6,052 articles
Collatz conjecture
The Collatz conjecture, also called the 3x + 1 problem, is an unsolved number theory problem stating that iterating 3n + 1 for odd numbers and n/2 for even numbers carries every positive integer to 1.
Collectively exhaustive events
Collectively exhaustive events, also called jointly exhaustive events, are events in probability theory that together cover the entire sample space, so at least one must occur.
Collinearity
Collinearity is the property of a set of points all lying on one straight line; three or more points are collinear when a line passes through every one of them.
Combination
A combination, also known as a mathematical combination, is a selection of items in which order is ignored, counted by the binomial coefficient n choose k.
Combinational logic
Combinational logic, also called combinatorial logic, is digital circuitry whose outputs depend only on the current inputs, with no memory, building blocks such as adders, multiplexers, and ALUs.
Combinatorial design
Combinatorial design theory studies arrangements of a finite set into blocks meeting balance conditions, like Steiner triple systems, and is used to plan experiments and test software.
Combinatorial representation theory
Combinatorial representation theory describes representations of groups and algebras by explicit combinatorial objects such as tableaux and permutations, so that dimensions and character values become counts and weighted sums.
Combinatorial species
A combinatorial species is a rule that assigns structures to every finite set and transports them along bijections, introduced by André Joyal in 1981 as a unified theory of generating functions.
Combinatorics
Combinatorics, also called combinatorial analysis or combinatorial mathematics, is the branch of mathematics that studies the enumeration, combination, and permutation of sets of elements, with wide applications in computer science.
Combinatorics on words
Combinatorics on words, also known as word combinatorics, is the branch of discrete mathematics that studies sequences of symbols from a finite alphabet, including their patterns, repetitions, and equations.
Combinatory logic
Combinatory logic, also known as combinatory algebra, is a formal system for describing functions without variable binding, using only combinators such as S and K.
COmbined Compromise SOlution (COCOSO)
The COmbined Compromise SOlution (COCOSO) is a multi-criteria decision-making method, introduced by Morteza Yazdani and colleagues in 2019, that ranks alternatives by combining weighted-sum and weighted-product scores.
Common knowledge (logic)
Common knowledge is a property of a proposition among a group: everyone knows it, everyone knows that everyone knows it, and so on without end.
Communicating sequential processes
Communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems, introduced by Tony Hoare in 1978, where processes communicate through synchronized events.
Communication-avoiding algorithms
Communication-avoiding algorithms are numerical linear algebra algorithms restructured to minimize data movement between memory levels and processors, because communication is the bottleneck; examples include CALU and TSQR.
Community detection in networks
Community detection in networks is a family of algorithms that partition a graph's nodes into groups more densely connected internally than to the rest of the network.
Commutation theorem for traces
The commutation theorem for traces is a result in von Neumann algebra theory stating that an algebra with a semifinite trace is the commutant of its opposite algebra.
Commutative property
The commutative property, or commutative law, is the property of a binary operation that swapping the order of its two inputs never changes the result.
Commutative ring
A commutative ring is a ring in which multiplication is commutative, meaning a·b = b·a for all elements; examples include the integers, the rationals, and the real numbers.
Commutator
A commutator is a group element of the form [g,h] = g⁻¹h⁻¹gh that equals the identity exactly when g and h commute, measuring noncommutativity in group theory.
Commutator subgroup
The commutator subgroup, also called the derived subgroup, of a group is the subgroup generated by all commutators; it is the unique smallest normal subgroup whose quotient is abelian.
Comodule
A comodule, also called a corepresentation, is a vector space with a coaction map from a coalgebra, the arrow-reversed analog of a module over an algebra.
Comonad
A comonad is a category-theory structure dual to a monad: an endofunctor with a counit and comultiplication, arising from adjunctions and used in sheaf cohomology.
Comonotonicity
Comonotonicity is an extremal form of positive dependence among random variables, where each is a non-decreasing function of a common factor, central to actuarial science and financial mathematics.
Compact operator
A compact operator is a bounded linear operator between Banach spaces that maps the unit ball to a relatively compact set, behaving like a finite-dimensional matrix.
Compact space
A compact space, also known as a compact topological space or compactum, is a topological space in which every open cover contains a finite subcover.
Compact-open topology
The compact-open topology is a topology on continuous function spaces, generated by functions mapping compact sets into open sets, used in homotopy theory and functional analysis.
Compactness theorem
The compactness theorem is a theorem of first-order logic stating that a set of sentences has a model if every finite subset does, first proved by Gödel in 1930.
Companion matrix
A companion matrix is an n × n matrix whose characteristic and minimal polynomial equal a given monic polynomial, used to find polynomial roots as eigenvalues.
Comparison of Gaussian process software
Comparison of Gaussian process software evaluates packages such as scikit-learn, GPflow, GPyTorch, and Stan, which differ in platform, inference method, scalability, and the numerical results they produce.