MATH3901 Online Resources
Introduction
This page relates to MATH3901
Metric Spaces as it was given in the year 2000.
The 1999 exam is available.
See below for tutorial sheets
and lecture notes.
The lecturer for the course was
R. B. Howlett,
Room 523 Carslaw Building.
(Email bobh@maths.usyd.edu.au).
Course objectives
 To gain proficiency in dealing with abstract
concepts, with emphasis on clear explanations of such concepts
to others.
 To gain proficiency in the art of writing proofs.
 To gain familiarity with the concepts of "metric space"
and "topological space", and to see how these provide a
context in which standard concepts of mathematical analysis,
such as convergence and continuity, can be studied.
 To understand the concepts of completeness and compactness
of metric spaces.
 To understand the Contraction Mapping Theorem, and see how it
can be applied to prove the existence of solutions of equations
of various kinds.
Reference books
Students may find the following books of use.
 "An Introduction to Topology and Modern Analysis", by
G. F. Simmons
 "Introduction to Metric and Topological Spaces", by
W. A. Sutherland
 "Introductory Functional Analysis with Applications", by
E. Kreyszig
 "Metric Spaces" by E. Copson
Lecture notes
All notes and other course material accessible from this
page are subject to copyright. Persons other than enrolled
students at the University of Sydney must obtain the author's
permission if they wish to reproduce this material for any
purpose other than their own private study.
To read these pdf files you will need Adobe's Acrobat Reader
(which is free). Click the icon below to go to the Acrobat Reader
download page at Adobe's web site. Windows and Macintosh
users can alternatively obtain Acrobat Reader from a local
University of Sydney site
(Macintosh,
Windows).
Note that these are the lectures from the year 2000.
They may be totally different from this year's version of the course!
Tutorials and assignments
Here are the tutorial questions from 2000.
There is probably little overlap between these
and this year's tutorials.
