Discrete Mathematics

This semester-long course develops the fundamental theory, structures, and techniques of discrete mathematics. Discrete mathematics is an extremely broad and diverse subject, with a variety of connections to other branches of mathematics (including number theory, abstract algebra, and others), as well as applications to fields outside of mathematics (including computer science, optimization, operations research, and engineering). Topics that we will explore in this course include enumerative combinatorics, partitions, generating functions, principles of inclusion and exclusion, induction and recursion, and introductory graph theory. This challenging course provides an ideal environment for students to improve and deepen their abilities to observe patterns, engage in mathematical reasoning, formulate conjectures, and construct rigorous mathematical proofs. We will learn how to prove results and solve problems that may be somewhat different than those that students have seen previously, and we will develop the foundations and mathematical maturity necessary to be broadly successful in higher-level mathematics (and other fields).