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MATH3901 Online Resources


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

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).

Download Acrobat Reader

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.