Math 367 syllabus

Combinatorial Enumeration

Course Description:  

An introduction to the mathematical theory of counting. Basic counting principles, permutations and combinations, partitions, recurrence relations, and a selection of more advanced topics such as generating functions, combinatorial designs, Ramsey theory, or group actions and Polya theory. 

Prerequisites:   MA 126 or consent of instructor. MA 320 is strongly recommended.   

Textbook:   Applied Combinatorics (Fifth edition) by Alan Tucker. Published by Wiley (2007).

ISBN: 978-0-471-73507-6. 

Topics:   The topics covered in this course may include basic graph theory, circuits, graph coloring, trees, permutations, combinations, generating functions, recurrence relations, and the inclusion-exclusion principle.  

Learning Objectives

- Understand basic graphs and be able to apply graph theory to solve some to real-world problems.

- Understand a range of graph theoretic results involving Euler cycles, Hamiltonian circuits, graph coloring, trees and searching.

- Be able to solve a wide variety of problems involving ordered and unordered selections.

- Understand the importance of generating functions in combinatorics and be able to use generating functions to solve a variety of combinatorial problems.

- Be able to model and solve a range of combinatorial problems using recurrence relations.

- Understand the Inclusion-Exclusion Principle and be able to use it to solve some combinatorial problems.   

 

Last Updated February 12, 2014