Math 273: Combinatorics I
(Graduate combinatorics, 1st semester)
Fall 2023
Instructor: 
Sam Hopkins (call me "Sam") Office: Annex III (Graduate School)  #220 Email: sam.hopkins@howard.edu 

Classes: 
MonWedFri, 12:10pm1:00pm  
Course format: 
Online (via Zoom: link will be emailed)  
Office hours: 
By appointment (email me to set up a time)  
Course content: 
This is the 1st semester of graduate combinatorics. 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 cover the following:


Prerequisites: 
Calculus, linear algebra, undergraduate algebra (groups, rings, fields)  
Main texts: 
R.P. Stanley, Enumerative combinatorics, Vol. I, 2nd ed. F. Ardila, Algebraic and geometric methods in enumerative combinatorics, Part 1. Problems will come from Stanley, but the lectures will more closely follow Ardila. 

Other nice sources: 
H. Wilf, generatingfunctionology. B. Sagan, Combinatorics: the Art of Counting.  
Syllabus: 
Click here for the class syllabus.  
Class notes: 
The following notes are from the Fall 2021 iteration of the class, which we are closely following: Batch 1; Batch 2; Batch 3; Batch 4; Batch 5; Batch 6; Batch 7; Batch 8; Batch 9 (Change "_bw.pdf" to "_gray.pdf" for grayscale versions.) 

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 with whom they collaborated. 

Homework assignments: 
Problems will mostly be exercises from Stanley, plus some problems I come up with.
