Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Computation in the research is prominent.^[1] Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include:

• computational science, also known as scientific computation or computational engineering
• solving mathematical problems by computer simulation as opposed to analytic methods of applied mathematics
• numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations
• stochastic methods,^[2] such as Monte Carlo methods and other representations of uncertainty in scientific computation, for example stochastic finite elements
• the mathematics of scientific computation^[3] (the theoretical side involving mathematical proofs^[4]), in particular numerical analysis, the theory of numerical methods (but theory of computation and complexity of algorithms belong to theoretical computer science)
• symbolic computation and computer algebra systems
• computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics (search for mathematical structures such as groups), number theory (primality testing and factorization), cryptography, and computational algebraic topology
• computational linguistics, the use of mathematical and computer techniques in natural languages
• Computational geometry
• Computational topology
• Computational number theory
• Algorithmic information theory
• Algorithmic game theory

References[link]

Further reading[link]

• Cucker, F. (2003). Foundations of Computational Mathematics: Special Volume. Handbook of Numerical Analysis. North-Holland Publishing. ISBN 978-0-444-51247-5. 
• Harris, J. W.; Stocker, H. (1998). Handbook of Mathematics and Computational Science. Springer-Verlag. ISBN 978-0-387-94746-4. 
• Hartmann, A.K. (2009). Practical Guide to Computer Simulations. World Scientific. ISBN 978-981-283-415-7. http://www.worldscibooks.com/physics/6988.html. 
• Yang, X. S. (2008). Introduction to Computational Mathematics. World Scientific Publishing. ISBN 978-981-281-817-1. 
• Nonweiler, T. R. (1986). Computational Mathematics: An Introduction to Numerical Approximation. John Wiley and Sons. ISBN 978-0-470-20260-9. 
• Gentle, J. E. (2007). Foundations of Computational Science. Springer-Verlag. ISBN 978-0-387-00450-1. 

External links[link]

• Foundations of Computational Mathematics: a non-profit organization

Fariba Fahroo is an American mathematician and Program Manager of Computational Mathematics at the Air Force Office of Scientific Research. Along with I. M. Ross, she has published seminal papers in pseudospectral optimal control theory.^{[1][2][3][4][5] [6] [7] [8] [9]} The Ross-Fahroo lemma and the Ross-Fahroo pseudospectral method are named after her. In 2010, she received (jointly with Ross), the prestigious AIAA Mechanics and Control of Flight Award for fundamental contributions to flight mechanics.

See also[link]

• Ross–Fahroo pseudospectral methods
• Ross–Fahroo lemma

References[link]

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Avi Wigderson (Hebrew: אבי ויגדרזון‎; b. 9 September 1956^[1]) is an Israeli mathematician and computer scientist, a professor of mathematics at the Institute for Advanced Study in Princeton. His research interests include complexity theory, parallel algorithms, graph theory, cryptography, distributed computing, and neural networks.^[2]

Biography[link]

Wigderson did his undergraduate studies at the Technion in Haifa, Israel, graduating in 1980, and went on to graduate study at Princeton University. He received his Ph.D. in 1983 for work in computational complexity under the supervision of Richard Lipton.^[3] After short-term positions at the University of California, Berkeley, the IBM Almaden Research Center in San Jose, California, and the Mathematical Sciences Research Institute in Berkeley, he joined the faculty of Hebrew University in 1986. In 1999 he also took a position at the Institute for Advanced Study, and in 2003 he gave up his Hebrew University position to take up full-time residence at the IAS.^[2]

Awards and honors[link]

Wigderson received the Nevanlinna Prize in 1994 for his work on computational complexity.^[4] Along with Omer Reingold and Salil Vadhan he won the 2009 Gödel Prize for work on the zig-zag product of graphs, a method of combining smaller graphs to produce larger ones used in the construction of expander graphs.^[5]

References[link]

External links[link]

• Avi Wigderson's home page.
• DBLP: Avi Wigderson.

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