Computational mathematics

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A black and white rendition of the Yale Babylonian Collection's Tablet YBC 7289 (c. 1800-1600 BCE), showing a Babylonian approximation to the square root of 2 (1 24 51 10 w: sexagesimal) in the context of Pythagoras' Theorem for an isosceles triangle. The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888. Ybc7289-bw.jpg
A black and white rendition of the Yale Babylonian Collection's Tablet YBC 7289 (c. 1800–1600 BCE), showing a Babylonian approximation to the square root of 2 (1 24 51 10 w: sexagesimal) in the context of Pythagoras' Theorem for an isosceles triangle. The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888.

Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations. [1]

Contents

Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations (computer algebra), the study of what can (and cannot) be computerized in mathematics (effective methods), which computations may be done with present technology (complexity theory), and which proofs can be done on computers (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:

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Computational science, also known as scientific computing or scientific computation (SC), is a rapidly growing field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems.

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Computational finance

Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems.

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Computational statistics

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Peter Bürgisser is a Swiss mathematician and theoretical computer scientist who deals with algorithmic algebra and algebraic complexity theory.

Complexity and Real Computation is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For instance, this theory is capable of addressing a question posed in 1991 by Roger Penrose in The Emperor's New Mind: "is the Mandelbrot set computable?"

References

  1. National Science Foundation, Division of Mathematical Science, Program description PD 06-888 Computational Mathematics, 2006. Retrieved April 2007.
  2. "NSF Seeks Proposals on Stochastic Systems". SIAM News. August 19, 2005. Archived from the original on February 5, 2012. Retrieved February 2, 2015.
  3. Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM.
  4. Mathematics of Computation, Journal overview. Retrieved April 2007.

Further reading