Winter 2015
Course meets: Tuesday and Thursday 1:102:30 in 4088 East Hall.
Instructor: Sergey Fomin, 4868 East Hall, 7646297, fomin@umich.edu
Office hours: Tuesday 2:404:00 and Thursday 4:105:30 in 4868 East Hall.
Grader: Benjamin Branman, bbranman@umich.edu.
Course homepage: http://www.math.lsa.umich.edu/~fomin/566w15.html
Level: introductory graduate/advanced undergraduate.
Prerequisites: Familiarity with formal proofs, and with basic notions of combinatorics. Linear algebra will be used throughout.
Student work expected: several problem sets.
Synopsis: This course is an overview of applications of algebra (mostly linear algebra) to combinatorics (mostly enumerative combinatorics). Topics include: introduction to algebraic graph theory; applications of linear algebra to enumeration of matchings, tilings, and spanning trees; combinatorics of electric networks; partially ordered sets, integer partitions, and Young tableaux. The course will emphasize problem solving (as opposed to theorybuilding).
Optional text: R. P. Stanley, Algebraic Combinatorics: Walks, Trees, Tableaux, and More, Springer, 2013. The text of this book (without exercises) is available at the link above.
Additional texts (none required):
Topics covered (very tentative list, subject to change):
