Computational mathematics
{{Short description|Area of mathematics}}
{{Math topics TOC}}
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Computational mathematics is the study of the interaction between mathematics and calculations done by a computer.National Science Foundation, Division of Mathematical Science, [https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5390 Program description PD 06-888 Computational Mathematics], 2006. Retrieved April 2007.
A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity, numerical methods and computer algebra.
Computational mathematics refers also to the use of computers for mathematics itself. This includes mathematical experimentation for establishing conjectures (particularly in number theory), the use of computers for proving theorems (for example the four color theorem), and the design and use of proof assistants.
Areas of computational mathematics
Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include:
- Computational sciences, also known as scientific computation or computational engineering
- Systems sciences, for which directly requires the mathematical models from Systems engineering
- Solving mathematical problems by computer simulation as opposed to traditional engineering methods.
- Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations
- Stochastic methods,{{cite web |url=http://www.siam.org/news/general.php?id=121 |title=NSF Seeks Proposals on Stochastic Systems |publisher=SIAM News |date=August 19, 2005 |access-date=February 2, 2015 |archive-url=https://web.archive.org/web/20120205070148/http://www.siam.org/news/general.php?id=121 |archive-date=February 5, 2012 |url-status=dead }} such as Monte Carlo methods and other representations of uncertainty in scientific computation
- The mathematics of scientific computation,Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. [http://www.siam.org/about/science/publications.php Distributed by SIAM].Mathematics of Computation, [https://www.ams.org/mcom/aboutmcom.html Journal overview]. Retrieved April 2007. in particular numerical analysis, the theory of numerical methods
- Computational complexity
- Computer algebra and computer algebra systems
- Computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics, combinatorics, number theory, and computational algebraic topology
- Cryptography and computer security, which involve, in particular, research on primality testing, factorization, elliptic curves, and mathematics of blockchain
- Computational linguistics, the use of mathematical and computer techniques in natural languages
- Computational algebraic geometry
- Computational group theory
- Computational geometry
- Computational number theory
- Computational topology
- Computational statistics
- Algorithmic information theory
- Algorithmic game theory
- Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting.
- Experimental mathematics
Journals
Journals that publish contributions from computational mathematics include
See also
- {{portal-inline|Mathematics}}
- Computer-based mathematics education
- Mathematical software
- List of open-source software for mathematics
References
{{Reflist}}
Further reading
- {{cite book |last=Cucker |first=F. |year=2003 |title=Foundations of Computational Mathematics: Special Volume |series=Handbook of Numerical Analysis |publisher=North-Holland Publishing |isbn=978-0-444-51247-5 }}
- {{cite book |last=Harris |first=J. W. |last2=Stocker |first2=H. |year=1998 |title=Handbook of Mathematics and Computational Science |publisher=Springer-Verlag |isbn=978-0-387-94746-4 |url-access=registration |url=https://archive.org/details/handbookofmathem00harr }}
- {{cite book|last=Hartmann|first=A.K.|year=2009|title=Practical Guide to Computer Simulations|publisher=World Scientific|isbn=978-981-283-415-7|url=http://www.worldscibooks.com/physics/6988.html|access-date=May 3, 2012|archive-url=https://web.archive.org/web/20090211113048/http://worldscibooks.com/physics/6988.html|archive-date=February 11, 2009|url-status=dead}}
- {{cite book |last=Nonweiler |first=T. R. |year=1986 |title=Computational Mathematics: An Introduction to Numerical Approximation |publisher=John Wiley and Sons |isbn=978-0-470-20260-9 }}
- {{cite book |last=Gentle |first=J. E. |year=2007 |title=Foundations of Computational Science |publisher=Springer-Verlag |isbn=978-0-387-00450-1 }}
- {{cite book |first=R. E. |last=White |year=2003 |title=Computational Mathematics: Models, Methods, and Analysis with MATLAB |publisher=Chapman and Hall |isbn=978-1584883647}}
- {{cite book |first=X. S. |last=Yang |year=2008 |title=Introduction to Computational Mathematics |publisher=World Scientific |isbn=978-9812818171}}
- {{cite book |first=G. |last=Strang |year=2007 |title=Computational Science and Engineering |publisher=Wiley |isbn=978-0961408817}}
External links
- [http://focm-society.org/ Foundations of Computational Mathematics], a non-profit organization
- [http://www.journal-1.eu/index.htm International Journal of Computer Discovered Mathematics]
{{Areas of mathematics}}
{{Industrial and applied mathematics}}
{{Computational science}}