Computational mathematics

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods with the concept of computation. The field is different from theoretical and applied mathematics.

Overview

Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations, mathematical research, the study of algorithms and data structures, and the visualization of mathematical results. The field also includes the study of the mathematical properties of computational methods and various aspects of scientific computing.

History

The history of computational mathematics can be traced back to the ancient times. The abacus, a simple counting aid, could be considered the earliest form of computational mathematics. The development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century revolutionized mathematics and is a cornerstone of modern computational mathematics.

Fields of Computational Mathematics

Computational mathematics involves several fields, including:

• Computational geometry: This field deals with the study of algorithms which can be stated in terms of geometry.
• Computational number theory: Also known as algorithmic number theory, it involves the design, analysis and implementation of algorithms to solve problems in number theory.
• Computational algebra: This field involves the use of computers to solve problems in algebra.
• Computational calculus: This field involves the use of computers to solve problems in calculus.
• Computational statistics: This field involves the use of computers to solve problems in statistics.

Applications

Computational mathematics has wide applications in various fields such as physics, engineering, economics, biology, and computer science. It is used to solve complex mathematical problems, model natural phenomena, and simulate physical systems.

See also

• Mathematical software
• Numerical analysis
• Scientific computing
• Computational science