typical introductory courses: higher degree algebraic number and function fields, Diophantine equations, geometry of numbers / lattices, quadratic forms, discontinuous groups and and automorphic forms, Diophantine approximation, transcendental numbers, elliptic curves and arithmetic algebraic geometry, exponential and character sums, Zeta and L-functions, multiplicative and additive number theory, etc.

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

Questions on divisibility, gcd and lcm, congruences, linear Diophantine equations, Fermat's and Wilson's theorems, the Chinese Remainder theorem, primitive roots, quadratic congruences, quadratic number fields and other related topics which may be treated in first courses on number theory. More advanced topics should instead use the number-theory or other tags.

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Use this tag for questions about differential and integral calculus with more than one independent variable. Some related tags are (differential-geometry), (real-analysis), and (differential-equations).

For elementary questions about functions, notation, properties, and operations such as function composition. Consider also using the (graphing-functions) tag.

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses on "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such structures, use (differential-topology) instead. Use (symplectic-geometry), (riemannian-geometry), (complex-geometry), or (lie-groups) when more appropriate.

Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles and other topics relating to measuring triangles.

Questions on proving, manipulating and applying inequalities. Do not use this tag just because an inequality appears somewhere in your question.

This tag is for elementary questions on set theory, spanning topics usually found in introductory courses in set theory, in addition to review sections of graduate textbooks in the same field. Topics include intersections and unions, differences and complements, De Morgan's laws, Venn diagrams, relations and functions, countability and uncountability, etc. More advanced topics should use (set-theory) instead.

The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. This tag should not be used for elementary problems which involve both algebra and geometry.

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the following tags as well, if they fit the question: (model-theory), (set-theory), (computability), and (proof-theory). This tag is not for logical puzzles, use (puzzle).

For both basic and advanced questions on polynomials in any number of variables, including, but not limited to solving for roots, factoring, and checking for irreducibility.

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)