MAT 415 Combinatorics

Discrete Mathematics is a branch of mathematics concerning countable discrete structures. Discrete problems arise in many different areas of pure mathematics ranging from abstract algebra to probability theory, but there are many applied uses of combinatorial knowledge in fields such as computer science or physics. The goals of the course will be to develop skills in identifying typical problems and formulating, solving, and interpreting appropriate models. Topics of the course will include the Pigeonhole Principle, Ramsey Numbers, Algorithms (Greedy, Breadth-First, Depth-First, Brute Force), recurrence relations, Graph Theory (graphs, digraphs, trees, bipartite graphs, matchings, coloring, graph isomorphisms, planarity), multisets, compositions, permutations, integer partitions, ordinary and exponential generating functions, the Principle of Inclusion and Exclusion, and other topics as time or student interest permits.


1 Course Credit