MTH3160 - Analysis and topology

Leader: Professor Robert Bartnik

Offered

Clayton First semester 2007 (Day)

Synopsis

This unit will explore the power of mathematical generalisation, by showing how rather elementary techniques from the theory of abstract metric spaces, lead directly to proofs of fundamental results on ordinary differential equations and in geometry. Extending linear algebra to infinite-dimensional topological vector spaces leads to the general theory of Hilbert spaces, which has important applications in all areas of mathematics and the physical sciences.

Objectives

On completion of this unit students will be able to demonstrate: an understanding of the basic topological properties of metric spaces, and their applications to problems in other areas of mathematics; an understanding of Hilbert spaces and some of their applications; and communication skills and team work as appropriate for the discipline of mathematics.

Assessment

Three assignments: 10% each
Final examination: 70%

Contact hours

Three hours of lectures and one hour support class per week.

Prerequisites

MTH2021

Co-requisites

MTH2140 or MTH3140