Mathematics Of Computing
Computer mathematics may refer to: * Automated theorem proving, the proving of mathematical theorems by a computer program * Symbolic computation, the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects * Computational science, constructing numerical solutions and using computers to analyze and solve scientific and engineering problems * Theoretical computer science Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Associati ...

Automated Theorem Proving
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. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ...
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Symbolic Computation
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes ''exact'' computation with expressions containing variables that have no given value and are manipulated as symbols. Software applications that perform symbolic calculations are called '' computer algebra systems'', with the term ''system'' alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the la ...
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Computational Science
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, which uses advanced computing capabilities to understand and solve complex physical problems. While this typically extends into computational specializations, this field of study includes: * Algorithms ( numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.g, physical, biological, and social), engineering, and humanities problems * Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science In practical use, it is typically the application of compu ...
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