MATH 431-01, Topology, Spring 2008

Abstract

Much like geometry, topology is a study of how points sit in a space. What distinguishes topology from geometry is the type of transformations allowed before you really consider an object as “changed’’. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. This class will focus on point set topology which is not only interesting in its own right, but is crucial to the study of other mathematical fields such as real analysis and functional analysis. Keeping with the tradition of topology, this class will be taught by the Moore method in when the students will be given an outline of the subject via list of definitions, examples and theorems and the students will be expected to fill in the details. In this sense, the students themselves will be “writing the book’’ for the class. The students work will be presented in two ways: classroom presentation and turned-in homework.