Computational mathematics

Computational mathematics is a field of study that looks at how math, computer science, and algorithms work together. It helps us use computers to solve math problems in many areas of science and engineering.

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.

One big part of this field is using math to make computers work better and faster. This includes designing smart ways to solve problems, understanding how hard certain tasks are for computers, and finding new methods for calculations.

Computational mathematics also means using computers to do math itself. This can involve testing ideas to see if they might be true, proving math facts with the help of computers, and creating tools that help mathematicians check and write proofs.

Areas of computational mathematics

Computational mathematics began as a special part of applied mathematics in the early 1950s. Today, it includes many different areas, such as:

Computational sciences or scientific computation
Systems sciences using models from systems engineering
Solving problems using computer simulation
Numerical methods like numerical linear algebra and solving partial differential equations
Stochastic methods, including Monte Carlo methods for handling uncertainty
The theory behind numerical methods, known as numerical analysis
Computational complexity
Computer algebra and systems that help with algebraic calculations
Research helped by computers in areas like logic, discrete mathematics, and combinatorics
Cryptography and computer security, including studying primality testing, factorization, and elliptic curves
Computational linguistics, applying math and computers to study natural languages
Many other fields such as computational geometry, computational statistics, and experimental mathematics

Areas of computational mathematics

Journals

Related articles