Unsourced material may be challenged and discrete mathematics and its applications solution pdf. However, there is no exact definition of the term “discrete mathematics.
Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. The set of objects studied in discrete mathematics can be finite or infinite. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well. Some high-school-level discrete mathematics textbooks have appeared as well.
The history of discrete mathematics has involved a number of challenging problems which have focused attention within areas of the field. Theoretical computer science includes areas of discrete mathematics relevant to computing. Included within theoretical computer science is the study of algorithms for computing mathematical results. Theoretical computer science also includes the study of various continuous computational topics.
Combinatorics studies the way in which discrete structures can be combined or arranged. Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. 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.
Discrete probability distributions can be used to approximate continuous ones and vice versa. Many questions and methods concerning differential equations have counterparts for difference equations. Computational geometry applies algorithms to geometrical problems. Operations research provides techniques for solving practical problems in engineering, business, and other fields — problems such as allocating resources to maximize profit, or scheduling project activities to minimize risk.
Discretization concerns the process of transferring continuous models and equations into discrete counterparts, often for the purposes of making calculations easier by using approximations. 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. New York: The Clarendon Press Oxford University Press, p. Discrete Mathematics is the branch of Mathematics in which we deal with questions involving finite or countably infinite sets. Mathematical Association of America, 2008. Austrian Conference on AI, Vienna, Austria, September 19-21, 2001. Cyclic proofs of program termination in separation logic”.