Discrete Mathematics and Its Applications

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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. 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. Computational geometry applies algorithms to geometrical problems and representations of geometrical objects, while computer image analysis applies them to representations of images. e., determining the number) of combinatorial structures using tools from complex analysis and probability theory.

Rosen_Discrete_Mathematics_and_Its_Applications_7th_Edition

As well as discrete metric spaces, there are more general discrete topological spaces, finite metric spaces, finite topological spaces. Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. Logical formulas are discrete structures, as are proofs, which form finite trees [10] or, more generally, directed acyclic graph structures [11] [12] (with each inference step combining one or more premise branches to give a single conclusion).For example, in most systems of logic (but not in intuitionistic logic) Peirce's law ((( P→ Q)→ P)→ P) is a theorem. The study of mathematical proof is particularly important in logic, and has accumulated to automated theorem proving and formal verification of software.

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

It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing.At this level, discrete mathematics is sometimes seen as a preparatory course, like precalculus in this respect. 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. The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of discrete and continuous data. Topological combinatorics concerns the use of techniques from topology and algebraic topology/ combinatorial topology in combinatorics.