Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. The set of objects studied in discrete mathematics can be finite or infinite. 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. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. 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. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research. 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.

{"references": ["1.\tArumugam. S & Isaac. A. T, \"Modern Algebra\", Scitech Publications Pvt. Ltd, Chennai. 2.\tLiu. C. L \"Elements of Discrete Mathematics\", MC Graw Hill, Internation Edition. 3.\tTremblay. J. P & Manohar. R, \"Discrete Mathematics Structure with application to computer science\", TMH Edition 1007. 4.\tVeerarajan. T, \"Discrete Mathematics with Graph theory and Combinatorics\", Tata MCGraw \u2013Hill publishing company Limited, New Delhi."]}