This page contains information about MATH3901
**Metric Spaces**.

Information concerning senior level mathematics courses at the University of Sydney can be accessed via the World Wide Web as follows: Start from the School front page

http://www.maths.usyd.edu.au:8000/follow the link to

http://www.maths.usyd.edu.au:8000/u/UG/SM/MATH3901/as well as information and links for other courses.

Lectures for the course are held at 9:00 am on Tuesdays in Carslaw 275 and at 9:00 am on Thursdays in Carslaw 275. Students should also attend a tutorial each week, starting in the 2nd week of the semester. There are two tutorials available, one at 11am on Wednesdays in Carslaw 360, the other at 2pm E Av 403 11 am on Wednesdays in Eastern Avenue 403.

The lecturer for the course is Dr K-G Choo, Room 614 Carslaw Building. He may be contacted by email to kooc@maths.usyd.edu.au

- 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.

There will be a two-hour examination in June. More details on this will be given on the Examination Information Sheet which will be handed out before Stuvac.

Assessment for the course will be based on a two-hour final examination, which will be marked out of 100 and two assignments, which will be marked out of 5 each. The final mark is the better mark of

{examination mark, 90\% of Exam mark + 10\% of Assignment mark}

There will be 2 assignments each worth 5\%, to be collected on the following days: Thursday 5th April, Thursday 23rd May. Assignments may not be submitted by fax.

Note that while students are encouraged to discuss assignment problems among themselves, each person's final submitted work must be the product of individual effort, independent of the written work of others. Evidence of copying and plagiarism in assignments will be penalised according to University regulations.

My official office hours are Tuesday and Wednesday from 1pm to 2pm. However, I am also happy to see you to discuss the course and help you with your work at other times. Please call at my office anytime, or phone to make an appointment.

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

The textbook for the course is "Lectures on Metric Spaces", by K-G Choo. It will be available for purchase from KOPYSTOP (36 Mountain Street Broadway).

Interested students can also consult the lecture notes for last year (2000) given by Dr R. B. Howlett. For solutions to both tutorials and assignments, click MATH3901SOL Questions and Solutions

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), but this is not guaranteed to give you the latest version.

Tutorial solutions are also available from KOPYSTOP (Mountain Street, Broadway).

February 22 2000