Taken at its verbatim face value, the term discrete mathematics refers to mathematics concerned with mathematical structures which are discrete in the sense of discrete topological spaces, hence which do not involve topology and in particular do not involve analysis (“calculus”).
With the hindsight of the nPOV one could usefully say that discrete mathematics, in this sense, is the topic of (models of) bare homotopy type theory, in contrast to its cohesive refinement to cohesive homotopy type theory.
However, in common parlance the term discrete mathematics is used much more restrictively:
On the one hand, it often appears as the title of those introductory courses in the undergraduate mathematics and computer science curricula which are expressly independent of differential calculus and instead concerned with discussing prerequisites such as naïve set theory, basic predicate logic, an introduction to proofs, and maybe elementary number theory, and possibly aimed at providing an overview of combinatorics, graph theory and associated algorithms (e.g. Molluzzo & Buckley 1986).
On the other hand, in research mathematics the term discrete mathematics is mainly used (see the references below) as a synonym for combinatorics and closely related fields (or subfields): finite geometry and incidence geometry, coding theory and Boolean functions, combinatorics of posets, matroid theory, convex geometry and polytopes, packings, tilings, etc.
See also:
Textbook accounts for undergraduates:
John C. Molluzzo, Fred Buckley, A First Course in Discrete Mathematics, Waveland Press (1986) ISBN 13:978-0-88133-940-6
Gary Chartrand, Ping Zhang: Discrete Mathematics Waveland Press (2011) ISBN:978-1577667308
Kenneth Rosen, Discrete Mathematics and its Applications, McGraw Hill (2019) ISBN:978-1-259-67651-2, pdf
Last revised on June 16, 2022 at 09:12:30. See the history of this page for a list of all contributions to it.