Last modified: 22 May 2019 17:07
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.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
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:
This course alternates with MX4549 Geometry.
Information on contact teaching time is available from the course guide.
1st Attempt: 1 two-hour written examination (80%) and continuous assessment (20%)
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.
In-course assessment will be marked and feedback provided to the students.