Lists of mathematics topics
527369
222795636
2008-07-01T04:04:44Z
Oleg Alexandrov
153314
Reverted edits by [[Special:Contributions/71.233.212.161|71.233.212.161]] ([[User talk:71.233.212.161|talk]]) to last version by Lambiam
<onlyinclude><!-- See [[Wikipedia talk:Featured lists#Proposed change to all featured lists]] for an explanation of this and other inclusion tags below -->
This article itemizes the various '''lists''' of '''[[mathematics]] topics'''. Some of these lists link to hundreds of articles; some link only to a few. The extremely long [[list of mathematics articles]] contains all mathematical articles in alphabetical order. This article brings together the same content organised in a manner better suited to browsing.</onlyinclude>
The purpose of this list is ''not'' similar to that of the [[Mathematics Subject Classification]] formulated by the [[American Mathematical Society]]. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, ''[[Mathematical Reviews]]'' and ''[[Zentralblatt MATH]]''. This list has some items that would not fit in such a classification, such as [[list of exponential topics]] and [[list of factorial and binomial topics]], which may surprise the reader with the diversity of their coverage.
==Fields of mathematics==
<onlyinclude>
===Basic mathematics===
These lists cover topics typically taught in secondary education or in the first year of university.
*[[List of basic discrete mathematics topics]] [[Talk:List of basic discrete mathematics topics| ]]
*[[List of calculus topics]] [[Talk:List of calculus topics| ]]
*[[List of geometry topics]] [[Talk:List of geometry topics| ]]
*[[List of topics in logic]] [[Talk:List of topics in logic| ]]
*[[List of trigonometry topics]] [[Talk:List of trigonometry topics| ]]
**[[List of basic trigonometry topics]] [[Talk:List of basic trigonometry topics| ]]
*[[List of trigonometric identities]] [[Talk:List of trigonometric identities| ]]</onlyinclude>
===Advanced mathematics===
====Algebra====
[[Algebra]] includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called ''group''.
*[[List of abstract algebra topics]] [[Talk:List of abstract algebra topics| ]]
*[[List of algebraic structures]]
*[[List of Boolean algebra topics]] [[Talk:List of Boolean algebra topics| ]]
*[[List of category theory topics]] [[Talk:List of category theory topics| ]]
*[[List of commutative algebra topics]] [[Talk:List of commutative algebra topics| ]]
*[[List of homological algebra topics]] [[Talk:List of homological algebra topics| ]]
*[[List of group theory topics]] [[Talk:List of group theory topics| ]]
*[[List of linear algebra topics]] [[Talk:List of linear algebra topics| ]]
*[[Glossary of field theory]] [[Talk:Glossary of field theory| ]]
*[[Glossary of group theory]] [[Talk:Glossary of group theory| ]]
*[[Glossary of linear algebra]] [[Talk:Glossary of linear algebra| ]]
*[[Glossary of ring theory]] [[Talk:Glossary of ring theory| ]]
*[[List of cohomology theories]] [[Talk:List of cohomology theories| ]]
====Calculus and analysis====
[[Image:Gibbs phenomenon 10.png|thumb|200px|right|[[Fourier series]] approximation of square wave in five steps.]]
[[Calculus]] studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. [[Mathematical analysis|Analysis]] studies the same subjects, but on a more rigorous level, and also topics that evolved from calculus.
*[[List of complex analysis topics]] [[Talk:List of complex analysis topics| ]]
*[[List of functional analysis topics]] [[Talk:List of functional analysis topics| ]]
**[[List of vector spaces in mathematics]] [[Talk:List of vector spaces in mathematics| ]]
*[[List of integration and measure theory topics]] [[Talk:List of integration and measure theory topics| ]]
*[[List of harmonic analysis and representation theory topics]] [[Talk:List of harmonic analysis and representation theory topics| ]]
**[[List of Fourier analysis topics]] [[Talk:List of Fourier analysis topics| ]]
*[[List of multivariable calculus topics]] [[Talk:List of multivariable calculus topics| ]]
*[[List of nonlinear partial differential equations]] [[Talk:List of nonlinear partial differential equations| ]]
*[[List of real analysis topics]] [[Talk:List of real analysis topics| ]]
*[[List of variational topics]] [[Talk:List of variational topics| ]]
*[[Glossary of tensor theory]] [[Talk:Glossary of tensor theory| ]]
====Geometry and topology====
[[Image:Ford circles.png|200px|right|thumb|[[Ford circle]]s — A circle rests upon each fraction in lowest terms. Each touches its neighbors without crossing.]]
[[Geometry]] is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. [[Topology]] developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
*[[List of geometry topics]] [[Talk:List of geometry topics| ]]
*[[List of geometric shapes]] [[Talk:List of geometric shapes| ]]
*[[List of curve topics]] [[Talk:List of curve topics| ]]
*[[List of triangle topics]] [[Talk:List of triangle topics| ]]
*[[List of circle topics]] [[Talk:List of circle topics| ]]
**[[List of topics related to π]] [[Talk:List of topics related to π| ]]
*[[List of general topology topics]] [[Talk:List of general topology topics| ]]
*[[List of differential geometry topics]] [[Talk:List of differential geometry topics| ]]
*[[List of algebraic geometry topics]] [[Talk:List of algebraic geometry topics| ]]
**[[List of algebraic surfaces]] [[Talk:List of algebraic surfaces| ]]
*[[List of algebraic topology topics]] [[Talk:List of algebraic topology topics| ]]
**[[List of cohomology theories]] [[Talk:List of cohomology theories| ]]
*[[List of geometric topology topics]] [[Talk:List of geometric topology topics| ]]
*[[List of knot theory topics]] [[Talk:List of knot theory topics| ]]
*[[List of Lie group topics]] [[Talk:List of Lie group topics| ]]
*[[Glossary of differential geometry and topology]] [[Talk:Glossary of differential geometry and topology| ]]
*[[Glossary of general topology]] [[Talk:Glossary of general topology| ]]
*[[Glossary of Riemannian and metric geometry]] [[Talk:Glossary of Riemannian and metric geometry| ]]
*[[Glossary of scheme theory]] [[Talk:Glossary of scheme theory| ]]
====Discrete mathematics====
[[Discrete mathematics]] concerns itself with the study of finite sets. This is in contrast with analysis and geometry, which study continua: between every two distinct points, however close together, one can always find another point.
*[[List of combinatorics topics]] [[Talk:List of combinatorics topics| ]]
*[[List of graph theory topics]] [[Talk:List of graph theory topics| ]]
*[[Glossary of graph theory]] [[Talk:Glossary of graph theory| ]]
====Logic====
[[Image:Venn A intersect B.svg|thumb|200px|right|[[Venn diagram]]s are illustrations of set theoretical, mathematical or logical relationships.]]
[[Logic]] is the foundation which underlies [[mathematical logic]] and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.
*[[List of Boolean algebra topics]] [[Talk:List of Boolean algebra topics| ]]
*[[List of computability and complexity topics]] [[Talk:List of computability and complexity topics| ]]
*[[List of first-order theories]]
*[[List of large cardinal properties]][[Talk:List of large cardinal properties| ]]
*[[List of mathematical logic topics]] [[Talk:List of mathematical logic topics| ]]
*[[Glossary of order theory]] [[Talk:Glossary of order theory| ]]
*[[List of set theory topics]] [[Talk:List of set theory topics| ]]
====Number theory====
[[Number theory]] studies the natural, or whole, numbers. One of the central concepts in number theory is that of the [[prime number]], and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.
*[[List of algebraic number theory topics]][[Talk:List of algebraic number theory topics| ]]
*[[List of number theory topics]] [[Talk:List of number theory topics| ]]
*[[List of recreational number theory topics]][[Talk:List of recreational number theory topics| ]]
*[[Glossary of arithmetic and Diophantine geometry]][[Talk:Glossary of arithmetic and Diophantine geometry| ]]
*[[List of prime numbers]]—not just a table, but a list of various different ''kinds'' of prime numbers (each with an accompanying table)
===Applied mathematics===
====Computing====
[[Image:Raytraced image jawray.jpg|thumb|200px|right|[[Ray tracing]] is a process based on computational mathematics.]]
The fields of mathematics and computing intersect both in [[computer science]], the study of algorithms and data structures, and in [[scientific computing]], the study of algorithmic methods for solving problems in mathematics, science and engineering.
*[[List of algorithm general topics]] [[Talk:List of algorithm general topics| ]]
*Lists for computational topics in geometry and graphics
**[[List of combinatorial computational geometry topics]] [[Talk:List of combinatorial computational geometry topics| ]]
**[[List of computer graphics and descriptive geometry topics]] [[Talk:List of computer graphics and descriptive geometry topics| ]]
**[[List of numerical computational geometry topics]] [[Talk:List of numerical computational geometry topics| ]]
*[[List of computer vision topics]]
*[[List of formal language and literal string topics]] [[Talk:List of formal language and literal string topics| ]]
*[[List of network theory topics]] [[Talk:List of network theory topics| ]]
*[[List of numerical analysis topics]] [[Talk:List of numerical analysis topics| ]]
*[[List of terms relating to algorithms and data structures]] [[Talk:List of terms relating to algorithms and data structures| ]]
====Dynamical systems====
[[Image:Limitcycle.jpg|right|200px|thumb|Phase portrait of a continuous-time dynamical system, the [[Van der Pol oscillator]].]]
In a [[dynamical system]], a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
*[[List of dynamical systems and differential equations topics]] [[Talk:List of dynamical systems and differential equation topics| ]]
*[[List of partial differential equation topics]] [[Talk:List of partial differential equation topics| ]]
====Game theory====
[[Game theory]] is a branch of [[mathematics]] that uses [[model (abstract)|models]] to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including [[economics]], [[evolutionary biology]], [[political science]], [[social psychology]] and [[military strategy]].
*[[:Category:Game theory]]
*[[Glossary of game theory]]
====Information theory and Signal processing====
[[Information theory]] is a branch of [[applied mathematics]] and [[electrical engineering]] involving the quantification of [[information]]. Historically, information theory was developed to find fundamental limits on compressing and reliably [[communication|communicating]] data.
[[Signal processing]] is the analysis, interpretation, and manipulation of [[signal (electrical engineering)|signal]]s. Signals of interest include [[audio signal processing|sound]], [[image processing|images]], biological signals such as [[ECG]], [[radar]] signals, and many others. Processing of such signals includes [[electronic filter|filtering]], storage and reconstruction, separation of information from [[noise]], [[data compression|compression]], and [[feature extraction]].
*[[List of information theory topics]]
*[[:Category:Signal processing]]
*[[:Category:Coding theory]]
*[[List of algebraic coding theory topics]] [[Talk:List of algebraic coding theory topics| ]]
*[[:Category:Cryptography]]
*[[Wikipedia:WikiProject Cryptography/List of cryptography topics|List of cryptography topics]] [[Wikipedia talk:WikiProject Cryptography/List of cryptography topics| ]]
*[[:Category:Data compression]]
*[[:Category:Detection theory]]
====Mathematical physics====
[[Mathematical physics]] is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"<sup id="fn_1_back">[[#fn 1|1]]</sup>.
*[[List of mathematical topics in classical mechanics]] [[Talk:List of mathematical topics in classical mechanics| ]]
*[[List of mathematical topics in quantum theory]] [[Talk:List of mathematical topics in quantum theory| ]]
*[[List of mathematical topics in relativity]] [[Talk:List of mathematical topics in relativity| ]]
*[[List of string theory topics]] [[Talk:List of string theory topics| ]]
*[[List of wave topics]] [[Talk:List of wave topics| ]]
====Probability and statistics====
[[Image:Normal approximation to binomial.png|200px|right|thumb|The "bell curve" — the probability density function of the [[normal distribution]].]]
[[Probability theory]] is the formalization and study of the mathematics of uncertain events or knowledge. The related field of [[statistics]] concerns the mathematics and science of collecting and analyzing data.
*[[List of probability distributions]] [[Talk:List of probability distributions| ]]
*[[List of probability topics]] [[Talk:List of probability topics| ]]
*[[List of statistical topics]] [[Talk:List of statistical topics| ]]
*[[List of stochastic processes topics]] [[Talk:List of stochastic processes topics| ]]
====Operations research====
[[Operations research]] is the study and use of mathematical models, statistics and algorithms to aid in decision-making, typically with the goal of improving or optimizing performance of real-world systems.
==Methodology==
*[[List of graphical methods]] [[Talk:List of graphical methods| ]]
*[[List of mathematics-based methods]] [[Talk:List of mathematics-based methods| ]]
*[[List of rules of inference]] [[Talk:List of rules of inference| ]]
==Mathematical statements==
A mathematical statement amounts to a [[proposition]] or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.
*[[List of algorithms]] [[Talk:List of algorithms| ]]
*[[List of axioms]] [[Talk:List of axioms| ]]
*[[List of conjectures]] [[Talk:List of conjectures| ]]
**[[Erdős conjecture]] [[Talk:Erdős conjecture| ]]— a list of conjectures by [[Paul Erdős]]
*[[Combinatorial principles]] [[Talk:Combinatorial principles| ]]
*[[List of equations]] [[Talk:List of equations| ]]
*[[List of formulae involving π]] [[Talk:List of formulae involving π| ]]
*[[List of fundamental theorems]] [[Talk:List of fundamental theorems| ]]
*[[List of mathematical identities]] [[Talk:List of mathematical identities| ]]
*[[List of inequalities]] [[Talk:List of inequalities| ]]
*[[List of lemmas]] [[Talk:List of lemmas| ]]
*[[List of mathematical proofs]] [[Talk:List of mathematical proofs| ]]
*[[List of NP-complete problems]] [[Talk:List of NP-complete problems| ]]
*[[List of statements undecidable in ZFC]] [[Talk:List of statements undecidable in ZFC| ]]
*[[List of undecidable problems]] [[Talk:List of undecidable problems| ]]
*[[List of theorems]] [[Talk:List of theorems| ]]
==General concepts==
*[[List of convexity topics]] [[Talk:List of convexity topics| ]]
*[[List of exceptional set concepts]] [[Talk:List of exceptional set concepts| ]]
*[[List of exponential topics]] [[Talk:List of exponential topics| ]]
*[[List of factorial and binomial topics]] [[Talk:List of factorial and binomial topics| ]]
*[[List of fractal topics]] [[Talk:List of fractal topics| ]]
*[[List of logarithmic topics]] [[Talk:List of logarithmic topics| ]]
*[[List of numeral system topics]] [[Talk:List of numeral system topics| ]]
*[[List of order topics]] [[Talk:List of order topics| ]]
*[[List of partition topics]] [[Talk:List of partition topics| ]]
*[[List of polynomial topics]] [[Talk:List of polynomial topics| ]]
*[[List of properties of sets of reals]][[Talk:List of properties of sets of reals| ]]
*[[List of transforms]] [[Talk:List of transforms| ]]
*[[List of permutation topics]] [[Talk:List of permutation topics| ]]
==Mathematical objects==
Among mathematical objects are numbers, functions, sets, a great variety of things called "spaces" of one kind or another, algebraic structures such as rings, groups, or fields, and many other things.
*[[List of mathematical examples]] [[Talk:List of mathematical examples| ]]
*[[List of curves]] [[Talk:List of curves| ]]
*[[List of complex reflection groups]]
*[[List of complexity classes]] [[Talk:List of complexity classes| ]]
*[[List of examples in general topology]]
*[[List of finite simple groups]] [[Talk:List of finite simple groups| ]]
*[[List of Fourier-related transforms]] [[Talk:List of Fourier-related transforms| ]]
*[[List of mathematical functions]] [[Talk:List of mathematical functions| ]]
*[[List of mathematical knots and links]] [[Talk:List of mathematical knots and links| ]]
*[[List of manifolds]] [[Talk:List of manifolds| ]]
*[[List of mathematical shapes]] [[Talk:List of mathematical shapes| ]]
*[[List of matrices]] [[Talk:List of matrices| ]]
*[[List of numbers]] [[Talk:List of numbers| ]]
*[[List of polygons, polyhedra and polytopes]] [[Talk:List of polygons, polyhedra and polytopes| ]]
*[[List of regular polytopes]] [[Talk:List of regular polytopes| ]]
*[[List of simple Lie groups]]
*[[List of small groups]] [[Talk:List of small groups| ]]
*[[List of special functions and eponyms]] [[Talk:List of special functions and eponyms| ]]
*[[List of algebraic surfaces]] [[Talk:List of algebraic surfaces| ]]
*[[List of surfaces]] [[Talk:List of surfaces| ]]
*[[Table of Lie groups]] [[Talk:Table of Lie groups| ]]
== Equations named after people ==
*[[Scientific equations named after people]] [[Talk:Scientific equations named after people| ]]
==About mathematics==
*[[List of mathematical societies]][[Talk:List of mathematical societies| ]]
*[[List of letters used in mathematics and science]] [[Talk:List of letters used in mathematics and science| ]]
*[[List of mathematics competitions]] [[Talk:List of mathematics competitions| ]]
*[[List of mathematics history topics]] [[Talk:List of mathematics history topics| ]]
*[[List of publications in mathematics]] [[Talk:List of publications in mathematics| ]]
===Mathematicians===
[[Mathematician]]s study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical [[computer science]] and [[theoretical physics]]).
*[[List of geometers]] [[Talk:List of geometers| ]]
*[[List of logicians]] [[Talk:List of logicians| ]]
*[[List of mathematicians]] [[Talk:List of mathematicians| ]]
*[[List of probabilists]] [[Talk:List of probabilists| ]]
*[[List of statisticians]] [[Talk:List of statisticians| ]]
=== Work of particular mathematicians ===
*[[List of things named after Paul Erdős]] [[Talk:List of things named after Paul Erdős| ]]
*[[List of topics named after Leonhard Euler]] [[Talk:List of topics named after Leonhard Euler| ]]
*[[List of topics named after Carl Friedrich Gauss]] [[Talk:List of topics named after Carl Friedrich Gauss| ]]
*[[List of topics named after Srinivasa Ramanujan]] [[Talk:List of topics named after Srinivasa Ramanujan| ]]
==Reference tables==
*[[List of mathematical reference tables]] [[Talk:List of mathematical reference tables| ]]
*[[List of moments of inertia]] [[Talk:List of moments of inertia| ]]
*[[Table of derivatives]] [[Talk:Table of derivatives| ]]
===Integrals===
In calculus, the [[integral]] of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions.
*[[List of integrals]] [[Talk:List of integrals| ]]
*[[List of integrals of arc hyperbolic functions]] [[Talk:List of integrals of arc hyperbolic functions| ]]
*[[List of integrals of exponential functions]] [[Talk:List of integrals of exponential functions| ]]
*[[List of integrals of hyperbolic functions]] [[Talk:List of integrals of hyperbolic functions| ]]
*[[List of integrals of inverse trigonometric functions]] [[Talk:List of integrals of inverse trigonometric functions| ]]
*[[List of integrals of irrational functions]] [[Talk:List of integrals of irrational functions| ]]
*[[List of integrals of logarithmic functions]] [[Talk:List of integrals of logarithmic functions| ]]
*[[List of integrals of rational functions]] [[Talk:List of integrals of rational functions| ]]
*[[List of integrals of trigonometric functions]] [[Talk:List of integrals of trigonometric functions| ]]
==Meta-lists==
*[[List of mathematical theories]] [[Talk:List of mathematical theories| ]]
*[[List of mathematics articles]] [[Talk:List of mathematics articles| ]]
*[[List of mathematics categories]] [[Talk:List of mathematics categories| ]]
==External links and references==
*[http://www.ams.org/msc 2000 Mathematics Subject Classification] from the [[American Mathematical Society]]. Many research journals in mathematics ask authors to classify their papers according to this scheme; the classifications appear in the published work.
*[http://www.math-atlas.org The Mathematical Atlas]
== Notes ==
*{{fnb|1}} Definition from the ''Journal of Mathematical Physics'' [http://jmp.aip.org/jmp/staff.jsp].
[[Category:Mathematics-related lists| ]]
[[Category:Lists of lists|Mathematics]]
[[it:Indici per la matematica]]