Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Topics that go beyond discrete objects include transcendental numbers, diophantine approximation, p-adic analysis and function fields. In university curricula, discrete mathematics appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time.

Discrete Mathematics - Concepts, Formulas, Problems and Solutions Discrete Mathematics - Concepts, Formulas, Problems and Solutions

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. g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. 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. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a recurrence relation or difference equation.

It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing.

Discrete Mathematics and Its Applications Sixth Edition 2006 Discrete Mathematics and Its Applications Sixth Edition 2006

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Many questions and methods concerning differential equations have counterparts for difference equations.

Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from "continuous" mathematics are often employed as well. Information theory also includes continuous topics such as: analog signals, analog coding, analog encryption.

Discrete Mathematics Courses and Programs | edX Best Online Discrete Mathematics Courses and Programs | edX

Computational geometry applies algorithms to geometrical problems and representations of geometrical objects, while computer image analysis applies them to representations of images. For instance, where there are integral transforms in harmonic analysis for studying continuous functions or analogue signals, there are discrete transforms for discrete functions or digital signals. Difference equations are similar to differential equations, but replace differentiation by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Main article: Information theory The ASCII codes for the word "Wikipedia", given here in binary, provide a way of representing the word in information theory, as well as for information-processing algorithms.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. 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). Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems. Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics.