Discrete Mathematics


Isaac Newton created calculus as a means of analyzing the smooth motion of objects, from falling apples to swinging asteroids. Indeed, calculus is an ideal tool for understanding phenomena where the setting is a continuum. By contrast, discrete mathematics is the realm of finite and countable phenomena.  Two central topics in discrete mathematics are i) combinatorics–advanced counting and arrangements, and ii) graph theory– the mathematics of networks.   Important contemporary examples include the study of social networks, analysis of efficiency of algorithms, combinatorial design of experiments, as well as routing, assignment, and scheduling problems. Discrete Mathematics tools are essential in operations research, computer science, and many other fields from epidemiology to protein folding and to telecommunications.


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