The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

The Elementary Math Education course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in October 2019. Team LeadBradford Findell                                Ohio State UniversityContent ContributorsVictor Ferdinand                               Ohio State UniversityHea-Jin Lee                                      Ohio State University LimaJenny Sheldon                                  Ohio State UniversityBart Snapp                                       Ohio State UniversityRajeev Swami                                  Central State UniversityRon Zielker                                       Ohio Dominican UniversityLibrarianCarolyn Sanders                               Central State UniversityReview TeamAlice Taylor                                       University of Rio Grande

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.