MATH40240 Combinatorics

Academic Year 2020/2021

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.

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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:
I will make pre-recorded lectures available. The timetabled lecture slots will be used for F2F meetings with small groups of students, either in person in a class room, or on-line in a virtual class room. 
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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