Discrete Math

Discrete mathematics, broadly speaking, is the “study of discrete objects.” As opposed to objects that vary smoothly, such as the real numbers, discrete mathematics has been described as the mathematics of countable sets. Because of the absence of an all-encompassing definition, the best way to understand what discrete mathematics entails is to enumerate some of the topics it covers: graph theory, combinatorics, set theory, logic, discrete probability theory, number theory, certain topics in algebra (numerical semigroups and monoids, for instance), discrete geometry, and several topics in game theory.

Of these topics, Princeton offers separate courses on graph theory, combinatorics, logic, discrete geometry, and game theory. Set theory, number theory, probability, and the “discrete” topics in algebra come up in their own right in various other courses, where they can be studied in more depth.

Finally, it should be stated that discrete mathematics is very closely associated with computer science. As a result, many of the topics can be studied as integral parts of either of the two disciplines. In fact, there are a couple of courses offered by Princeton’s COS department which are really discrete mathematics courses in disguise. Students majoring in either of the two also often end up taking courses from the other, and as a result there is constant exchange and collaboration between the two departments.

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