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{{MathTopicTOC}}
The following [[Outline (list)|outline]] is provided as an overview of and topical guide to mathematics:

'''[[Mathematics]]''' is a field of study that investigates topics such as number, space, structure, and change. For more on the relationship between [[mathematics]] and [[science]], refer to the article on [[science#Mathematics|science]].

{{TOC limit|limit=2}}

==Nature of mathematics==
*[[Definitions of mathematics]] – Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions, all of which are controversial.
*[[Philosophy of mathematics]] – its aim is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives.

===Mathematics is===
*an [[academic discipline]] – branch of knowledge that is taught at all levels of education and researched typically at the college or university level. Disciplines are defined (in part), and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to which their practitioners belong.
*a [[formal science]] – branch of knowledge concerned with the properties of formal systems based on definitions and rules of inference. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the physical world.

===General reference===

====Classification systems====
*[[List of Dewey Decimal Classes#500-599 – Science|Mathematics in the Dewey Decimal Classification system]]

*''[[Mathematics Subject Classification]]'' – 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.

====Reference databases====
*''[[Mathematical Reviews]]'' – journal and online database published by the American Mathematical Society (AMS) that contains brief synopses (and occasionally evaluations) of many articles in mathematics, statistics and theoretical computer science.
*''[[Zentralblatt MATH]]'' – 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 uses the Mathematics Subject Classification codes for organizing their reviews by topic.

==Subjects==

===Quantity===
[[Mathematics#Quantity|Quantity]] –
*[[Arithmetic]] –
*[[Natural number]]s –
*[[Integer]]s –
*[[Rational number]]s –
*[[Real number]]s –
*[[Complex number]]s –
*[[Hypercomplex number]]s –
*[[Infinity]] –

===Structure===
[[Mathematics#Structure|Structure]] –
*[[Abstract algebra]] –
*[[Linear algebra]] –
*[[Number theory]] –
*[[Order theory]] –
*[[Function (mathematics)]] –

===Space===
[[Mathematics#Space|Space]] –
*[[Geometry]] –
*[[Algebraic geometry]] –
*[[Trigonometry]] –
*[[Differential geometry]] –
*[[Topology]] –
*[[Fractal geometry]] –

===Change===
[[Mathematics#Change|Change]] –
*[[Calculus]] –
*[[Vector calculus]] –
*[[Differential equation]]s –
*[[Dynamical system]]s –
*[[Chaos theory]] –
*[[Mathematical analysis|Analysis]] –

===Foundations and philosophy===
[[Foundations of mathematics]] –
*[[Philosophy of mathematics]] –
*[[Category theory]] –
*[[Set theory]] –
*[[Type theory]] –

===Mathematical logic===
{{see also|Outline of mathematical logic}}
[[Mathematical logic]] –
*[[Model theory]] –
*[[Proof theory]] –
*[[Recursion theory]] –
*[[Set theory]] –
*[[Type theory]] –

===Discrete mathematics===
[[Discrete mathematics]] –
*[[Combinatorics]]
*[[Theory of computation]]
*[[Cryptography]]
*[[Graph theory]]

===Applied mathematics===
[[Applied mathematics]] –
*[[Mathematical physics]] –
*[[Mechanics|Analytical mechanics]] –
*[[Fluid mechanics|Mathematical fluid dynamics]] –
*[[Numerical analysis]] –
*[[Control theory]] –
*[[Dynamical system]]s –
*[[Mathematical optimization]] –
*[[Operations research]] –
*[[Probability]] –
*[[Statistics]] –
*[[Game theory]] –
*[[Mathematical economics]] –
*[[Financial mathematics]] –
*[[Information theory]] –
*[[Cryptography]] –
*[[Mathematical biology]] –

==History==
{{main|History of mathematics}}
*[[Babylonian mathematics]]
*[[Egyptian mathematics]]
*[[Indian mathematics]]
*[[Greek mathematics]]
*[[Chinese mathematics]]
**[[Abacus]]
*[[History of the Hindu–Arabic numeral system]]
*[[Islamic mathematics]]
*[[Japanese mathematics]]
*[[History of algebra]]
*[[History of geometry]]
*[[History of mathematical notation]]
*[[History of trigonometry]]
*[[History of writing numbers]]

==Psychology==
*[[Mathematics education]]
*[[Numeracy]]
*[[Numerical Cognition]]
*[[Subitizing]]
*[[Mathematical anxiety]]
*[[Dyscalculia]]
*[[Acalculia]]
*[[Ageometresia]]
*[[Number sense]]
*[[Numerosity adaptation effect]]
*[[Approximate number system]]
*[[Mathematical maturity]]

==Influential mathematicians==
See [[:Category:Lists of mathematicians|Lists of mathematicians]]

==Mathematical notation==
{{main|Mathematical notation}}
* [[List of mathematical abbreviations]]
* [[List of mathematical symbols]]
* [[List of mathematical symbols by subject]]
* [[Table of mathematical symbols by introduction date]]
* [[Notation in probability and statistics]]
* [[Table of logic symbols]]
* [[Physical constant]]s
* [[Greek letters used in mathematics, science, and engineering]]
* [[Latin letters used in mathematics]]
* [[Mathematical alphanumeric symbols]]
* [[Mathematical operators and symbols in Unicode]]
* [[ISO 31-11]] (Mathematical signs and symbols for use in physical sciences and technology)


==See also==
*[[Lists of mathematics topics]]
*[[Areas of mathematics]]
*[[Glossary of areas of mathematics]]

== External links ==
{{Sister project links|Mathematics}}
*[http://www.maa.org/press/maa-reviews/the-basic-library-list-maas-recommendations-for-undergraduate-libraries MAA Reviews – The Basic Library List – Mathematical Association of America]
*[http://www.math.ucdavis.edu/~saito/books.html Naoki's Recommended Books, compiled by Naoki Saito, U. C. Davis]
*[http://www.math.cornell.edu/~hatcher/Other/topologybooks.pdf A List of Recommended Books in Topology, compiled by Allen Hatcher, Cornell U.]
*[http://ncatlab.org/nlab/show/books+in+algebraic+geometry Books in algebraic geometry in nLab]

{{Areas of mathematics}}
{{Outlines}}

[[Category:Mathematics| ]]
[[Category:Fields of mathematics| ]]
[[Category:Wikipedia outlines|Mathematics]]

Outline of mathematics - Revision history

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