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## 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 Level Undergraduate 4 Second Sub Session 15 credits (7.5 ECTS credits) Aberdeen No Dr Richard Hepworth

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### 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.
• 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

### Contact Teaching Time

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

### Teaching Breakdown

Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

### Summative Assessments

#### Design Project: Individual

Assessment Type Weighting Summative 20 4 x Individual Project Homework (5% each)
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Project Report/Dissertation

Assessment Type Weighting Summative 35 Group Project Final Report
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Oral Presentation: Group

Assessment Type Weighting Summative 15 Group Project Video Presentation (pre-recorded)
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Project Report/Dissertation

Assessment Type Weighting Summative 30 Individual Project Final Report
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Formative Assessment

There are no assessments for this course.

### Resit Assessments

#### Resubmission of failed elements (pass marks carried forward)

Assessment Type Summative Individual tasks will be assigned in place of group work
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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