Discrete mathematics is the study of structures within the realm of mathematics that can be considered discrete rather than continuous. The term discrete can be considered analogous to discrete variables. . Objects that are studied in this branch of mathematics include graphs, integers, and statements in logic. It willfully excludes topics in continuous mathematics like real numbers, Euclidean geometry, and calculus. To put it in simple words, discrete mathematics can be characterized as the branch of mathematics that deals with countable sets. However, what is really interesting is that there is no exact definition for this branch of mathematics.
The set of objects studied in this branch of mathematics can be either finite or infinite. Research in this part of mathematics increased rapidly in the latter half of the twentieth century mainly due to the exponentially fast-paced development of digital computers that operate in discrete steps and store data in discrete bits. Notations and concepts from discrete mathematics are especially useful in studying and describing problems and objects in branches of computer science, like programming languages, computer algorithms, cryptography, software development, and automated theorem proving. On the other hand, computer implementations are very important in applying ideas from this branch of mathematics to solve real-world problems, like in the case of operations research.
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