MATH 4420 - Introduction to Combinatorics II

(MQR-AS, SMR-AS)

Spring. 4 credits. Student option grading.

Prerequisite: MATH 2210, MATH 2230, MATH 2940, or equivalent. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Offered alternate years. Co-meets with MATH 5420.

Staff.

Continuation of MATH 4410, 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). There is an introduction to 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.