Efforts are made to process the submission of Notes short articles quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics. Discrete Mathematics also publishes occasional Special Issues containing selected papers, often from a particular conference.

Such issues are fully refereed and adhere to the normal high standards of the journal. This journal has an Open Archive.

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All published items, including research articles, have unrestricted access and will remain permanently free to read and download 48 months after publication. All papers in the Archive are subject to Elsevier's user license. Since 1st September , we have made over , archived mathematics articles freely available to the mathematics community. Home Journals Discrete Mathematics. Submit Your Paper Enter your login details below. Username Password I forgot my password Register new account. Username Password I forgot my password. Track accepted paper Once production of your article has started, you can track the status of your article via Track Your Accepted Article.

Schaum's Outline of Discrete Mathematics, 2nd ed. Applications of Discrete Mathematics, 4th ed.

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Discrete Mathematics in the Schools. A New Kind of Science. Renze, John and Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Unlimited random practice problems and answers with built-in Step-by-step solutions.

The telecommunication industry has also motivated advances in discrete mathematics, particularly in graph theory and information theory. 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. Several fields of discrete mathematics, particularly theoretical computer science, graph theory, and combinatorics , are important in addressing the challenging bioinformatics problems associated with understanding the tree of life.

Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and mathematical logic.

### Discrete Mathematics

Included within theoretical computer science is the study of algorithms for computing mathematical results. Computability studies what can be computed in principle, and has close ties to logic, while complexity studies the time, space, and other resources taken by computations. Automata theory and formal language theory are closely related to computability. Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical problems, while computer image analysis applies them to representations of images.

Theoretical computer science also includes the study of various continuous computational topics. Information theory involves the quantification of information.

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Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. Information theory also includes continuous topics such as: Logic is the study of the principles of valid reasoning and inference , as well as of consistency , soundness , and completeness. For classical logic, it can be easily verified with a truth table.

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The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software. Logical formulas are discrete structures, as are proofs , which form finite trees [14] or, more generally, directed acyclic graph structures [15] [16] with each inference step combining one or more premise branches to give a single conclusion. The truth values of logical formulas usually form a finite set, generally restricted to two values: Concepts such as infinite proof trees or infinite derivation trees have also been studied, [17] e.

Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets including finite sets are the main focus. The beginning of set theory as a branch of mathematics is usually marked by Georg Cantor 's work distinguishing between different kinds of infinite set , motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics.

Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics. Combinatorics studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects - e. Analytic combinatorics concerns the enumeration i.

## Discrete Mathematics

In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae. Design theory is a study of combinatorial designs , which are collections of subsets with certain intersection properties. Partition theory studies various enumeration and asymptotic problems related to integer partitions , and is closely related to q-series , special functions and orthogonal polynomials.

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Originally a part of number theory and analysis , partition theory is now considered a part of combinatorics or an independent field. Order theory is the study of partially ordered sets , both finite and infinite. Graph theory, the study of graphs and networks , is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right.

They are among the most ubiquitous models of both natural and human-made structures.

## Discrete mathematics

They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology , e.

Algebraic graph theory has close links with group theory. There are also continuous graphs , however for the most part research in graph theory falls within the domain of discrete mathematics. Discrete probability theory deals with events that occur in countable sample spaces. On the other hand, continuous observations such as the weights of birds comprise real number values and would typically be modeled by a continuous probability distribution such as the normal.

Discrete probability distributions can be used to approximate continuous ones and vice versa. For highly constrained situations such as throwing dice or experiments with decks of cards , calculating the probability of events is basically enumerative combinatorics. Number theory is concerned with the properties of numbers in general, particularly integers.