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219 relations: Affine space, Alan Turing, Alan Turing: The Enigma, Algebraic geometry, Algebraic graph theory, Algebraic structure, Algebraic variety, Algorithm, Analog signal, Analysis, Analytic number theory, Applied mathematics, Arithmetic, Association for Computing Machinery, Asymptotic analysis, Auction theory, Automata theory, Automated theorem proving, Axiom, Bertrand's ballot theorem, Binary relation, Bioinformatics, Bletchley Park, Bojan Mohar, Boolean algebra, Calculus, Cardinality, Carsten Thomassen, Clay Mathematics Institute, Coding theory, Cold War, Colossus computer, Combination, Combinatorial design, Combinatorial topology, Combinatorics, Completeness (logic), Complex analysis, Complexity class, Computability, Computational geometry, Computational topology, Computer, Computer graphics (computer science), Computer science, Computer-aided design, Concrete Mathematics, Consistency, Continuous function, Continuous modelling, ..., Control theory, Countable set, Critical path method, Cryptanalysis, Cryptography, Cyberchase, Data, Database, David Hilbert, Decision theory, Derivative, Descriptive set theory, Dice, Differential equation, Differential game, Diophantine approximation, Diophantine equation, Diophantine set, Directed acyclic graph, Discrete differential geometry, Discrete exterior calculus, Discrete Fourier transform, Discrete geometry, Discrete logarithm, Discrete modelling, Discrete Morse theory, Discrete space, Discrete transform, Donald Knuth, Dynamical system (definition), Economy, Electrical engineering, Enumeration, Enumerative combinatorics, Fair division, Field (mathematics), Finite difference, Finite field, Finite set, Finite topological space, Formal language, Formal verification, Four color theorem, Fulkerson Prize, Function (mathematics), Function field of an algebraic variety, Fuzzy logic, Game theory, Gödel's incompleteness theorems, Generating function, Geometry of numbers, Georg Cantor, Graph (discrete mathematics), Graph theory, Graphon, Group (mathematics), Harmonic analysis, Hilbert's problems, Hilbert's second problem, Hilbert's tenth problem, Hybrid system, Image analysis, Inference, Infinitary logic, Infinite set, Information, Information theory, Integer, Integral transform, Intersection (set theory), Intuitionistic logic, Knot theory, Linear programming, Localization of a ring, Logic gate, Markov chain, Martingale (probability theory), Mathematical analysis, Mathematical Association of America, Mathematical logic, Mathematical maturity, Mathematical optimization, Mathematical proof, Mathematical structure, Metric space, Millennium Prize Problems, Modular arithmetic, Monoid, Network theory, Normal distribution, NP (complexity), Number theory, Numerical analysis, Operations research, Order theory, Oren Patashnik, Orthogonal polynomials, Outline of discrete mathematics, P (complexity), P versus NP problem, P-adic analysis, Partially ordered set, Partition (number theory), Partition of a set, Peirce's law, Permutation, Petri net, Phylogenetic tree, Playing card, Polynomial ring, Precalculus, Premise, Primality test, Prime number, Prisoner's dilemma, Probability distribution, Probability theory, Process calculus, Process optimization, Programming language, Proof theory, Public-key cryptography, Q-Pochhammer symbol, Queueing theory, Random House, Real number, Recurrence relation, Relational algebra, Ring (mathematics), Ronald Graham, Rule of inference, Safety-critical system, Sample space, Scheduling (computing), Semigroup, Sequence, Set (mathematics), Social choice theory, Software development, Soundness, Special functions, Spectrum of a ring, Statement (logic), Symbolic method (combinatorics), Tangent space, Telecommunication, Tessellation, The Art of Computer Programming, Theoretical computer science, Time-scale calculus, Topological combinatorics, Topological graph theory, Topological property, Topology, Topology (chemistry), Transcendental number, Tree structure, Truth table, Truth value, Twelvefold way, United States dollar, Utility, Very-large-scale integration, Video game, Voting, Well-formed formula, World War II, Yuri Matiyasevich, Zariski tangent space. Expand index (169 more) »
Affine space
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
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Alan Turing
Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.
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Alan Turing: The Enigma
Alan Turing: The Enigma (1983) is a biography of the British mathematician, codebreaker, and early computer scientist, Alan Turing (1912–1954) by Andrew Hodges.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic graph theory
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs.
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Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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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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Analog signal
An analog signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal.
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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 number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
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Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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Association for Computing Machinery
The Association for Computing Machinery (ACM) is an international learned society for computing.
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Asymptotic analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
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Auction theory
Auction theory is an applied branch of economics which deals with how people act in auction markets and researches the properties of auction markets.
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Automata theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
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Automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Bertrand's ballot theorem
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with p > q, what is the probability that A will be strictly ahead of B throughout the count?" The answer is The result was first published by W. A. Whitworth in 1878, but is named after Joseph Louis François Bertrand who rediscovered it in 1887.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Bioinformatics
Bioinformatics is an interdisciplinary field that develops methods and software tools for understanding biological data.
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Bletchley Park
Bletchley Park was the central site for British (and subsequently, Allied) codebreakers during World War II.
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Bojan Mohar
Bojan Mohar is a Slovenian and Canadian mathematician, specializing in graph theory.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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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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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Carsten Thomassen
Carsten Thomassen (born August 22, 1948 in Grindsted) is a Danish mathematician.
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Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.
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Coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications.
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Cold War
The Cold War was a state of geopolitical tension after World War II between powers in the Eastern Bloc (the Soviet Union and its satellite states) and powers in the Western Bloc (the United States, its NATO allies and others).
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Colossus computer
Colossus was a set of computers developed by British codebreakers in the years 1943–1945 to help in the cryptanalysis of the Lorenz cipher.
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Combination
In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.
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Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
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Combinatorial topology
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
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Computability
Computability is the ability to solve a problem in an effective manner.
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Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
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Computational topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Computer graphics (computer science)
Computer graphics is a sub-field of Computer Science which studies methods for digitally synthesizing and manipulating visual content.
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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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Computer-aided design
Computer-aided design (CAD) is the use of computer systems to aid in the creation, modification, analysis, or optimization of a design.
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Concrete Mathematics
Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, first published in 1989, is a textbook that is widely used in computer-science departments as a substantive but light-hearted treatment of the analysis of algorithms.
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Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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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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Continuous modelling
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes).
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Control theory
Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.
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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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Critical path method
The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities.
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Cryptanalysis
Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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Cyberchase
Cyberchase is an American/Canadian animated educational children's television series on PBS Kids.
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Data
Data is a set of values of qualitative or quantitative variables.
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Database
A database is an organized collection of data, stored and accessed electronically.
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David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
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Decision theory
Decision theory (or the theory of choice) is the study of the reasoning underlying an agent's choices.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Descriptive set theory
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces.
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Dice
Dice (singular die or dice; from Old French dé; from Latin datum "something which is given or played") are small throwable objects with multiple resting positions, used for generating random numbers.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Differential game
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system.
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Diophantine approximation
In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers.
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Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
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Diophantine set
In mathematics, a Diophantine equation is an equation of the form P(x1,..., xj, y1,..., yk).
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Directed acyclic graph
In mathematics and computer science, a directed acyclic graph (DAG), is a finite directed graph with no directed cycles.
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Discrete differential geometry
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry.
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Discrete exterior calculus
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes.
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Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
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Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
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Discrete logarithm
In the mathematics of the real numbers, the logarithm logb a is a number x such that, for given numbers a and b. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that.
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Discrete modelling
Discrete modelling is the discrete analogue of continuous modelling.
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Discrete Morse theory
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by.
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Discrete space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
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Discrete transform
In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency.
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Donald Knuth
Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.
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Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.
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Economy
An economy (from Greek οίκος – "household" and νέμoμαι – "manage") is an area of the production, distribution, or trade, and consumption of goods and services by different agents.
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Electrical engineering
Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism.
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Enumeration
An enumeration is a complete, ordered listing of all the items in a collection.
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Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.
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Fair division
Fair division is the problem of dividing a set of goods or resources between several people who have an entitlement to them, such that each person receives his/her due share.
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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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Finite difference
A finite difference is a mathematical expression of the form.
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Finite topological space
In mathematics, a finite topological space is a topological space for which the underlying point set is finite.
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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
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Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.
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Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
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Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS).
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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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Function field of an algebraic variety
In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.
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Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.
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Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Geometry of numbers
In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Graphon
In graph theory and statistics, a graphon is a symmetric measurable function W:^2\to, that is important in the study of dense graphs.
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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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Harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).
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Hilbert's problems
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
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Hilbert's second problem
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems.
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Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.
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Hybrid system
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both flow (described by a differential equation) and jump (described by a state machine or automaton).
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Image analysis
Image analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques.
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Inference
Inferences are steps in reasoning, moving from premises to logical consequences.
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Infinitary logic
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Information
Information is any entity or form that provides the answer to a question of some kind or resolves uncertainty.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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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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Integral transform
In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.
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Knot theory
In topology, knot theory is the study of mathematical knots.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Localization of a ring
In commutative algebra, localization is a systematic method of adding multiplicative inverses to a ring.
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Logic gate
In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.
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Markov chain
A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".
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Martingale (probability theory)
In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Mathematical maturity
Mathematical maturity is an informal term used by mathematicians to refer to a mixture of mathematical experience and insight that cannot be directly taught.
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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 proof
In mathematics, a proof is an inferential argument for a mathematical statement.
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Mathematical structure
In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Network theory
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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NP (complexity)
In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Operations research
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.
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Order theory
Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.
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Oren Patashnik
Oren Patashnik (born 1954) is a computer scientist.
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Orthogonal polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
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Outline of discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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P-adic analysis
In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of ''p''-adic numbers.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Partition (number theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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Peirce's law
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Petri net
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems.
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Phylogenetic tree
A phylogenetic tree or evolutionary tree is a branching diagram or "tree" showing the evolutionary relationships among various biological species or other entities—their phylogeny—based upon similarities and differences in their physical or genetic characteristics.
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Playing card
A playing card is a piece of specially prepared heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic, marked with distinguishing motifs and used as one of a set for playing card games.
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Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
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Precalculus
In mathematics education, precalculus is a course that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus.
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Premise
A premise or premiss is a statement that an argument claims will induce or justify a conclusion.
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Primality test
A primality test is an algorithm for determining whether an input number is prime.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Prisoner's dilemma
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Process calculus
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems.
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Process optimization
Process optimization is the discipline of adjusting a process so as to optimize some specified set of parameters without violating some constraint.
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Programming language
A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.
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Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
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Public-key cryptography
Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.
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Q-Pochhammer symbol
In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.
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Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues.
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Random House
Random House is an American book publisher and the largest general-interest paperback publisher in the world.
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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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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Relational algebra
Relational algebra, first created by Edgar F. Codd while at IBM, is a family of algebras with a well-founded semantics used for modelling the data stored in relational databases, and defining queries on it.
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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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Ronald Graham
Ronald Lewis "Ron" Graham (born October 31, 1935) is an American mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".
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Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
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Safety-critical system
A safety-critical system or life-critical system is a system whose failure or malfunction may result in one (or more) of the following outcomes.
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Sample space
In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
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Scheduling (computing)
In computing, scheduling is the method by which work specified by some means is assigned to resources that complete the work.
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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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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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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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Social choice theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense.
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Software development
Software development is the process of conceiving, specifying, designing, programming, documenting, testing, and bug fixing involved in creating and maintaining applications, frameworks, or other software components.
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Soundness
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Spectrum of a ring
In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by \operatorname(R), is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space.
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Statement (logic)
In logic, the term statement is variously understood to mean either: In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement.
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Symbolic method (combinatorics)
In combinatorics, especially in analytic combinatorics, the symbolic method is a technique for counting combinatorial objects.
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Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
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Telecommunication
Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or other electromagnetic systems.
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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The Art of Computer Programming
The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.
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Theoretical computer science
Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
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Time-scale calculus
In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid discrete–continuous dynamical systems.
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Topological combinatorics
The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this turned into the field of algebraic topology.
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Topological graph theory
In mathematics, topological graph theory is a branch of graph theory.
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Topological property
In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
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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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Topology (chemistry)
In chemistry, topology provides a convenient way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space.
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Transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.
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Tree structure
A tree structure or tree diagram is a way of representing the hierarchical nature of a structure in a graphical form.
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Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).
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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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Twelvefold way
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
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United States dollar
The United States dollar (sign: $; code: USD; also abbreviated US$ and referred to as the dollar, U.S. dollar, or American dollar) is the official currency of the United States and its insular territories per the United States Constitution since 1792.
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Utility
Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time.
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Very-large-scale integration
Very-large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining hundreds of thousands of transistors or devices into a single chip.
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Video game
A video game is an electronic game that involves interaction with a user interface to generate visual feedback on a video device such as a TV screen or computer monitor.
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Voting
Voting is a method for a group, such as, a meeting or an electorate to make a decision or express an opinion, usually following discussions, debates or election campaigns.
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Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
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World War II
World War II (often abbreviated to WWII or WW2), also known as the Second World War, was a global war that lasted from 1939 to 1945, although conflicts reflecting the ideological clash between what would become the Allied and Axis blocs began earlier.
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Yuri Matiyasevich
Yuri Vladimirovich Matiyasevich, (Ю́рий Влади́мирович Матиясе́вич; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist.
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Zariski tangent space
In algebraic geometry, the Zariski tangent space is a construction that defines a tangent space at a point P on an algebraic variety V (and more generally).
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References
[1] https://en.wikipedia.org/wiki/Discrete_mathematics
