MATH 382 Combinatorics


Combinatorics is the field of mathematics which studies counting. Combinatorial problems arise algebra, probability theory, topology, graph theory, and geometry, and have applications in fields such as evolutionary biology, statistical physics, and computer science. Topics selected from basic counting principles, Ramsey theory, the pigeonhole principle, the inclusion/exclusion principle, recurrence relations, generating functions, partially ordered sets, systems of distinct representatives, combinatorial designs, graphs, directed graphs, partitions, combinatorial optimization, enumeration under group action, and an introduction to coding theory.