Mathematics

=== Calculus and analysis ===
{{Main|Calculus|Mathematical analysis}}
[[File:Cauchy sequence illustration.svg|thumb|A [[Cauchy sequence]] consists of elements such that all subsequent terms of a term become arbitrarily close to each other as the sequence progresses (from left to right).]]

Calculus, formerly called infinitesimal calculus, was introduced independently and simultaneously by 17th-century mathematicians [[Isaac Newton|Newton]] and [[Leibniz]].<ref>{{cite book |last=Guicciardini |first=Niccolo |author-link=Niccolò Guicciardini |editor1-last=Schliesser |editor1-first=Eric |editor2-last=Smeenk |editor2-first=Chris |year=2017 |chapter=The Newton–Leibniz Calculus Controversy, 1708–1730 |title=The Oxford Handbook of Newton |series=Oxford Handbooks |publisher=[[Oxford University Press]] |doi=10.1093/oxfordhb/9780199930418.013.9 |isbn=978-0-19-993041-8 |oclc=975829354 |chapter-url=https://core.ac.uk/download/pdf/187993169.pdf |url-status=live |archive-url=https://web.archive.org/web/20221109163253/https://core.ac.uk/download/pdf/187993169.pdf |archive-date=November 9, 2022 |access-date=February 9, 2024}}</ref> It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by [[Euler]] with the introduction of the concept of a [[function (mathematics)|function]] and many other results.<ref>{{cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |date=September 1998 |title=Leonhard Euler |website=MacTutor |publisher=[[University of St Andrews]] |publication-place=Scotland, UK |url=https://mathshistory.st-andrews.ac.uk/Biographies/Euler/ |url-status=live |archive-url=https://web.archive.org/web/20221109164921/https://mathshistory.st-andrews.ac.uk/Biographies/Euler/ |archive-date=November 9, 2022 |access-date=February 9, 2024}}</ref> Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis" is commonly used for advanced parts.

Analysis is further subdivided into [[real analysis]], where variables represent [[real number]]s, and [[complex analysis]], where variables represent [[complex number]]s. Analysis includes many subareas shared by other areas of mathematics which include:<ref name=MSC/>
* [[Multivariable calculus]]
* [[Functional analysis]], where variables represent varying functions;
* [[Integration (mathematics)|Integration]], [[measure theory]] and [[potential theory]], all strongly related with [[probability theory]] on a [[Continuum (set theory)|continuum]];
* [[Ordinary differential equation]]s;
* [[Partial differential equation]]s;
* [[Numerical analysis]], mainly devoted to the computation on computers of solutions of ordinary and partial differential equations that arise in many applications.