The following outline is provided as an overview of and topical guide to formal science: Formal science – branches of knowledge that are concerned with formal systems, such as those under the branches of: logic, mathematics, computer science, statistics, and some aspects of linguistics. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules.

Branches of formal science

Logic

Mathematics

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

– search for fundamental truths in pattern, quantity, and change. ''(See also Branches of Mathematics and AM
Mathematics Subject Classification
'' **

Algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

– one of the main branches of mathematics, it concerns the study of structure, relation and quantity. ***

Abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...

- the study of algebraic structures ****

Group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...

– studies the algebraic structures known as groups. *****

Group representation In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used ...

– describe abstract groups in terms of linear transformations of vector spaces **** Field theory – branch of mathematics which studies the properties of fields ****

Ring theory In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their r ...

– study of ring–algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers *****

Associative algebra In mathematics, an associative algebra ''A'' is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field ''K''. The addition and multiplic ...

– associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R *****

Non-associative algebra A non-associative algebra (or distributive algebra) is an algebra over a field where the binary operation, binary multiplication operation is not assumed to be associative operation, associative. That is, an algebraic structure ''A'' is a non-ass ...

– K-vector space (or more generally a module) A equipped with a K-bilinear map *****

Commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prom ...

- the branch of algebra that studies commutative rings, their ideals, and modules over such rings ****** Ideal theory - the theory of ideals in commutative rings *****

Non-commutative algebra In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist ''a'' and ''b'' in the ring such that ''ab'' and ''ba'' are different. Equivalently, a ''noncommutative ring'' is a ring that is not ...

- the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings **** Wheel theory – studies the algebraic structures known as wheels. ****

Universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study ...

– field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures ***

Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrice ...

– branch of mathematics concerning finite or countably infinite dimensional vector spaces, as well as linear mappings between such spaces. ****

Vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...

– mathematical structure formed by a collection of vectors: objects that may be added together and multiplied ("scaled") by numbers, called scalars in this context. ***

Multilinear algebra Multilinear algebra is a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of ''p' ...

– extends the methods of linear algebra ***

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...

– algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds ***

Homological algebra Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topolo ...

– branch of mathematics which studies homology in a general algebraic setting ***

Category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...

– area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non-category-theoretical sense), where these collections satisfy some basic conditions ***

Lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bou ...

– partially ordered set in which any two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). ****

Order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

– branch of mathematics which investigates our intuitive notion of order using binary relations. ***

Differential algebra In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule. A n ...

– algebras equipped with a derivation, which is a unary function that is linear and satisfies the Leibniz product rule. **

Analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

– branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions ***

Real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...

– branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. ****

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

– branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. ***

Complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

– branch of mathematical analysis that investigates functions of complex numbers ***

Functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defi ...

– branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense ****

Operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators ...

– branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators. ***

Non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta ...

– branch of classical mathematics that formulates analysis using a rigorous notion of an infinitesimal number. ***

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 ex ...

– 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. ***

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. The theory of complex-valued numerical functions on the ''p''-adic numbers is part of the theory of l ...

– branch of number theory that deals with the mathematical analysis of functions of p-adic numbers. ***

Ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...

– ordinary differential equation (ODE) is an equation in which there is only one independent variable and one or more derivatives of a dependent variable with respect to the independent variable, so that all the derivatives occurring in the equation are ordinary derivatives. ***

Partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

– differential equation that contains unknown multivariable functions and their partial derivatives. **

Probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

– branch of mathematics concerned with probability, the analysis of random phenomena. ***

Measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...

– systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. ***

Ergodic theory Ergodic theory ( Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expr ...

– branch of mathematics that studies dynamical systems with an invariant measure and related problems. ***

Stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that ap ...

– collection of random variables; this is often used to represent the evolution of some random value, or system, over time. **

Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

– branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. ***

Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

– major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing. ***

General topology In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometri ...

– branch of topology which studies properties of topological spaces and structures defined on them. ***

Algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

– branch of mathematics which uses tools from abstract algebra to study topological spaces ***

Geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originate ...

– study of manifolds and maps between them, particularly embeddings of one manifold into another. ***

Differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

– field dealing with differentiable functions on differentiable manifolds ***

Algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

– branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry ***

Differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and mult ...

– mathematical discipline that uses the techniques of differential calculus and integral calculus, as well as linear algebra and multilinear algebra, to study problems in geometry ***

Projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, ...

– study of geometric properties that are invariant under projective transformations ***

Affine geometry In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle. As the notion of '' parallel lines'' is one of the main properties that is ...

– study of geometric properties which remain unchanged by affine transformations ***

Non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean g ...

– either of two specific geometries that are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. ***

Convex geometry In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of ...

– branch of geometry studying convex sets, mainly in Euclidean space. ***

Discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic ge ...

– branch of geometry that studies combinatorial properties and constructive methods of discrete geometric objects. **

Trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...

– branch of mathematics that studies relationships involving lengths and angles of triangles **

Number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

– branch of pure mathematics devoted primarily to the study of the integers ***

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. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diri ...

– branch of number theory that uses methods from mathematical analysis to solve problems about the integers ***

Algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic o ...

– major branch of number theory which studies algebraic structures related to algebraic integers *** Geometric number theory – studies convex bodies and integer vectors in n-dimensional space **

Logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

and

Foundations of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...

– subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic. ***

Set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

– branch of mathematics that studies sets, which are collections of objects ***

Proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding part ...

– branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques ***

Model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (math ...

– study of (classes of) mathematical structures (e.g. groups, fields, graphs, universes of set theory) using tools from mathematical logic ***

Recursion theory 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 sinc ...

– branch of mathematical logic and computer science that originated in the 1930s with the study of computable functions and Turing degrees ***

Modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend ot ...

– type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality ***

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. In particular, systems ...

– symbolic logic system differing from classical logic in its definition of the meaning of a statement being true **

Applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...

– branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. ***

Mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...

– study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis ****

Probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

– likelihood or chance that something is the case or will happen ****

Econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...

– application of mathematics and statistical methods to economic data **** Actuarial science – discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. ****

Demography Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as ed ...

– statistical study of human populations and sub-populations. ***

Approximation theory In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by ''best'' and ''simpler'' wil ...

– study of how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. ***

Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...

Operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...

– study of the application of advanced analytical methods to help make better decisions ****

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. Linear programming is ...

– mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships ***

Dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a ...

– concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space ****

Chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to hav ...

– study of the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect. ****

Fractal geometry In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...

– mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. ***

Mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

– development of mathematical methods for application to problems in physics ****

Quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

– theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. ****

Statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...

– branch of physics that applies probability theory, which contains mathematical tools for dealing with large populations, to the study of the thermodynamic behavior of systems composed of a large number of particles. ***

Information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

– branch of applied mathematics and electrical engineering involving the quantification of information. ***

Cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adv ...

– study of means of obscuring information, such as codes and ciphers ***

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. It is closely related to many other areas of mathematics and has many a ...

– branch of mathematics concerning the study of finite or countable discrete structures ****

Coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied ...

– study of the properties of codes and their fitness for a specific application ***

Graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

– study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection ***

Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

– study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."

Statistics

Statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...

– collection, analysis, interpretation, and presentation of data. **

Computational statistics Computational statistics, or statistical computing, is the bond between statistics and computer science. It means statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computin ...

– interface between statistics and computer science. *** Data mining – process that results in the discovery of new patterns in large data sets *** Regression – estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are held fixed. ***

Simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

– Simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics or behaviors of the selected physical or abstract system or process. The model represents the system itself, whereas the simulation represents the operation of the system over time. ****

Bootstrap (statistics) Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confiden ...

– method for assigning measures of accuracy to sample estimates (Efron and Tibshirani 1993). **

Design of experiments The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

– design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not ***

Block design In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that frequency of the elements satisfies certain conditions making the collection of bl ...

– set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. ***

Analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician ...

– collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. ***

Response surface methodology In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM ...

– explores the relationships between several explanatory variables and one or more response variables. **

Engineering statistics Engineering statistics combines engineering and statistics using scientific methods for analyzing data. Engineering statistics involves data concerning manufacturing processes such as: component dimensions, tolerances, type of material, and fabri ...

– Engineering statistics combines engineering and statistics **

Spatial statistics Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early devel ...

– any of the formal techniques which study entities using their topological, geometric, or geographic properties. **

Social statistics Social statistics is the use of statistical measurement systems to study human behavior in a social environment. This can be accomplished through polling a group of people, evaluating a subset of data obtained about a group of people, or by obse ...

– use of statistical measurement systems to study human behavior in a social environment **

Statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form ...

ling – formalization of relationships between variables in the form of mathematical equations ***

Biostatistics Biostatistics (also known as biometry) are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experimen ...

– application of statistics to a wide range of topics in biology. ****

Epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evi ...

– study of the distribution and patterns of health-events, health-characteristics and their causes or influences in well-defined populations. ***

Multivariate analysis Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the diff ...

– observation and analysis of more than one statistical variable at a time. ****

Structural equation model Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral scienc ...

– statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions. ****

Time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...

– sequence of data points, measured typically at successive time instants spaced at uniform time intervals. ***

Reliability theory Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ...

– describes the probability of a system completing its expected function during an interval of time. ***

Quality control Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements". This approach place ...

– process by which entities review the quality of all factors involved in production. **

Statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...

– provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. ***

Decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...

– identifies the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. ***

– study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. ****

– likelihood or chance that something is the case or will happen. ** Sample Survey – process of selecting a sample of elements from a target population in order to conduct a survey. ***

Sampling theory In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians atte ...

– study of the collection, organization, analysis, and interpretation of data. ***

Survey methodology Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey da ...

– field that studies the sampling of individuals from a population with a view towards making statistical inferences about the population using the sample.

Systems science

* Systems science – interdisciplinary field of science that studies the nature of complex systems in nature, society, and science. **

– field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology, and philosophy; studies the behavior of dynamical systems that are highly sensitive to initial conditions. **

Complex systems A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication sy ...

and Complexity Theory – studies how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. **

Cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...

– interdisciplinary study of the structure of regulatory systems. ***

Biocybernetics Biocybernetics is the application of cybernetics to biological science disciplines such as neurology and multicellular systems. Biocybernetics plays a major role in systems biology, seeking to integrate different levels of information to understan ...

– application of cybernetics to biological science, composed of biological disciplines that benefit from the application of cybernetics: neurology, multicellular systems and others. ***

Engineering cybernetics Engineering cybernetics also known as technical cybernetics or cybernetic engineering, is the branch of cybernetics concerned with applications in engineering, in fields such as control engineering and robotics. History Qian Xuesen (Hsue-Shen Tsi ...

– field of cybernetics, which deals with the question of control engineering of mechatronic systems as well as chemical or biological systems. ***

Management cybernetics Management cybernetics is concerned with the application of cybernetics to management and organizations. "Management cybernetics" was first introduced by Stafford Beer in the late 1950s and introduces the various mechanisms of self-regulation appli ...

– field of cybernetics concerned with management and organizations. ***

Medical cybernetics Medical cybernetics is a branch of cybernetics which has been heavily affected by the development of the computer, which applies the concepts of cybernetics to medical research and practice. At the intersection of systems biology, systems medicin ...

– branch of cybernetics which has been heavily affected by the development of the computer, which applies the concepts of cybernetics to medical research and practice. ***

New Cybernetics Second-order cybernetics, also known as the cybernetics of cybernetics, is the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to such a critique. It is cybernetics where "the role of the observer ...

– study of self-organizing systems according to Peter Harries-Jones (1988), "looking beyond the issues of the "first", "old" or "original" cybernetics and their politics and sciences of control, to the autonomy and self-organization capabilities of complex systems". ***

Second-order cybernetics Second-order cybernetics, also known as the cybernetics of cybernetics, is the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to such a critique. It is cybernetics where "the role of the observer ...

– investigates the construction of models of cybernetic systems. **

Control theory Control theory is a field of mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive ...

– Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The external input of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. ***

Control engineering Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls o ...

– engineering discipline that applies control theory to design systems with desired behaviors. ***

Control systems A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...

– device, or set of devices to manage, command, direct or regulate the behavior of other devices or system. ***

– concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. **

– study of the use of advanced analytical methods to help make better decisions. **

Systems dynamics System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays. Overview System dynamics is a methodology and mathematical ...

– approach to understanding the behaviour of complex systems over time. ***

Systems analysis Systems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees system analysis as a problem-solving technique that ...

– study of sets of interacting entities, including computer systems analysis. **

Systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

General systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

– interdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research. *** Linear time-invariant systems – investigates the response of a linear and time-invariant system to an arbitrary input signal. *** Mathematical system theory – area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. ***

Systems biology Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic ...

– several related trends in bioscience research, and a movement that draws on those trends. ***

Systems ecology Systems ecology is an interdisciplinary field of ecology, a subset of Earth system science, that takes a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general syst ...

– interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. ***

Systems engineering Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinki ...

– interdisciplinary field of engineering focusing on how complex engineering projects should be designed and managed over their life cycles. ***

Systems neuroscience Systems neuroscience is a subdiscipline of neuroscience and systems biology that studies the structure and function of neural circuits and systems. Systems neuroscience encompasses a number of areas of study concerned with how nerve cells behave ...

– subdiscipline of neuroscience and systems biology that studies the function of neural circuits and systems. ***

Systems psychology Systems psychology is a branch of both theoretical psychology and applied psychology that studies human behaviour and experience as complex systems. It is inspired by systems theory and systems thinking, and based on the theoretical work of Roger ...

– branch of applied psychology that studies human behaviour and experience in complex systems.

Computer science

Computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

(outline) – study of the theoretical foundations of information and computation and their implementation and application in computer systems. ''(See also Branches of Computer Science and AC
Computing Classification System
'' **

Theory of computation In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how algorithmic efficiency, efficiently they can be solved or t ...

– branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm ***

Automata 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. The word ''automata'' comes from the Greek word αὐτόματο� ...

– study of mathematical objects called abstract machines or automata and the computational problems that can be solved using them. ****

Formal languages In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sy ...

– set of strings of symbols. ***

Computability theory 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 sinc ...

– branch of mathematical logic and computer science that originated in the 1930s with the study of computable functions and Turing degrees. ***

Computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved ...

– branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other *** Concurrency theory – In computer science, concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other **

Algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

– step-by-step procedure for calculations ***

Randomized algorithms A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performan ...

– algorithm which employs a degree of randomness as part of its logic. *** Distributed algorithms – algorithm designed to run on computer hardware constructed from interconnected processors *** Parallel algorithms – algorithm which can be executed a piece at a time on many different processing devices, and then put back together again at the end to get the correct result. **

Data structures In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, ...

– particular way of storing and organizing data in a computer so that it can be used efficiently. **

Computer architecture In computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. At a more detailed level, the ...

– In computer science and engineering, computer architecture is the practical art of selecting and interconnecting hardware components to create computers that meet functional, performance and cost goals and the formal modeling of those systems. ***

VLSI design This is a list of academic journal An academic journal or scholarly journal is a periodical publication in which scholarship relating to a particular academic discipline is published. Academic journals serve as permanent and transparent foru ...

– process of creating integrated circuits by combining thousands of transistors into a single chip **

Operating systems An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs. Time-sharing operating systems schedule tasks for efficient use of the system and may also in ...

– set of software that manages computer hardware resources and provides common services for computer programs ** Computer communications (networks) – collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information ***

– branch of applied mathematics and electrical engineering involving the quantification of information ***

Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, p ...

– global system of interconnected computer networks that use the standard Internet protocol suite (often called TCP/IP, although not all applications use TCP) to serve billions of users worldwide. ****

World Wide Web The World Wide Web (WWW), commonly known as the Web, is an information system enabling documents and other web resources to be accessed over the Internet. Documents and downloadable media are made available to the network through web ...

– part of the Internet; system of interlinked hypertext documents accessed via the Internet. *** Wireless computing – any type of computer network that is not connected by cables of any kind. ****

Mobile computing Mobile computing is human–computer interaction in which a computer is expected to be transported during normal usage, which allows for the transmission of data, voice, and video. Mobile computing involves mobile communication, mobile hardware ...

– form of human–computer interaction by which a computer is expected to be transported during normal usage. **

Computer security Computer security, cybersecurity (cyber security), or information technology security (IT security) is the protection of computer systems and networks from attack by malicious actors that may result in unauthorized information disclosure, t ...

– branch of computer technology known as information security as applied to computers and networks. ***

reliability Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (disambiguation), a property of some disk arrays in computer storage * High availability * Reliability (computer networking), a ...

– system design approach and associated service implementation that ensures a prearranged level of operational performance will be met during a contractual measurement period. ***

– practice and study of hiding information. *** Fault-tolerant computing – property that enables a system (often computer-based) to continue operating properly in the event of the failure of (or one or more faults within) some of its components **

Distributed computing A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another from any system. Distributed computing is a field of computer sci ...

– field of computer science that studies distributed systems ***

Grid computing Grid computing is the use of widely distributed computer resources to reach a common goal. A computing grid can be thought of as a distributed system with non-interactive workloads that involve many files. Grid computing is distinguished from ...

– federation of computer resources from multiple administrative domains to reach a common goal **

Parallel computing Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different f ...

– form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently ("in parallel"). ***

High-performance computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems. Overview HPC integrates systems administration (including network and security knowledge) and parallel programming into a mult ...

– computer at the frontline of current processing capacity, particularly speed of calculation **

Quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...

– device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data **

Computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

– graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware. ***

Image processing An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensio ...

– any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or a set of characteristics or parameters related to the image *** Scientific visualization – interdisciplinary branch of science according to Friendly (2008) "primarily concerned with the visualization of three-dimensional phenomena (architectural, meteorological, medical, biological, etc.), where the emphasis is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps with a dynamic (time) component". ***

Computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

– branch of computer science devoted to the study of algorithms which can be stated in terms of geometry **

Software engineering Software engineering is a systematic engineering approach to software development. A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term '' ...

– application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software; that is the application of engineering to software ***

Formal methods In computer science, formal methods are mathematically rigorous techniques for the specification, development, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the exp ...

– particular kind of mathematically based techniques for the specification, development and verification of software and hardware systems ****

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 met ...

– 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 **

Programming language theory 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 clos ...

– study of the design and implementation of

formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sym ...

s known as

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

s which are used to communicate instructions to a machine, particularly a computer ***

Programming paradigms Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, su ...

– fundamental style of computer programming ****

Object-oriented programming Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of ...

– programming paradigm using "objects" – data structures consisting of data fields and methods together with their interactions – to design applications and computer programs ****

Functional programming In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions tha ...

– programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data ***

Program semantics 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. Semantics describes the processes ...

– field concerned with the rigorous mathematical study of the meaning of programming languages ***

Type theory In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a founda ...

– any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general ***

Compilers In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that ...

– computer program (or set of programs) that transforms source code written in a programming language (the source language) into another computer language (the target language, often having a binary form known as object code) ***

Concurrent programming languages Concurrent computing is a form of computing in which several computations are executed '' concurrently''—during overlapping time periods—instead of ''sequentially—''with one completing before the next starts. This is a property of a syst ...

– form of computing in which programs are designed as collections of interacting computational processes that may be executed in parallel **

Information science Information science (also known as information studies) is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. ...

– interdisciplinary field primarily concerned with the analysis, collection, classification, manipulation, storage, retrieval and dissemination of information ***

Database In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases ...

– organized collection of data, today typically in digital form ****

Relational database A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relati ...

– collection of data items organized as a set of formally described tables from which data can be accessed easily ****

Distributed database A distributed database is a database in which data is stored across different physical locations. It may be stored in multiple computers located in the same physical location (e.g. a data centre); or maybe dispersed over a network of interconnect ...

– database in which storage devices are not all attached to a common CPU. ****

Object database An object database or object-oriented database is a database management system in which information is represented in the form of objects as used in object-oriented programming. Object databases are different from relational databases which a ...

– database management system in which information is represented in the form of objects as used in object-oriented programming ***

Multimedia Multimedia is a form of communication that uses a combination of different content forms such as text, audio, images, animations, or video into a single interactive presentation, in contrast to tradit ...

– media and content that uses a combination of different content forms. ***

hypermedia Hypermedia, an extension of the term hypertext, is a nonlinear medium of information that includes graphics, audio, video, plain text and hyperlinks. This designation contrasts with the broader term ''multimedia'', which may include non-interacti ...

– computer-based information retrieval system that enables a user to gain or provide access to texts, audio and video recordings, photographs and computer graphics related to a particular subject. *** Data mining – process that results in the discovery of new patterns in large data sets ***

Information retrieval Information retrieval (IR) in computing and information science is the process of obtaining information system resources that are relevant to an information need from a collection of those resources. Searches can be based on full-text or other c ...

– area of study concerned with searching for documents, for information within documents, and for metadata about documents, as well as that of searching structured storage, relational databases, and the World Wide Web. **

Artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech ...

– branch of computer science that deals with intelligent behavior, learning, and adaptation in machines. ***

Automated reasoning In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer prog ...

– field dedicated to giving machines the ability to imitate the cognitive process of

reasoning Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, langu ...

. ****

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. Automated reasoning over mathematical proof was a ...

- branch of automated reasoning concerned with proving mathematical theorems ***

Computer vision Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the human ...

– field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions. ***

Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

– scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases ****

Artificial neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected unit ...

– mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks ***

Natural language processing Natural language processing (NLP) is an interdisciplinary subfield of linguistics, computer science, and artificial intelligence concerned with the interactions between computers and human language, in particular how to program computers to proc ...

– field of computer science, artificial intelligence (also called machine learning), and linguistics concerned with the interactions between computers and human (natural) languages. ****

Computational linguistics Computational linguistics is an interdisciplinary field concerned with the computational modelling of natural language, as well as the study of appropriate computational approaches to linguistic questions. In general, computational linguistics ...

– interdisciplinary field dealing with the statistical or rule-based modeling of natural language from a computational perspective. ***

Expert systems In artificial intelligence, an expert system is a computer system emulating the decision-making ability of a human expert. Expert systems are designed to solve complex problems by reasoning through bodies of knowledge, represented mainly as if� ...

– computer system that emulates the decision-making ability of a human expert ***

Robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...

– branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots ** Human-computer interaction – study, planning, and design of the interaction between people (users) and computers. ***

– study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). *** Algebraic (symbolic) computation – relates to algorithms and software for manipulating mathematical expressions and equations in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols. Software applications that perform symbolic calculations are called computer algebra systems. ***

Computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

– study of algorithms for performing number theoretic computations ***

Computational mathematics Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation.National Science Foundation, Division of Mathematical ScienceProgram description PD 06-888 Computational Mathematics 2006 ...

– involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods *** Scientific computing (Computational science) – *** Computational biology (bioinformatics) – involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, behavioral, and social systems. ***

Computational science Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disc ...

– subfield of computer science concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems ***

Computational chemistry Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of mo ...

– branch of chemistry that uses principles of computer science to assist in solving chemical problems ***

Computational neuroscience Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to u ...

– study of brain function in terms of the information processing properties of the structures that make up the nervous system. ***

Computer-aided engineering Computer-aided engineering (CAE) is the broad usage of computer software to aid in engineering analysis tasks. It includes , , , durability and optimization. It is included with computer-aided design (CAD) and computer-aided manufacturing (CAM) ...

– broad usage of computer software to aid in engineering tasks. ****

Finite element analysis The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

– numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations. ****

Computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate ...

– branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. ***

Computational economics Computational Economics is an interdisciplinary research discipline that involves computer science, economics, and management science.''Computational Economics''."About This Journal"an"Aims and Scope" This subject encompasses computational model ...

– research discipline at the interface between computer science and economic and management science ***

Computational sociology Computational sociology is a branch of sociology that uses computationally intensive methods to analyze and model social phenomena. Using computer simulations, artificial intelligence, complex statistical methods, and analytic approaches like soc ...

– branch of sociology that uses computationally intensive methods to analyze and model social phenomena. ***

Computational finance Computational finance is a branch of applied computer science that deals with problems of practical interest in finance.Rüdiger U. Seydel, '' tp://nozdr.ru/biblio/kolxo3/F/FN/Seydel%20R.U.%20Tools%20for%20Computational%20Finance%20(4ed.,%20Sprin ...

– cross-disciplinary field which relies on computational intelligence, mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions *** Humanities computing (Digital Humanities) – area of research, teaching, and creation concerned with the intersection of computing and the disciplines of the humanities **

Information systems An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, store, and distribute information. From a sociotechnical perspective, information systems are composed by four components: task, people ...

– study of complementary networks of hardware and software that people and organizations use to collect, filter, process, create, and distribute data *** Business informatics – discipline combining information technology (IT), informatics and management concepts. ***

Information technology Information technology (IT) is the use of computers to create, process, store, retrieve, and exchange all kinds of data . and information. IT forms part of information and communications technology (ICT). An information technology syste ...

– ***

Management information systems A management information system (MIS) is an information system used for decision-making, and for the coordination, control, analysis, and visualization of information in an organization. The study of the management information systems involves pe ...

– provides information that is needed to manage organizations efficiently and effectively ***

Health informatics Health informatics is the field of science and engineering that aims at developing methods and technologies for the acquisition, processing, and study of patient data, which can come from different sources and modalities, such as electronic hea ...

– discipline at the intersection of information science, computer science, and health care.

External links

2010 Mathematics Subject Classification
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