DRAFT. This version of the catalogue is a draft version and subject to change.
Unless you have been specifically directed here, you probably want to use the main catalogue.
Last modified: 23 Apr 2026 13:16
A knot is a closed curve in three dimensions. How can we tell if two knots are the same? How can we tell if they are different? This course answers these questions by developing many different "invariants" of knots. It is a pure mathematics course, drawing on simple techniques from a variety of places, but with an emphasis on examples, computations and visual reasoning.
| Study Type | Undergraduate | Level | 4 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
|
||
Knots have been studied mathematically since the 19th century, and knot theory connects with many other areas of pure maths and even theoretical physics. This course concentrates on knot invariants: numbers, polynomials or groups that try to "measure" properties of the knots. Classic invariants such as the colouring group will lead to more modern ones like the Jones polynomial, which was only discovered in the mid-1980s.
Topics will include the following:
Syllabus
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour exam |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
There are no assessments for this course.
| Assessment Type | Summative | Weighting | ||
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Best of (resit exam mark) or (resit exam mark with carried forward CA marks) |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Understand | Understand the idea of invariants of knots. |
| Factual | Remember | Be able to define the invariants covered in the course (including linking number, colourability, Alexander polynomial, Jones polynomial, genus). |
| Procedural | Apply | Be able to compute the invariants covered in the course in a variety of examples. |
| Procedural | Understand | Be able to prove the invariance of the invariants covered in the course, using Reidemeister moves. |
| Procedural | Analyse | Be able to distinguish knots and links using their invariants. |
| Procedural | Create | Be able to use the techniques of the course to understand and work with invariants and constructions not explicitly covered. |
We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.
