Discrete Mathematics and Its Applications

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At this level, discrete mathematics is sometimes seen as a preparatory course, like precalculus in this respect. Discrete algebras include: Boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages. It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing.

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Main article: Theoretical computer science Complexity studies the time taken by algorithms, such as this sorting routine. Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness.In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc.

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Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets [4] (finite sets or sets with the same cardinality as the natural numbers). Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. Although the space in which the curves appear has a finite number of points, the curves are not so much sets of points as analogues of curves in continuous settings. For example, in most systems of logic (but not in intuitionistic logic) Peirce's law ((( P→ Q)→ P)→ P) is a theorem.Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems.