Mathematics and statistics

Selmer group

A Selmer group is a finitely generated subgroup of a Galois cohomology group satisfying local conditions everywhere, named for Ernst Sejersted Selmer and central to descent on elliptic curves.

Semantic theory of truth

The semantic theory of truth, also called Tarski's definition of truth, is a definition of truth for formalized languages developed by Alfred Tarski in the 1930s.

Semantics (logic)

Semantics, also called the semantics of logic, is the part of logic assigning truth conditions to formal-language sentences, chiefly through the model-theoretic semantics introduced by Alfred Tarski.

Semi-decidability

Semi-decidability, also known as recursive enumerability, is a property of decision problems in computability theory: a procedure halts on yes instances but may run forever on no instances.

Semi-implicit method

A semi-implicit method is a time-integration scheme for differential equations that treats stiff terms implicitly and the rest explicitly, gaining stability while avoiding iterative solvers.

Semi-major and semi-minor axes

The semi-major and semi-minor axes are the half-lengths of an ellipse's longest and shortest diameters, meeting at right angles at its center, with the semi-major axis measuring orbital size.

Semi-Markov model

A semi-Markov model is a multistate stochastic process whose next transition depends on how long it has spent in the current state, relaxing the Markov model's memoryless sojourn times.

Semi-Markov process

A semi-Markov process is a stochastic process whose visited states form a Markov chain, but whose holding times in each state follow arbitrary distributions rather than exponential ones.

Semi-structured data

Semi-structured data is data with some structure beyond plain text, such as tags or nested fields, but no fixed schema; XML and JSON are the most widespread formats.

Semicircle law

The semicircle law is a theorem of random matrix theory stating that the eigenvalues of a large random Hermitian matrix converge to a half-circle-shaped density.

Semicontinuity is a one-sided weakening of continuity for real-valued functions, where upper or lower semicontinuity permits jumps in one direction; introduced by René Baire in 1899, it underlies existence of minimizers.

Semidefinite programming

Semidefinite programming is a convex optimization technique that optimizes a linear function of a symmetric matrix under positive semidefinite constraints, generalizing linear programming and underpinning approximation algorithms, control theory, and machine learning.

Semidirect product

The semidirect product in group theory builds a group from two subgroups, one of which is normal, with an action of one on the other twisting the multiplication.

Semigroup

A semigroup is an algebraic structure consisting of a non-empty set with an associative binary operation, sitting between a magma and a monoid in the hierarchy of algebraic structures.

Semigroup algebra

A semigroup algebra, also called a semigroup ring, is a ring of finite formal sums of semigroup elements multiplied by the semigroup operation, generalizing the polynomial ring.

Semilattice

A semilattice, also called an upper or lower semilattice, is a set with an associative, commutative, idempotent operation, equivalently a poset where every pair has a join or meet.

Semimartingale

A semimartingale is a càdlàg adapted stochastic process decomposable into a local martingale plus a finite variation process, the largest class of integrators usable in Itô calculus.

Semiparametric efficiency

Semiparametric efficiency is a theory in statistics that extends the Cramér–Rao bound to models with an infinite-dimensional nuisance parameter, giving the smallest achievable asymptotic variance.

Semiparametric model

A semiparametric model is a statistical model that combines a finite-dimensional parameter of interest with an infinite-dimensional nuisance component, sitting between parametric and nonparametric models.

Semiprime

A semiprime, also called a 2-almost prime or biprime, is a natural number that is the product of exactly two primes, like 15 = 3 × 5.

Semiring

A semiring is an algebraic structure with addition and multiplication in which multiplication distributes over addition, but subtraction is not required; the natural numbers are the basic example.

Semisimple module

A semisimple module, also called a completely reducible module, is a module that is a direct sum of simple submodules; it underlies the representation theory of finite groups.

Senary

Senary, also called heximal or seximal, is the base-6 positional numeral system using digits 0 through 5, attested in yam-counting languages of southern New Guinea.

Sensitivity analysis

Sensitivity analysis, also called what-if analysis, studies how uncertainty in a model's output can be apportioned to its inputs, complementing uncertainty analysis in model building.

Sensitivity analysis for unmeasured confounding

Sensitivity analysis for unmeasured confounding is a family of statistical methods assessing how strong hidden confounding would have to be to change an observational study's causal conclusion.

Sensitivity and specificity

Sensitivity and specificity are paired statistical measures of a diagnostic test's performance: the probability that a person with the condition tests positive, and that a person without it tests negative.

Separable extension

A separable field extension is an algebraic field extension in which every element's minimal polynomial has no repeated roots, a condition required for Galois extensions.

Separable space

In topology, a separable space (separable topological space) contains a countable dense subset. The rationals are dense in the reals, making the real line separable.

Separation logic

Separation logic is an extension of Hoare logic for verifying programs that manipulate heap-allocated pointer structures, using a separating conjunction for disjoint memory; it won the 2016 Gödel Prize.