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In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use co... | Wikipedia/Algorithm |
A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database; however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider... | Wikipedia/Geographic_information_system |
In mathematics and other fields, a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; howev... | Wikipedia/Lemma_(mathematics) |
Tarski–Grothendieck set theory (TG, named after mathematicians Alfred Tarski and Alexander Grothendieck) is an axiomatic set theory. It is a non-conservative extension of Zermelo–Fraenkel set theory (ZFC) and is distinguished from other axiomatic set theories by the inclusion of Tarski's axiom, which states that for e... | Wikipedia/Tarski–Grothendieck_set_theory |
In set theory, the intersection of two sets
A
{\displaystyle A}
and
B
,
{\displaystyle B,}
denoted by
A
∩
B
,
{\displaystyle A\cap B,}
is the set containing... | Wikipedia/Intersection_(set_theory) |
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding.
Equivalently, every first-order formula is equivalent to a universal formula.
This notion was introduced by Abraham Robinson.
== Model companion and model completion ==
A companion of a theory... | Wikipedia/Model_complete_theory |
Network performance refers to measures of service quality of a network as seen by the customer.
There are many different ways to measure the performance of a network, as each network is different in nature and design. Performance can also be modeled and simulated instead of measured; one example of this is using state ... | Wikipedia/Network_performance |
Industrial process control (IPC) or simply process control is a system used in modern manufacturing which uses the principles of control theory and physical industrial control systems to monitor, control and optimize continuous industrial production processes using control algorithms. This ensures that the industrial m... | Wikipedia/Industrial_process_control |
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs.
Semantics describe... | Wikipedia/Semantics_(computer_science) |
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean func... | Wikipedia/Boolean_function |
Photograph manipulation involves the transformation or alteration of a photograph. Some photograph manipulations are considered to be skillful artwork, while others are considered to be unethical practices, especially when used to deceive. Motives for manipulating photographs include political propaganda, altering the ... | Wikipedia/Photograph_manipulation |
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction.
== Representation ==
Function application is usually depicted by ... | Wikipedia/Function_application |
In computer science, a record (also called a structure, struct, or compound data type) is a composite data structure – a collection of fields, possibly of different data types, typically fixed in number and sequence.
For example, a date could be stored as a record containing a numeric year field, a month field represe... | Wikipedia/Record_(computer_science) |
A computer network is a collection of communicating computers and other devices, such as printers and smart phones. In order to communicate, the computers and devices must be connected by wired media like copper cables, optical fibers, or by wireless communication. The devices may be connected in a variety of network t... | Wikipedia/Computer_network |
In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra:
(
... | Wikipedia/Minimal_axioms_for_Boolean_algebra |
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability... | Wikipedia/Computability_theory |
In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols. All atomic formulas are thus of the form
P
... | Wikipedia/Monadic_predicate_calculus |
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with... | Wikipedia/Computer_graphics |
Network architecture is the design of a computer network. It is a framework for the specification of a network's physical components and their functional organization and configuration, its operational principles and procedures, as well as communication protocols used.
In telecommunications, the specification of a netw... | Wikipedia/Network_architecture |
In mathematics, the Elementary Theory of the Category of Sets or ETCS is a set of axioms for set theory proposed by William Lawvere in 1964. Although it was originally stated in the language of category theory, as Leinster pointed out, the axioms can be stated without references to category theory.
ETCS is a basic exam... | Wikipedia/Elementary_Theory_of_the_Category_of_Sets |
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (... | Wikipedia/Naive_set_theory |
In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator (type constructor). A kind system is essentially a simply typed lambda calculus "one level up", endowed with a primitive type, denoted
... | Wikipedia/Kind_(type_theory) |
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory.
== Basics ==
=== Cardinal numbers ===
Set theory as conceived... | Wikipedia/Paradoxes_of_set_theory |
Networking hardware, also known as network equipment or computer networking devices, are electronic devices that are required for communication and interaction between devices on a computer network. Specifically, they mediate data transmission in a computer network. Units which are the last receiver or generate data ar... | Wikipedia/Networking_hardware |
In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by S, so S(n) = n + 1. For example, S(1) = 2 and S(2) = 3. The successor function is one of the basic components used to build a primitive recursive function.
Successor operations are ... | Wikipedia/Successor_function |
The Journal of Functional Programming is a peer-reviewed scientific journal covering the design, implementation, and application of functional programming languages, spanning the range from mathematical theory to industrial practice. Topics covered include functional languages and extensions, implementation techniques,... | Wikipedia/Journal_of_Functional_Programming |
In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely characterizing the model's structure.
In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories ... | Wikipedia/Categorical_theory |
Concurrency refers to the ability of a system to execute multiple tasks through simultaneous execution or time-sharing (context switching), sharing resources and managing interactions. Concurrency improves responsiveness, throughput, and scalability in modern computing, including:
Operating systems and embedded syste... | Wikipedia/Concurrency_(computer_science) |
See also Naive set theory for the mathematical topic.
Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. Originally published by Van Nostrand in 1960, it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
It is on the li... | Wikipedia/Naive_Set_Theory_(book) |
Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in a dynamic environment in order to maximize a reward signal. Reinforcement learning is one of the three basic machine learning paradigms, alongside supervised le... | Wikipedia/Reinforcement_learning |
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
A nullary union refers to a union of zero (
0
{\displaystyle 0}
... | Wikipedia/Union_(set_theory) |
In computer science, the expressive power (also called expressiveness or expressivity) of a language is the breadth of ideas that can be represented and communicated in that language. The more expressive a language is, the greater the variety and quantity of ideas it can be used to represent.
For example, the Web Ontol... | Wikipedia/Expressive_power_(computer_science) |
Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BC). Deduction is inference deri... | Wikipedia/Inference |
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video g... | Wikipedia/Free_choice_inference |
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if A is a subset of some set X, then the indicator function of A is the function
1
... | Wikipedia/Indicator_function |
Boolean algebras are models of the equational theory of two values; this definition is equivalent to the lattice and ring definitions.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sententi... | Wikipedia/Boolean_algebras_canonically_defined |
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal machine, a model of computation that can be used... | Wikipedia/Lambda_calculus |
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by
dom
(
f
)
{\displaystyle \operatorname {dom} (f)}
or
dom
f
{\displays... | Wikipedia/Domain_of_a_function |
In the mathematical field of set theory, an ultrafilter on a set
X
{\displaystyle X}
is a maximal filter on the set
X
.
{\displaystyle X.}
In other words, it is a collection of subsets of
X
... | Wikipedia/Ultrafilter_(set_theory) |
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to cognitive science and mathematical logic. The word automata comes from the Greek word αὐτόματος, which means "self... | Wikipedia/Automata_theory |
Application security (short AppSec) includes all tasks that introduce a secure software development life cycle to development teams. Its final goal is to improve security practices and, through that, to find, fix and preferably prevent security issues within applications. It encompasses the whole application life cycle... | Wikipedia/Application_security |
A modeling language is any artificial language that can be used to express data, information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure of a programming language.
== Overview ==
A modeling lan... | Wikipedia/Modeling_language |
Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including linguistics, mathematics, and software... | Wikipedia/Programming_language_theory |
In computer programming, an anonymous function (function literal, expression or block) is a function definition that is not bound to an identifier. Anonymous functions are often arguments being passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a functio... | Wikipedia/Anonymous_function |
In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use co... | Wikipedia/Algorithm_design |
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The comp... | Wikipedia/Model_of_computation |
A discourse relation (also coherence relation or rhetorical relation) is a description of how two segments of discourse are logically and/or structurally connected to one another.
A widely upheld position is that in coherent discourse, every individual utterance is connected by a discourse relation with a context eleme... | Wikipedia/Segmented_discourse_representation_theory |
Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. Toge... | Wikipedia/Solid_modeling |
In computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing app... | Wikipedia/Formal_methods |
Rendering is the process of generating a photorealistic or non-photorealistic image from input data such as 3D models. The word "rendering" (in one of its senses) originally meant the task performed by an artist when depicting a real or imaginary thing (the finished artwork is also called a "rendering"). Today, to "re... | Wikipedia/Rendering_(computer_graphics) |
A network scheduler, also called packet scheduler, queueing discipline (qdisc) or queueing algorithm, is an arbiter on a node in a packet switching communication network. It manages the sequence of network packets in the transmit and receive queues of the protocol stack and network interface controller. There are sever... | Wikipedia/Network_scheduler |
In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence
φ
,
{\displaystyle \varphi ,}
the theory
T
... | Wikipedia/Complete_theory |
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.
== Origin ==
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. T... | Wikipedia/Semantic_theory_of_truth |
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe.
Since ma... | Wikipedia/Finite_model_theory |
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.
== Origin ==
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. T... | Wikipedia/Kripke's_theory_of_truth |
Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure of valid arguments. If an argument with true premises follows a rule of inference then the conclusion cannot be false. Modus ponens, an influential rule of inference, con... | Wikipedia/Rule_of_inference |
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid paradoxes, especiall... | Wikipedia/Class_(set_theory) |
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in early 1970s, based on the theoretical foundation of logic of computable functions previously proposed by Dana Scott. Work on the LCF system introduced the general-purp... | Wikipedia/Logic_for_Computable_Functions |
In functional programming, monads are a way to structure computations as a sequence of steps, where each step not only produces a value but also some extra information about the computation, such as a potential failure, non-determinism, or side effect. More formally, a monad is a type constructor M equipped with two op... | Wikipedia/Monad_(functional_programming) |
The simply typed lambda calculus (
λ
→
{\displaystyle \lambda ^{\to }}
), a form
of type theory, is a typed interpretation of the lambda calculus with only one type constructor (
→
{... | Wikipedia/Simply_typed_lambda_calculus |
The following system is Mendelson's (1997, 289–293) ST type theory.
ST is equivalent with Russell's ramified theory plus the Axiom of reducibility.
The domain of quantification is partitioned into an ascending hierarchy of types, with all individuals assigned a type. Quantified variables range over only one type; hen... | Wikipedia/ST_type_theory |
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems.
Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundat... | Wikipedia/Theory_of_types |
Software design is the process of conceptualizing how a software system will work before it is implemented or modified.
Software design also refers to the direct result of the design process – the concepts of how the software will work which consists of both design documentation and undocumented concepts.
Software desi... | Wikipedia/Software_design |
Type inference, sometimes called type reconstruction,: 320 refers to the automatic detection of the type of an expression in a formal language. These include programming languages and mathematical type systems, but also natural languages in some branches of computer science and linguistics.
== Nontechnical explanati... | Wikipedia/Type_inference |
In computer networking, a network service is an application running at the network layer and above, that provides data storage, manipulation, presentation, communication or other capability which is often implemented using a client–server or peer-to-peer architecture based on application layer network protocols.
Each s... | Wikipedia/Network_service |
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT includes a level of abstract mental representations (discourse representation s... | Wikipedia/Discourse_representation_theory |
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historicall... | Wikipedia/Zermelo–Fraenkel_set_theory |
The Kripke–Platek set theory (KP), pronounced , is an axiomatic set theory developed by Saul Kripke and Richard Platek.
The theory can be thought of as roughly the predicative part of Zermelo–Fraenkel set theory (ZFC) and is considerably weaker than it.
== Axioms ==
In its formulation, a Δ0 formula is one all of who... | Wikipedia/Kripke–Platek_set_theory |
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used f... | Wikipedia/Interpretation_function |
Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.
The same first-order language with "
=
{\displaystyle =}
" and "
∈
{\displaystyle \in }
" of classical set th... | Wikipedia/Constructive_set_theory |
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.
== Origin ==
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. T... | Wikipedia/Tarski's_theory_of_truth |
Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards. The tools work together in a design flow that chip designers use to design and analyze entire semicond... | Wikipedia/Electronic_design_automation |
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which ... | Wikipedia/Proof_theory |
In set theory, the complement of a set A, often denoted by
A
c
{\displaystyle A^{c}}
(or A′), is the set of elements not in A.
When all elements in the universe, i.e. all elements under consideration, are considered to be ... | Wikipedia/Complement_(set_theory) |
In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions. It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity, topological phase transition, wetting as well as non-equilibrium phase transition... | Wikipedia/Statistical_field_theory |
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities
q
˙
... | Wikipedia/Hamiltonian_mechanics |
The NASA Deep Space Network (DSN) is a worldwide network of spacecraft communication ground segment facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary spacecraft missions. It also performs radio and radar astronomy observations for the ex... | Wikipedia/NASA_Deep_Space_Network |
In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.
The prefix super- comes from the theory of supersymmetry in theoretical phy... | Wikipedia/Superalgebra |
There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise ... | Wikipedia/Particle_physics_and_representation_theory |
In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel.
== Notation ==
... | Wikipedia/Decoding_methods |
Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to model how individuals would behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is mainly prescriptive and conce... | Wikipedia/Decision_theory |
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry,... | Wikipedia/Neuroscience |
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.
Conformal field theory has important app... | Wikipedia/Conformal_field_theory |
In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional scalar).
The Clifford algebra Cl3,0(... | Wikipedia/Algebra_of_physical_space |
In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus i... | Wikipedia/Malliavin_calculus |
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, the Lagrangian is invariant under these transformations.
The term "gauge" ref... | Wikipedia/Gauge_theory |
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabil... | Wikipedia/Entropy_(information_theory) |
The Internet Engineering Task Force (IETF) is a standards organization for the Internet and is responsible for the technical standards that make up the Internet protocol suite (TCP/IP). It has no formal membership roster or requirements and all its participants are volunteers. Their work is usually funded by employers ... | Wikipedia/Internet_Engineering_Task_Force |
Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called because it contains only bosons in the spectrum.
In the 1980s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string th... | Wikipedia/Bosonic_string_theory |
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differ... | Wikipedia/Ordinary_differential_equation |
In mathematics and mathematical physics, potential theory is the study of harmonic functions.
The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions call... | Wikipedia/Potential_theory |
In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theo... | Wikipedia/Gauge_theory_(mathematics) |
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa constructed these codes for the first time in 1982.
== History ==
The name of these codes has evolved since the publication of Goppa's paper describing them. Histor... | Wikipedia/Algebraic_geometric_code |
In cryptography, an adversary (rarely opponent, enemy) is an entity whose aim is to prevent the users of the cryptosystem from achieving their goal (primarily privacy, integrity, and availability of data), often with malicious intent. An adversary's efforts might take the form of attempting to discover secret data, cor... | Wikipedia/Adversary_(cryptography) |
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist.
== Overview of methods ==
=== Finite di... | Wikipedia/Numerical_methods_for_partial_differential_equations |
In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological quantum field theory.
== Overview ==
There are two main versions of topol... | Wikipedia/Topological_string_theory |
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamilt... | Wikipedia/Perturbation_theory_(quantum_mechanics) |
Tensor software is a class of mathematical software designed for manipulation and calculation with tensors.
== Standalone software ==
SPLATT is an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave/MATLAB API.
Cadabra is a co... | Wikipedia/Tensor_software |
In information theory, redundancy measures the fractional difference between the entropy H(X) of an ensemble X, and its maximum possible value
log
(
|
A
X
... | Wikipedia/Redundancy_(information_theory) |
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativ... | Wikipedia/Spacetime_algebra |
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