From Wikipedia, the free encyclopedia
Area of mathematics
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 is the study of the interaction between mathematics and calculations done by a computer.
[1]
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,
[2] such as
Monte Carlo methods and other representations of
uncertainty in scientific computation
The mathematics of scientific computation,
[3]
[4] 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
See also
References
^
National Science Foundation , Division of Mathematical Science,
Program description PD 06-888 Computational Mathematics , 2006. Retrieved April 2007.
^
"NSF Seeks Proposals on Stochastic Systems" . SIAM News. August 19, 2005. Archived from
the original on February 5, 2012. Retrieved February 2, 2015 .
^ Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985.
Distributed by SIAM .
^
Mathematics of Computation ,
Journal overview . Retrieved April 2007.
Further reading
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 . Archived from
the original on February 11, 2009. Retrieved May 3, 2012 .
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 .
White, R. E. (2003). Computational Mathematics: Models, Methods, and Analysis with MATLAB . Chapman and Hall.
ISBN
978-1584883647 .
Yang, X. S. (2008). Introduction to Computational Mathematics . World Scientific.
ISBN
978-9812818171 .
Strang, G. (2007). Computational Science and Engineering . Wiley.
ISBN
978-0961408817 .
External links