production
Skip to Content

MX4540: KNOTS (2020-2021)

Last modified: 24 Jun 2020 14:31


Course Overview

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.





Course Details

Study Type Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Richard Hepworth

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

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:

  • Knots and links.
  • Linking number.
  • Colourings,determinants and the colouring group.
  • The Alexander polynomial.
  • The Jones polynomial.
  • The Genus.

Syllabus

  • Knots and links
  • Diagrams and Reidemeister moves
  • Sums, mirrors and reverses
  • The linking number
  • Colourability
  • The determinant
  • The colouring group
  • Alexander Polynomial
  • Jones polynomial: definition, computations, properties
  • Jones polynomial and alternating links
  • The genus of a knot and prime knots

In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 1 during University weeks 25 - 29, 31 - 34, 38 - 39
  • 1 Tutorial during University weeks 26 - 29, 31 - 34, 38 - 39

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

Online forum contribution (assessed through out the course) - 25%

Group project (11 weeks) - 25%

2 x course assessments (1 week each) - 25% each

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

For each assessment on which a student scored E1 or less, the student will complete an appropriate resit assessment, as detailed below.  The course score will then be determined based on the weighted average of the resit assessments, together with those original assessments that scored D3 or above.

Course Assessments:
The student will complete a resit assessment of the same format and covering the same material, again with 1 week to complete the assessment.

Online forum contribution:
The student will be allowed, over the course of 1 week, to make new contributions to the discussion forum, and to make a new choice of the 5 discussions they will submit to the forum.

Group Project:
The student will be given a tailored homework-style assessment, based on the topic of their group project, with 2 weeks to complete the assessment.

Alternative Resit Arrangements for students who took the course in Academic Year 2019/20 and C8 students

Course Assessments:
The student will complete a resit assessment of the same format and covering the same material, again with 1 week to complete the assessment.

Online forum contribution:
The student will be allowed, over the course of 1 week, to make new contributions to the discussion forum, and to make a new choice of the 5 discussions they will submit to the forum.

Group Project:
The student will be given a tailored homework-style assessment, based on the topic of their group project, with 2 weeks to complete the assessment.

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome

Compatibility Mode

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.