Mathematics Subject Classification
Encyclopedia
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme
collaboratively produced by staff of and based on the coverage of the two major mathematical reviewing databases, Mathematical Reviews
and Zentralblatt MATH
. It is used by many mathematics journals
, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The current version is MSC2010.
The first level is represented by a two digit number, the second by a letter, and the third by another two digit number. For example:
and Biography
", "Mathematics Education
", and for the overlap with different sciences. Physics
(i.e. mathematical physics) is particularly well represented in the classification scheme with a number of different categories including:
All valid MSC classification codes must have at least the first level identifier.
For example, for Differential Geometry the top level code is 53, and the second level codes are:
In addition the special second level code "-" is used for specific kinds of materials. These codes are of the form:
The second and third level of these codes are always the same - only the first level changes. It is not valid to put 53- as a classification, either 53 on its own, or better yet a more specific code should be used.
The third level code 99 exists in every category and means none of the above, but in this section
MSC Primary 03C90; Secondary 03-02;
is often used. Due to the large overlap between Mathematics and Physics research is it quite common to see both PACS and MSC codes on research papers, particularly for multidisciplinary journals and repositories such as the arXiv
.
The ACM Computing Classification System
is a similar hierarchical classification scheme for Computer Science
. There is some overlap between the AMS and ACM classification schemes, in subjects related to both mathematics and computer science, however the two schemes differ in the details of their organization of those topics.
The classification scheme used on the arXiv is chosen to reflect the papers submitted. As arXiv is multidisciplinary its classification scheme does not fit entirely with the MSC, ACM or PACS classification schemes. It is common to see codes from one or more of these schemes on individual papers.
Applied mathematics
Classification scheme
In metadata a classification scheme is a hierarchical arrangement of kinds of things or groups of kinds of things. Typically it is accompanied by descriptive information of the classes or groups. A classification scheme is intended to be used for an arrangement or division of individual objects...
collaboratively produced by staff of and based on the coverage of the two major mathematical reviewing databases, Mathematical Reviews
Mathematical Reviews
Mathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
and Zentralblatt MATH
Zentralblatt MATH
Zentralblatt MATH is a service providing reviews and abstracts for articles in pure and applied mathematics, published by Springer Science+Business Media. It is a major international reviewing service which covers the entire field of mathematics...
. It is used by many mathematics journals
Academic journal
An academic journal is a peer-reviewed periodical in which scholarship relating to a particular academic discipline is published. Academic journals serve as forums for the introduction and presentation for scrutiny of new research, and the critique of existing research...
, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The current version is MSC2010.
Structure
The MSC is a hierarchical scheme, with three levels of structure. A classification can be two, three or five digits long, depending on how many levels of the classification scheme are used.The first level is represented by a two digit number, the second by a letter, and the third by another two digit number. For example:
- 53 is the classification for Differential Geometry
- 53A is the classification for Classical Differential Geometry
- 53A45 is the classification for Vector and TensorTensorTensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
Analysis
First level
At the top level 64 mathematical disciplines are labeled with a unique 2 digit number. As well as the typical areas of mathematical research, there are top level categories for "HistoryHistory
History is the discovery, collection, organization, and presentation of information about past events. History can also mean the period of time after writing was invented. Scholars who write about history are called historians...
and Biography
Biography
A biography is a detailed description or account of someone's life. More than a list of basic facts , biography also portrays the subject's experience of those events...
", "Mathematics Education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
", and for the overlap with different sciences. Physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
(i.e. mathematical physics) is particularly well represented in the classification scheme with a number of different categories including:
- Fluid MechanicsFluid mechanicsFluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
- Quantum mechanicsQuantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
- GeophysicsGeophysicsGeophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
- OpticsOpticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
and electromagnetic theory
All valid MSC classification codes must have at least the first level identifier.
Second level
The second level codes are a single letter from the Latin alphabet. These represent specific areas covered by the first level discipline. The second level codes vary from discipline to discipline.For example, for Differential Geometry the top level code is 53, and the second level codes are:
- A for Classical Differential Geometry
- B for Local Differential Geometry
- C for Global Differential Geometry
- D for Sympletic Geometry and Contact Geometry
In addition the special second level code "-" is used for specific kinds of materials. These codes are of the form:
- 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 53-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 53-02 Research exposition (monographs, survey articles)
- 53-03 Historical (must also be assigned at least one classification number from Section 01)
- 53-04 Explicit machine computation and programs (not the theory of computation or programming)
- 53-06 Proceedings, conferences, collections, etc.
The second and third level of these codes are always the same - only the first level changes. It is not valid to put 53- as a classification, either 53 on its own, or better yet a more specific code should be used.
Third level
Third level codes are the most specific, usually corresponding to a specific kind of mathematical object or a well known problem or research area.The third level code 99 exists in every category and means none of the above, but in this section
Using the scheme
The AMS recommends that papers submitted to its journals for publication have one primary classification and one or more optional secondary classifications. A typical MSC subject class line on a research paper looks likeMSC Primary 03C90; Secondary 03-02;
Relation to other classification schemes
For physics papers the Physics and Astronomy Classification SchemePhysics and Astronomy Classification Scheme
PACS is acronym for Physics and Astronomy Classification Scheme.PACS numbers, developed by the American Institute of Physics, have been used in Physical Review since 1975 to identify fields and sub-fields of physics.- External links :...
is often used. Due to the large overlap between Mathematics and Physics research is it quite common to see both PACS and MSC codes on research papers, particularly for multidisciplinary journals and repositories such as the arXiv
ArXiv
The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...
.
The ACM Computing Classification System
ACM Computing Classification System
The ACM Computing Classification System is a subject classification system for computer science devised by the Association for Computing Machinery...
is a similar hierarchical classification scheme for Computer Science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
. There is some overlap between the AMS and ACM classification schemes, in subjects related to both mathematics and computer science, however the two schemes differ in the details of their organization of those topics.
The classification scheme used on the arXiv is chosen to reflect the papers submitted. As arXiv is multidisciplinary its classification scheme does not fit entirely with the MSC, ACM or PACS classification schemes. It is common to see codes from one or more of these schemes on individual papers.
General / foundations
- 00: General (Includes topics such as recreational mathematicsRecreational mathematicsRecreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
, philosophy of mathematicsPhilosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
and Mathematical modelMathematical modelA mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
ing.) - 01: HistoryHistory of mathematicsThe area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
and biography - 03: Mathematical logicMathematical logicMathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and foundationsFoundations of mathematicsFoundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
, including model theoryModel theoryIn mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, computability theoryComputability theoryComputability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
, set theorySet theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, proof theoryProof theoryProof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
, and algebraic logicAlgebraic logicIn mathematical logic, algebraic logic is the study of logic presented in an algebraic style.What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics and connected problems...
Discrete mathematics / algebra
- 05: CombinatoricsCombinatoricsCombinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
- 06: Order theoryOrder theoryOrder theory is a branch of mathematics which investigates our 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 introduces the field and gives some basic definitions...
- 08: General algebraic systems
- 11: Number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
- 12: Field theoryField theory (mathematics)Field theory is a branch of mathematics which studies the properties of fields. A field is a mathematical entity for which addition, subtraction, multiplication and division are well-defined....
and polynomialPolynomialIn mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s - 13: Commutative ringCommutative ringIn ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra....
s and algebrasCommutative algebraCommutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra... - 14: Algebraic geometryAlgebraic geometryAlgebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
- 15: LinearLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
and multilinear algebraMultilinear algebraIn mathematics, multilinear algebra 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-vectors and multivectors with Grassmann algebra.-Origin:In a vector space...
; matrix theory - 16: Associative rings and associative algebraAssociative algebraIn mathematics, an associative algebra A is an 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...
s - 17: Non-associative rings and non-associative algebraNon-associative algebraA non-associative algebra over a field K is a K-vector space A equipped with a K-bilinear map A × A → A. There are left and right multiplication maps...
s - 18: Category theoryCategory theoryCategory theory is an 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 , where these collections satisfy certain basic conditions...
; homological algebraHomological algebraHomological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and... - 19: K-theoryK-theoryIn mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
- 20: Group theoryGroup theoryIn mathematics and 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 as groups endowed with additional operations and...
and generalizations - 22: Topological groupTopological groupIn mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a...
s, Lie groupLie groupIn mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s, and analysis upon them
Analysis
- 26: Real functions, including derivativeDerivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s and integralIntegralIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
s - 28: MeasureMeasure (mathematics)In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...
and integrationIntegralIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus... - 30: Complex functions, including approximation theoryApproximation theoryIn mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
in the complex domainComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part... - 31: Potential theoryPotential theoryIn mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
- 32: Several complex variablesSeveral complex variablesThe theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...
and analytic spaceAnalytic spaceAn analytic space in the theory of functions of several complex variables is a generalization of the concept of an analytic manifold: heuristically, an analytic space is a set which is locally isomorphic to an analytic variety, while an analytic manifold is locally isomorphic to a complex euclidean...
s - 33: Special functionsSpecial functionsSpecial functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
- 34: Ordinary differential equationOrdinary differential equationIn mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s - 35: Partial differential equationPartial differential equationIn mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s - 37: Dynamical systemDynamical systemA dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s and Ergodic theoryErgodic theoryErgodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics.... - 39: Difference equations and functional equationFunctional equationIn mathematics, a functional equation is any equation that specifies a function in implicit form.Often, the equation relates the value of a function at some point with its values at other points. For instance, properties of functions can be determined by considering the types of functional...
s - 40: SequenceSequenceIn mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...
s, seriesSeries (mathematics)A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
, summability - 41: ApproximationsApproximation theoryIn mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
and expansions - 42: Harmonic analysisHarmonic analysisHarmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
, including Fourier analysis, Fourier transformFourier transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
s, trigonometric approximation, trigonometric interpolationTrigonometric interpolationIn mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and...
, and orthogonal functions - 43: Abstract harmonic analysisHarmonic analysisHarmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
- 44: Integral transforms, operational calculusOperational calculusOperational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.-History:...
- 45: Integral equationIntegral equationIn mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
s - 46: Functional analysisFunctional analysisFunctional 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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, including infinite-dimensional holomorphyInfinite-dimensional holomorphyIn mathematics, infinite-dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces , typically of infinite dimension...
, integral transforms in distribution spaces - 47: Operator theoryOperator theoryIn mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators.Operator theory also includes the study of algebras of operators....
- 49: Calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
and optimal controlOptimal controlOptimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
; optimizationOptimization (mathematics)In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
(including geometric integration theory)
Geometry and topology
- 51: GeometryGeometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
- 52: Convex geometryConvex geometryConvex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
and discrete geometryDiscrete geometryDiscrete 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 geometric objects, such as points, lines, planes, circles,... - 53: Differential geometry
- 54: General topologyGeneral topologyIn mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
- 55: Algebraic topologyAlgebraic topologyAlgebraic topology is a branch of mathematics which 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 up to homotopy equivalence.Although algebraic topology...
- 57: ManifoldManifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s - 58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphyInfinite-dimensional holomorphyIn mathematics, infinite-dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces , typically of infinite dimension...
)
Applied mathematicsApplied mathematicsApplied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
/ other
- 60 Probability theoryProbability theoryProbability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and stochastic processStochastic processIn probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es - 62 StatisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
- 65 Numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
- 68 Computer scienceComputer scienceComputer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
- 70 MechanicsMechanicsMechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
(including particle mechanics) - 74 Mechanics of deformable solids
- 76 Fluid mechanicsFluid mechanicsFluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
- 78 OpticsOpticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, electromagnetic theory - 80 Classical thermodynamicsThermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, heat transferHeat transferHeat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer... - 81 Quantum theoryQuantum theoryQuantum theory may mean:In science:*Quantum mechanics: a subset of quantum physics explaining the physical behaviours at atomic and sub-atomic levels*Old quantum theory under the Bohr model...
- 82 Statistical mechanicsStatistical mechanicsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, structure of matter - 83 RelativityTheory of relativityThe theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
and gravitational theory, including relativistic mechanicsRelativistic MechanicsRelativistic mechanics refers to any form of mechanics compatible with either theories of Special Relativity and General Relativity. It is a non-quantum mechanics of a system of particles or of a fluid in cases where some of the velocities are comparable to the speed of light.Special relativity... - 85 AstronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
and astrophysicsAstrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior... - 86 GeophysicsGeophysicsGeophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
- 90 Operations researchOperations researchOperations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
, mathematical programmingMathematical ProgrammingMathematical Programming, established in 1971, and published by Springer Science+Business Media, is the official scientific journal of the Mathematical Optimization Society. It currently consists of two series: A and B. The "A" series contains general publications. The "B" series focuses on topical... - 91 Game theoryGame theoryGame theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, economicsMathematical economicsMathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...
, socialMathematical sociologyMathematical sociology is the usage of mathematics to construct social theories. Mathematical sociology aims to take sociological theory, which is strong in intuitive content but weak from a formal point of view, and to express it in formal terms...
and behavioral sciencesMathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior... - 92 BiologyBiologyBiology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
and other natural scienceNatural scienceThe natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...
s - 93 Systems theorySystems theorySystems theory is the transdisciplinary 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...
; control, including optimal controlOptimal controlOptimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal... - 94 InformationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
and communicationCommunicationCommunication is the activity of conveying meaningful information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender's intent to communicate at the time of communication; thus communication can occur across vast...
, circuitsElectrical networkAn electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current... - 97 Mathematics educationMathematics educationIn contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
External links
- Mathematics Subject Classification 2010 The site where the MSC 2010 revision was carried out publicly in an MSCwiki. A view of the whole scheme and the changes made from MSC2000, as well as PDF files of the MSC and ancillary documents are there. A personal copy of the MSC in TiddlyWikiTiddlyWikiTiddlyWiki is an open source single page application wiki. A single HTML file contains CSS, JavaScript, and the content. The content is divided into a series of sections, or Tiddlers. A user is encouraged to read a TiddlyWiki by following links rather than sequentially scrolling down the...
form can be had also. - The American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
page on the Mathematics Subject Classification. - Description of the MSC by Dave Rusin.