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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.
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. [1] For example, of three gloves, at least two must be right-handed or at least two must be left-handed, because there are three objects but only two categories of handedness to put ...
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer.
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
Quantum threshold theorem (computer science) (theoretical computer science) Reversed compound agent theorem (probability) Rice's theorem (recursion theory, computer science) Rice–Shapiro theorem (computer science) Savitch's theorem (computational complexity theory) Schaefer's dichotomy theorem (computational complexity theory)
The theory of computation can be considered the creation of models of all kinds in the field of computer science. Therefore, mathematics and logic are used. In the last century, it separated from mathematics and became an independent academic discipline with its own conferences such as FOCS in 1960 and STOC in 1969, and its own awards such as the IMU Abacus Medal (established in 1981 as the ...
Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete ...
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability.