Topology (MATH31052)
- Lectures: via lecture notes and Podcasts
- Tutorials: via discussion board (starting from Tuesday each week) and
online life tutorials (Friday 10:00-11:00)
💬 Announcements
- The coursework has been marked. You can find your mark on Blackboard. Individual feeback is given via Turnitin. Solutions and generic feedback can be found here.
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- Week 9
- Fundamental Group, Applications (Brouwers Fixed Point Theorem)
- Week 10
- The Fudamental Group of the Circle
- Week 11
- Applications (Fundamental Theorem of Algebra), Revision
- Week 12
- Revision
- Important The deadline for coursework submissions has been pushed back by one week. The new deadline is 13:00 Friday 27 March.
💬 Discussion Topics
Background material
Course topics
1. Topological Equivalence
What is Topology? When are two subsets of Euclidean space equivalent from the view point of topology? How to check that two subsets are or are not topologically equivalent?2. Topological Spaces
Which data determines the topology of a subset of Euclidean space? How to generalise the idea of topological equivalence?3. Constructing New Spaces: Subspaces and Product Spaces
How to construct new topological spaces out of existing ones?4. Constructing New Spaces: Quotient Spaces
Is there a natural topology on the set of equivalence classes of a topological space?5. Hausdorff Spaces
How to define the limit of a sequence in a topological space? How to ensure, that limit points are unique?6. Compactness
How to generalise the Bolzano-Weierstraß Theorem to topological spaces?7. The Fundamental Group
An algebraic invariant of topological spaces.- Homework exercises, solutions will appear later at this place
8. The Fundamental Group of the Circle and Applications
- Homework exercises, solutions will appear later at this place
Weekly in-class exercises
Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12,Assessment and Feedback
Feedback
You will receive feedback on your understanding in this course- from the coursework
- during the tutorial
- from the online quizzes
- during my office hour, and
- via the generic feedback (and exam script viewing) on the final exam.
Coursework
The coursework is a take-home test. Starting from week 5 you will find the questions in the following PDF document.
You are encouraged to have a look at Manfred Lehn's valuable advice on how to work on problem assignments. The solutions have to be submitted via Blackboard/TurnitIn before 13:00 on Friday 27 March. The weighting of the coursework will be 20% of the final mark.
Examination
The format of the exam paper will be the same as in the last year, but different from previous years. There will be one section with six mandatory questions.
Solving the homework exercises is meant as an effective preparation for the exam. You might also have a look at the past papers below.