MATH237 - Mathematics IIC
For many centuries, mathematics has drawn the greater part of its inspiration from physics. Over the past fifty years, computing has generated many interesting problems which have stimulated new areas of mathematical research. As a result, the emphasis in mathematics has shifted somewhat from the continuous towards the discrete. The purpose of this unit is to give a grounding in discrete mathematics. It is important preparation for both theoretical computing and abstract algebra.
In the computational half of this unit, the unifying theme is the concept of a language as a system of character strings obeying certain rules. Although one tends to think of computers as devices for performing calculations, it is better to think of them as machines for manipulating strings of symbols. We shall study languages in general, as well as the connection between languages and machines that manipulate them. Finite state machines and finite state automata are important mathematical models of the computing process. They are used to answer a number of theoretical questions such as giving a finite description of a language that contains infinitely many strings.
In the mathematical half of this unit, the study of algorithms is the unifying thread. We shall study mathematical techniques such as inclusion-exclusion, generating functions and recurrence relations. Graphs, trees and networks are fundamental data structures for computing, and form a natural way for representing problems of transportation, scheduling and communication.
Prerequisites: MATH135(P) or corequisite MATH132 or corequisite MATH133.
Corequisites: MATH136 or COMP224 or COMP225 or ISYS224 or MATH132 or MATH133.
Not Counted for Credit With: None.