Introduction to Combinatorics II

4.0 credits · Graduate

Continuation of MATH 5410, although formally independent of the material covered there. The emphasis here is the study of certain combinatorial structures, such as Latin squares and combinatorial designs (which are of use in statistical experimental design), classical finite geometries and combinatorial geometries (also known as matroids, which arise in many areas from algebra and geometry through discrete optimization theory). We introduce partially ordered sets and lattices, including general Möbius inversion and its application, as well as the Polya theory of counting in the presence of symmetries. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.