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Computational mathematics
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<h2 id="areas-of-computational-mathematics">Areas of computational mathematics</h2> <p>Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include: </p> <ul><li><a href="/facts/Computational_science/PnVD19hw">Computational sciences</a>, also known as scientific computation or <a href="/facts/Computational_engineering/dvIJ5o36">computational engineering</a></li> <li><a href="/facts/Systems_science/necfqoog">Systems sciences</a>, for which directly requires the mathematical models from <a href="/facts/Systems_engineering/gFwRmkDp">Systems engineering</a></li> <li>Solving mathematical problems by <a href="/facts/Computer_simulation/Re6o8vzN">computer simulation</a> as opposed to traditional engineering methods.</li> <li><a href="/facts/Numerical_methods/QT9cYa9z">Numerical methods</a> used in scientific computation, for example <a href="/facts/Numerical_linear_algebra/jnS6Tteb">numerical linear algebra</a> and <a href="/facts/Numerical_solution/QT9cYa9z">numerical solution</a> of <a href="/facts/Partial_differential_equations/DyPsBlv7">partial differential equations</a></li> <li><a href="/facts/Stochastic/uMbgL94r">Stochastic</a> methods,<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> such as <a href="/facts/Monte_Carlo_methods/AkHjY7jc">Monte Carlo methods</a> and other representations of <a href="/facts/Uncertainty/VM9pnGvk">uncertainty</a> in scientific computation</li> <li>The mathematics of scientific computation,<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> in particular <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, the theory of numerical methods</li> <li><a href="/facts/Computational_complexity/Qenh22Ja">Computational complexity</a></li> <li><a href="/facts/Computer_algebra/hjun1KAX">Computer algebra</a> and <a href="/facts/Computer_algebra_system/jkLAC1U3">computer algebra systems</a></li> <li>Computer-assisted research in various areas of mathematics, such as <a href="/facts/Mathematical_logic/SaI7Y3wN">logic</a> (<a href="/facts/Automated_theorem_proving/vKGvuKFI">automated theorem proving</a>), <a href="/facts/Discrete_mathematics/XdRUnzUL">discrete mathematics</a>, <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a>, <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, and computational <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a></li> <li><a href="/facts/Cryptography/e94PEVau">Cryptography</a> and <a href="/facts/Computer_security/7E5dIy7G">computer security</a>, which involve, in particular, research on <a href="/facts/Primality_testing/dLMr8E0u">primality testing</a>, <a href="/facts/Factorization/tXrBXFh1">factorization</a>, <a href="/facts/Elliptic_curve_cryptography/YbjcXIWk">elliptic curves</a>, and mathematics of <a href="/facts/Blockchain/8H43GgWy">blockchain</a></li> <li><a href="/facts/Computational_linguistics/XmegJ6LC">Computational linguistics</a>, the use of mathematical and computer techniques in <a href="/facts/Natural_language/B4gLS7Kd">natural languages</a></li> <li><a href="/facts/Computational_algebraic_geometry/rh7RHVp3">Computational algebraic geometry</a></li> <li><a href="/facts/Computational_group_theory/Q9B5hL65">Computational group theory</a></li> <li><a href="/facts/Computational_geometry/eeaotQtl">Computational geometry</a></li> <li><a href="/facts/Computational_number_theory/7Lu5N57C">Computational number theory</a></li> <li><a href="/facts/Computational_topology/cuWIEkfA">Computational topology</a></li> <li><a href="/facts/Computational_statistics/noW2SBX8">Computational statistics</a></li> <li><a href="/facts/Algorithmic_information_theory/Tltn3I0Y">Algorithmic information theory</a></li> <li><a href="/facts/Algorithmic_game_theory/9NAnQcnx">Algorithmic game theory</a></li> <li><a href="/facts/Mathematical_economics/Dvy7j519">Mathematical economics</a>, the use of mathematics in economics, finance and, to certain extents, of accounting.</li> <li><a href="/facts/Experimental_mathematics/NfuxNMIz">Experimental mathematics</a></li></ul> <h2 id="journals">Journals</h2> <p>Journals that publish contributions from computational mathematics include </p> <ul><li><a href="/facts/ACM_Transactions_on_Mathematical_Software/3Ev3LTR8">ACM Transactions on Mathematical Software</a></li> <li><a href="/facts/Mathematics_of_Computation/KAFdf8sw">Mathematics of Computation</a></li> <li><a href="/facts/SIAM_Journal_on_Scientific_Computing/waxjpMla">SIAM Journal on Scientific Computing</a></li> <li><a href="/facts/SIAM_Journal_on_Numerical_Analysis/uUEWPahC">SIAM Journal on Numerical Analysis</a></li></ul> <h2 id="see-also">See also</h2> <ul><li> Mathematics portal</li> <li><a href="/facts/Computer-based_mathematics_education/UKY0968H">Computer-based mathematics education</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Cucker, F. (2003). <i>Foundations of Computational Mathematics: Special Volume</i>. Handbook of Numerical Analysis. North-Holland Publishing. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-444-51247-5.</li> <li>Harris, J. W.; Stocker, H. (1998). <a href="https://archive.org/details/handbookofmathem00harr"><i>Handbook of Mathematics and Computational Science</i></a>. Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-94746-4.</li> <li>Hartmann, A.K. (2009). <a href="https://web.archive.org/web/20090211113048/http://worldscibooks.com/physics/6988.html"><i>Practical Guide to Computer Simulations</i></a>. World Scientific. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-981-283-415-7. Archived from <a href="http://www.worldscibooks.com/physics/6988.html">the original</a> on February 11, 2009. Retrieved May 3, 2012.</li> <li>Nonweiler, T. R. (1986). <i>Computational Mathematics: An Introduction to Numerical Approximation</i>. John Wiley and Sons. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-470-20260-9.</li> <li>Gentle, J. E. (2007). <i>Foundations of Computational Science</i>. Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-00450-1.</li> <li>White, R. E. (2003). <i>Computational Mathematics: Models, Methods, and Analysis with MATLAB</i>. Chapman and Hall. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1584883647.</li> <li>Yang, X. S. (2008). <i>Introduction to Computational Mathematics</i>. World Scientific. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-9812818171.</li> <li>Strang, G. (2007). <i>Computational Science and Engineering</i>. Wiley. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0961408817.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://focm-society.org/">Foundations of Computational Mathematics</a>, a non-profit organization</li> <li><a href="http://www.journal-1.eu/index.htm">International Journal of Computer Discovered Mathematics</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>National Science Foundation, Division of Mathematical Science, Program description PD 06-888 Computational Mathematics, 2006. Retrieved April 2007. <a href="/wiki/National_Science_Foundation" target="_blank">/wiki/National_Science_Foundation</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>"NSF Seeks Proposals on Stochastic Systems". SIAM News. August 19, 2005. Archived from the original on February 5, 2012. Retrieved February 2, 2015. <a href="https://web.archive.org/web/20120205070148/http://www.siam.org/news/general.php?id=121" target="_blank">https://web.archive.org/web/20120205070148/http://www.siam.org/news/general.php?id=121</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM. <a href="http://www.siam.org/about/science/publications.php" target="_blank">http://www.siam.org/about/science/publications.php</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Mathematics of Computation, Journal overview. Retrieved April 2007. <a href="/wiki/Mathematics_of_Computation" target="_blank">/wiki/Mathematics_of_Computation</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> </ol>