Content

The first semester will cover general topology while the second semester will cover measure and integration. In more detail, the topics will be

The content will be a mix of general theory and specific examples.

Lectures

Lectures will be online due to Covid. Recordings and slides will be posted here and on Blackboard.

LectureDateTopic(s)VideoSlides
1 13 September 2021 Introduction Video Slides
2 13 September 2021 Comments on reading and writing proofs Video Slides
3 15 September 2021 From R to metric spaces Video Slides
4 20 September 2021 Balls, images, preimages, open and closed sets Video Slides
5 20 September 2021 Topological spaces, Hausdorff topologies Video Slides
6 23 September 2021 Neighbourhoods Video Slides
7 27 September 2021 Where are we going? Video Slides
8 27 September 2021 Directed sets, monotone functions Video Slides
9 30 September 2021 Limits, sums and integrals Video Slides
10 4 October 2021 Introduction to Set Theory Video Slides
11 4 October 2021 Zorn's Lemma, Cardinality Video Slides
12 7 October 2021 Countability, the Cantor Set and Zorn again Video Slides
13 11 October 2021 Indexed collections of sets, products Video Slides
14 11 October 2021 Interior, closure boundary Video Slides
15 14 October 2021 Stronger and weaker topologies Video Slides
16 18 October 2021 Subspace and quotient topologies Video Slides
17 18 October 2021 Product topology Video Slides
18 21 October 2021 Connectedness Video Slides
19 1 November 2021 Compactness Video Slides
20 1 November 2021 More compactness Video Slides
21 4 November 2021 The Extreme Value Theorem, Bolzano-Weierstrass and normal spaces Video Slides
22 8 November 2021 Introduction to metric spaces Video Slides
23 8 November 2021 Boundedness, Lipschitz and uniform continuity Video Slides
24 11 November 2021 Boundedness, Lipschitz and uniform continuity II Video Slides
25 15 November 2021 Filters and convergence Video Slides
26 15 November 2021 Cauchy filters and completeness Video Slides
27 18 November 2021 Another compactness criterion, minimal Cauchy filters Video Slides
28 22 November 2021 Completion I Video Slides
29 22 November 2021 Completion II Video Slides

Text

There is no official textbook for the module but I will post notes here and on Blackboard.

Exams

There will be single exam, covering both terms, at the end of the second term. It will be worth 80% of your course mark.

Tutorials

There are weekly tutorials in the Joly Lecture Theatre on Fridays at 10:00.

Assignments

There will be occasional assignments, which will count for 20% of your course mark. They will be posted here and on Blackboard. Solutions will be posted here once the assignment has been corrected.

AssignmentDate PostedDate DueProblemsSolutions
1 11 October 2021 20 October 2021 Problems Solutions
2 15 November 2021 24 November 2021 Problems

Practice Problems

I will post practice problems approximately weekly. This will not be marked, but I will posted solutions so you can check your work.

Problem SetDate PostedLectures CoveredProblemsSolutions
1 20 September 2021 1-3 Problems Solutions
2 27 September 2021 4-6 Problems Solutions
3 4 October 7-9 Problems Solutions
4 21 October 10-14 Problems Solutions
5 1 November 15-18 Problems Solutions
6 15 November 19-24 Problems Solutions

Discussion board

There is a discussion board available in Blackboard, which you can use to ask any questions you have.