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114 relations: Abelian group, Abstract algebra, Alexander horned sphere, Algebraic number field, Algorithm, Algorithmic inference, Almost everywhere, Analysis, Analytic function, Ariane 5, Axiom of choice, Baire category theorem, Banach–Tarski paradox, Bézout's theorem, Big O notation, Borel set, Byzantine fault tolerance, Calculus, Cantor function, Cantor set, Cardinality, Cauchy distribution, Central limit theorem, Cluster (spacecraft), Collision (computer science), Computational complexity theory, Computer science, Continuous function, Countable set, Counterintuitive, Denial-of-service attack, Differentiable function, Dimension (vector space), Dirac delta function, Distribution (mathematics), Division ring, Euclidean space, Exceptional isomorphism, Exceptional object, Field (mathematics), Field extension, Finitely generated abelian group, Fixed point (mathematics), Fractal, Fractal dimension, Freeman Dyson, Function (mathematics), General topology, Group (mathematics), Hash table, ..., Hausdorff dimension, Hausdorff paradox, Hausdorff space, Henri Poincaré, Holomorphic function, Hurwitz's theorem (composition algebras), Icosahedron, Indicator function, Infinity, Integer, Interval (mathematics), Irrational number, Karush–Kuhn–Tucker conditions, Laity, Lebesgue integration, Magma (algebra), Magnetic reconnection, Mathematical optimization, Mathematical physics, Mathematician, Mathematics, Measure (mathematics), Meromorphic function, Model theory, Monotonic function, Non-Euclidean geometry, Non-measurable set, Nonlinear programming, Nowhere continuous function, Numerical integration, Paradox, Pathological (mathematics), Peano axioms, Probability, Probability space, Pythagoras, Quicksort, Rational number, Real line, Real number, Riemann integral, Ring (mathematics), Ring of integers, Schoenflies problem, Semigroup, Semisimple Lie algebra, Set (mathematics), Sigma-algebra, Simple Lie group, Simply connected space, Smoothness, Space-filling curve, Sporadic group, Statistics, Sufficient statistic, Surjective function, Teratology, Topology, Uncountable set, Unique factorization domain, Unit square, Vector space, Weierstrass function, Well-behaved statistic. Expand index (64 more) »
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Alexander horned sphere
The Alexander horned sphere is a pathological object in topology discovered by.
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Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Algorithmic inference
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst.
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Almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.
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Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Ariane 5
Ariane 5 is a European heavy-lift launch vehicle that is part of the Ariane rocket family, an expendable launch system used to deliver payloads into geostationary transfer orbit (GTO) or low Earth orbit (LEO).
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Baire category theorem
The Baire category theorem (BCT) is an important tool in general topology and functional analysis.
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Banach–Tarski paradox
The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.
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Bézout's theorem
Bézout's theorem is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves which do not share a common component (that is, which do not have infinitely many common points).
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Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
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Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.
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Byzantine fault tolerance
Byzantine fault tolerance (BFT) is the dependability of a fault-tolerant computer system, particularly distributed computing systems, where components may fail and there is imperfect information on whether a component is failed.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Cantor function
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous.
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Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Cauchy distribution
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.
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Central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.
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Cluster (spacecraft)
Cluster was a constellation of four European Space Agency spacecraft which were launched on the maiden flight of the Ariane 5 rocket, Flight 501, and subsequently lost when that rocket failed to achieve orbit.
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Collision (computer science)
Collision is used in two slightly different senses in theoretical computer science and telecommunications.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Counterintuitive
A counterintuitive proposition is one that does not seem likely to be true when assessed using intuition, common sense, or gut feelings.
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Denial-of-service attack
In computing, a denial-of-service attack (DoS attack) is a cyber-attack in which the perpetrator seeks to make a machine or network resource unavailable to its intended users by temporarily or indefinitely disrupting services of a host connected to the Internet.
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Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
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Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
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Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Division ring
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Exceptional isomorphism
In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members ai and bj of two families, usually infinite, of mathematical objects, that is not an example of a pattern of such isomorphisms.
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Exceptional object
Many branches of mathematics study objects of a given type and prove a classification theorem.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Field extension
In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
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Finitely generated abelian group
In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements x1,..., xs in G such that every x in G can be written in the form with integers n1,..., ns.
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Fractal
In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.
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Fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
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Freeman Dyson
Freeman John Dyson (born 15 December 1923) is an English-born American theoretical physicist and mathematician.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Hash table
In computing, a hash table (hash map) is a data structure that implements an associative array abstract data type, a structure that can map keys to values.
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Hausdorff dimension
Hausdorff dimension is a measure of roughness in mathematics introduced in 1918 by mathematician Felix Hausdorff, and it serves as a measure of the local size of a space, taking into account the distance between its points.
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Hausdorff paradox
The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff.
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Hurwitz's theorem (composition algebras)
In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Indicator function
In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.
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Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Karush–Kuhn–Tucker conditions
In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are First-order necessary conditions for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
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Laity
A layperson (also layman or laywoman) is a person who is not qualified in a given profession and/or does not have specific knowledge of a certain subject.
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Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
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Magma (algebra)
In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.
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Magnetic reconnection
Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Non-measurable set
In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "size".
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Nonlinear programming
In mathematics, nonlinear programming is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
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Nowhere continuous function
In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain.
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
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Paradox
A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.
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Pathological (mathematics)
In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved.
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Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
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Probability
Probability is the measure of the likelihood that an event will occur.
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Probability space
In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly.
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Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.
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Quicksort
Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Ring of integers
In mathematics, the ring of integers of an algebraic number field is the ring of all integral elements contained in.
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Schoenflies problem
In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semisimple Lie algebra
In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras \mathfrak g whose only ideals are and \mathfrak g itself.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sigma-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.
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Simple Lie group
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Space-filling curve
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n-dimensional unit hypercube).
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Sporadic group
In group theory, a discipline within mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Sufficient statistic
In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Teratology
Teratology is the study of abnormalities of physiological development.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
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Unique factorization domain
In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.
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Unit square
In mathematics, a unit square is a square whose sides have length.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Weierstrass function
In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.
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Well-behaved statistic
Although the term well-behaved statistic often seems to be used in the scientific literature in somewhat the same way as is well-behaved in mathematics, that is, to mean 'non-pathological' it can also be assigned precise mathematical meaning, and in more than one way.
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References
[1] https://en.wikipedia.org/wiki/Pathological_(mathematics)
