MATH20122: Course Materials

Important || Introduction || Week 4 Test || Lecture Notes and Problems || Solutions to problems ||
Starter Problems || Past Examination Papers || This Year's Examination Paper || Corrections ||

Last updated 20 June 2018


The structure of the 2018 examination paper will be the same as that of 2017 (and therefore different from those of 2010--2016), so every question will be compulsory. Full details and sample papers are given below.


Please read this introduction to the lecture notes before the course begins. The recommended course text is Wilson Sutherland's book 'Introduction to Metric and Topological Spaces', OUP 2009.

Feel free to email me for assistance throughout the semester; but my preferred mode of communication is face-to-face, after lectures or during tutorials. This ensures better feedback in both directions. I shall try to use the new video technology to make proper podcasts of each lecture, so please shout out if I forget to wear the microphone!

Here is the course timetable.

Week 4 Test

The aim of the test is to encourage you to revise the foundations of the course as soon as possible, and to give you the chance to gain credit for learning the basics; it is not designed to ask awkward questions that will catch you out.

The subject matter of the test will be the first six lectures only. All definitions and examples of metrics should be learned, together with proofs that the various metrics satisfy the required axioms. If you have completed the Problems for weeks 1, 2, and 3 you will be very well prepared; their solutions will be online at least five days before the test.

Here are the solutions to the 2018 test, plus my feedback (coming soon).

Scripts will be returned in your Feedback Tutorial classes, where one-to-one feedback will be available.

Lecture Notes and Problems

The lecture notes for each of the 6 chapters will be posted here before they are begun in class; there will be one or two associated problem sheets, for discussion in the weekly feedback classes.

There are no Problems for week 4, so that everyone can focus on revision for the test.

Solutions to Problems

The solutions will be posted here during the week following the relevant feedback class.

Starter Problems

Just to help you to get started - by popular demand!!

Past Examination Papers

I hope the following feedback will help you to avoid some common ways of losing marks!

Here are solutions to the 2014 and 2015 examinations as well.

This Year's Examination Paper

The 2018 examination paper will have the same structure as that of 2017 (which was in a new format). It will consist of four compulsory questions. Every question will contain four parts, worth 5 marks each; this gives 20 marks per question,and 80 marks in total. The August resit will adopt the same format. The overall style and content of the questions will be unchanged from previous years.

To help with revision, here is a version of the 2011 examination paper in the new format, together with solutions and a marking scheme.

The subject matter of this course is main-stream pure mathematics, and cannot exist (nor be applied) without rigorous proofs. The examination paper will therefore ask for certain proofs from the lecture notes, although they will mainly be the type which input definitions and data, and rearrange them to produce the required output. The following list includes all rigorous proofs that are required for the 2018 May and August examinations.

Proofs that will never be required are:


Minor corrections and clarifications may be made to the notes whenever the need is brought to my attention. If major changes are required, they will be announced in lectures and posted here.