Math 8668: Combinatorial theory
(Graduate combinatorics, 1st semester)
Fall 2019
Instructor:  Sam Hopkins (call me "Sam")  
Office: Vincent Hall 204 Email: shopkins@umn.edu 

Classes:  MonWedFri 2:303:20pm, Ford Hall B60  
Office hours:  MonWed: 10:0011:00am, Vincent Hall 204  
Course content:  This is the first semester of the two semester Math 866869 sequence; Math 8669 will be taught by Chris Fraser in Spring 2020. 

We will study basic combinatorial objects (subsets, multisets, permutations, set/number partitions, compositions, graphs, trees, etc.), their enumeration, and additional structures they carry (such as partial orders). Roughly speaking we will discuss this in the first semester:


Prerequisites:  Calculus, linear algebra, undergraduate algebra (groups, rings, fields)  
Main text:  R.P. Stanley, Enumerative combinatorics, Vol. I, 2nd ed., Cambridge University Press. Available as a pdf online here. 

Other nice sources:  F. Ardila, Algebraic and geometric methods in enumerative combinatorics, Part I.  
H. Wilf, generatingfunctionology D. Stanton and D. White, Constructive combinatorics N. Loehr, Bijective combinatorics 

Class notes:  Batch 1, Batch 2, Batch 3, Batch 4, Batch 5  
Grading:  There will be 3 homework assignments for the semester.  
The grading of the assignments will depend on both the quality and quantity of homework turned in. Beyond that, I expect you to show up to class and be engaged. Collaboration on the homework is encouraged, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.  
Homework assignments:  Problems will be exercises from Stanley's EC1, or these bonus problems (BPs) I came up with.  
