MAT 204 Discrete Mathematics
Discrete Mathematics approaches questions that are finite in nature. Combinatorics provides formulas for the numbers of certain mathematical "objects". An example is to find the number of different ways one can fill a given rectangle with dominos. With the rise of the computer in the second half of the last century, optimization problems became more prominent, where one is supposed to find a "best" substructure in a given discrete structure. An example is to find a shortest path from A to B in a finite network. Counting principles, from simple ones to recurrence relations and generating functions, are presented, and algorithms for optimization problems on different discrete structures, like graphs, partially ordered sets, and others, are introduced and analyzed. The roles of proofs and algorithms for these questions are discussed thoroughly. Public key cryptography is also covered.