MATH40240 Combinatorics

Academic Year 2022/2023

The topic of this module is combinatorial aspects of knot theory. Tentative contents: knots and links; the combinatorial approach: polygonal knots and links; projections and diagrams; Reidemeister moves; knot invariants; colourings; the Alexander polynomial; the Kauffman bracket; the Jones polynomial.

[Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]

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Curricular information is subject to change

Learning Outcomes:

Students should be able to draw a number of named knots and links (unknot, trefoil knot, figure-8 knot, unlink, Hopf link, Whitehead link, Borromean rings, ...).

When presented with a knot (or link), the student should be able to compute the invariants of the knot (or link) that are considered in this module.

Student Effort Hours: 
Student Effort Type Hours
Lectures

18
Small Group

6
Tutorial

6
Specified Learning Activities

30
Autonomous Student Learning

50
Total

110
Approaches to Teaching and Learning:
The intention is to have all contact hours face-to-face.

Some of the lectures may be in blended or on-line format. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH20310 - Groups, Rings and Fields

Equivalents:
Combinatorics (MATH40070)


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Homeworks. Throughout the Trimester n/a Standard conversion grade scale 40% No

100

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Online automated feedback

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