620-353 Discrete Mathematics

25 points from the following: 200-level science mathematics subjects, 200 level science statistics subjects, and computer science 433-253.

Discrete mathematics is concerned with the study of objects which are finite in number and typically computable. At a computational level one seeks efficient algorithms for the listing and counting of the objects. Theory provides a way to these algorithms, and further provides links between seemingly disparate areas of discrete mathematics.

The main topics to be covered are enumeration and listings; ordered sets and lattices; designs, codes and finite geometry; automata, grammars and languages; and physical combinatorics. Designs are relevant to statistics, codes to communication engineering, grammars and languages to computer science, and physical combinatorics to mathematical physics.

A common theme throughout the course will be the constructive aspect of the subject, whereby algorithms are formulated for the enumeration and listing of discrete objects. Through studying this course students will gain an appreciation of the practical use of theoretical analysis, and will also gain experience in the implementation of algorithms.

The subject develops the student's generic skills including analytical thinking, computer programming ability, creativity via problem solving and presenting conclusions in a clear and comprehensive manner.

Up to 48 pages of written assignments during semester (20%) and a 3-hour end-of-semester written examination (80%).