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  6. MX4540: KNOTS

MX4540: KNOTS (2016-2017)

Last modified: 28 Jun 2018 10:27


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
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Richard Hepworth

Qualification Prerequisites

None.

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

  • Any Undergraduate Programme (Studied)
  • Either Programme Level 3 or Programme Level 4
  • Either MX3036 Metric and Topological Spaces (Studied) or MX3532 Metric and Topological Spaces (Passed)

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.

Contact Teaching Time

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

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%) and continuous assessment (20%)

Resit: If required and permitted by Regulations, there will be 1 two-hour written examination.
Only the marks obtained at the first attempt can count towards Honours classification.

Formative Assessment

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination. Students do practice questions in tutorials allowing formative assessment and feedback from the tutor.

Feedback

In-course assessment will be marked and feedback provided to the students.

Course Learning Outcomes

None.
 

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