Computational mathematics

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

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

Computational mathematics also means using computers to do math. This can involve testing ideas to see if they might be true, helping to prove math facts, and creating tools that assist mathematicians in checking and writing proofs.

Areas of computational mathematics

Computational mathematics started 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

Journals

See also: List of mathematics journals

Some journals that share ideas about computational mathematics include:

• ACM Transactions on Mathematical Software
• Mathematics of Computation
• SIAM Journal on Scientific Computing
• SIAM Journal on Numerical Analysis