Enumerative Combinatorics, Volume 1, (often referred to as EC1), by Richard Stanley. You can download the 2nd edition of EC1 and its errata from this webpage.
We will first review basic enumerative combinatorics in chapter 1, and then cover topics on integral polytopes and Ehrhart theory. We will finish with parts of chapter 3 in EC1.
Reference for material on Ehrhart theory:
Compute the Continuous Discretely: Integer-point Enumeration in Polyhedra, by Matthias Beck and Sinai Robins. A pdf version of the second edition is available on here.
Homework will be assigned on the homework webpage, and collected in the class on the due date. You will have at least one week between the homework is posted and the due date. Please go to the webpage for details.