Finite Math Problems

Finite Math Problems-38
Formal verification of statements in logic has been necessary for software development of safety-critical systems, and advances in automated theorem proving have been driven by this need.Computational geometry has been an important part of the computer graphics incorporated into modern video games and computer-aided design tools.Operations research remained important as a tool in business and project management, with the critical path method being developed in the 1950s.

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Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In graph theory, much research was motivated by attempts to prove the four color theorem, first stated in 1852, but not proved until 1976 (by Kenneth Appel and Wolfgang Haken, using substantial computer assistance).In logic, the second problem on David Hilbert's list of open problems presented in 1900 was to prove that the axioms of arithmetic are consistent.It draws heavily on graph theory and mathematical logic.Included within theoretical computer science is the study of algorithms for computing mathematical results.In 1970, Yuri Matiyasevich proved that this could not be done.The need to break German codes in World War II led to advances in cryptography and theoretical computer science, with the first programmable digital electronic computer being developed at England's Bletchley Park with the guidance of Alan Turing and his seminal work, On Computable Numbers.Gödel's second incompleteness theorem, proved in 1931, showed that this was not possible – at least not within arithmetic itself.Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits.

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