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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 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.
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 ...
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)
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.
The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science, and engineering. List of algorithm general topics; List of computability and complexity topics
A finite-state automaton from automata theory, a branch of theoretical computer science. Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely.
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 ...
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