Abstract

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum automorphism groups of finite graphs. We discuss here this question, notably with a number of negative results.

with Teo Banica, Glasgow Math J., to appear. Arxiv link here.

Differentiation Test

Test Tuesday 20 April 19:30 to 20:45. Five questions, one for each of the five sections in Chapter 3.

You can find old (e.g. Chapter 3) videos on my YT channel here. (Links to an external site.)

One more video that is actually Chapter 3 material (and the recording was a little messed up so no live writing… a new version will be in the Week 11 lectures.):

Week 10

Lectures

Revision of integration and integration by parts.

Here are last year’s lectures of the same material:

I recorded a lot of this material before in a live lecture: press here to watch live version (Links to an external site.) (84 minutes).

Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises. 

Try:

  • p. 165, Q.1-13
  • p. 171, Q.1-5

Additional Exercises: p. 171, Q. 6-9

Submit work for Canvas feedback by Sunday 18 April for video feedback after Monday 19 April.

Outlook

Week 11

Perhaps of the order of 1.5 hours of lectures on completing the square (Links to an external site.), and work (Links to an external site.).

Week 12

Perhaps of the order of 1.5 hours of lectures on centroids (Links to an external site.) of laminas and centres of gravity of solids of revolution (Links to an external site.).

Weeks 13 and 14

I will continue to provide learning support.

Assessment Schedule

Week 11  – 25% Differentiation Test (Zoom Tutorial in Week 10, after Easter)

Week 14 – 25% Integration Test (Zoom Tutorial in Week 13)

Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

Student Resources

Please see Student Resources (Links to an external site.) for information on the Academic Learning Centre, etc.

Assessment Corrections

Have finally been completed. Please check your grade and if you have any queries please don’t hesitate to email me.

Assessment 4

Written Assessment 2 will not be entirely unlike Written Assessment 1. The Week 12 Zoom will be Monday 26 April 15:00 instead of Tuesday 27 April.

25% Written Assessment 1, based on Weeks 6-10, so everything from p.74 to 106.

It will be a one hour assessment, but I am going to give ye 15 minutes grace, as well as 15 minutes to upload. The test will run therefore from 09.30 to 11.00, Tuesday 27 April. It is open book — you can use your manual, any Canvas materials, as well as Excel/VBA.

40% of the marks will be for Section 1.9

30% of the marks will be for Section 2.1

40% of the marks will be for Section 2.2

Academic Dishonesty will not be accepted and suspected breaches, such as communication with others during the assessment, will be pursued in line with this policy (Links to an external site.) (Links to an external site.)

Week 10

Lectures

 This (Links to an external site.) explains the connection between the Heat Equation and the Jacobi Method approximations to the Laplace Equation

There is a longer, more in-person (old, last year) version of the above material. How different they are I am not too sure.

Theory Exercises and Q & A

Q&A on Tuesday 13 April as normal: p.104, Q.1-3

Week 11

No more lectures, no more labs: you will focus on VBA Assessment 2. Q&A on Tuesday.

Week 12

No more lectures, no more labs: you will focus on Written Assessment 2. Q&A on Monday.

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

Student Resources

Please see Student Resources  download  for information on the Academic Learning Centre, etc..

You have to put time to work on Chapter 3:

  1. because without doing so you could be very, very lost on 35% Assignment 3, and
  2. because if you are going into Level 8 Structural Engineering it will be assumed that you are competent with the Chapter 3 material

Assignment 1 & 2 Corrections

These have finally been released. Apologies for the delay. Any queries do not hesitate to contact me.

Week 10

Lectures

No lectures: all MATH7021 time to be invested into Chapter 3 and Assignment 3. See Week 11, below, if you have completed Assignment 3 and are hoping to look ahead.

Exercises

As I send this, there are two slots for feedback over Easter with deadlines of today, 5 April, for feedback, tomorrow, 6 April, and 12 April for feedback 13 April.

If you are up to date on the Week 7 exercises, put some time into:

  • p.127, Q.1-11

Additional exercises p.130, Q.12-19.

Submit work for Canvas feedback by Monday 19 April for video feedback after Tuesday 20 March.

Weeks 11 and 12

Weeks 11 and 12 will be given over to Chapter 4. Perhaps of the order of 2 hours of lectures on Double Integrals (Links to an external site.) in Week 11 and of the order of 2 hours of lectures on Triple Integrals (Links to an external site.). Students who have already submitted Assignment 3 can look at the old lectures. The material is exactly the same… for the sake of of doing honest work I will be rerecording for Weeks 11 and 12, but if you want to get ahead you can watch these:

Week 11:

Week 12:

Re: Section 3.5 Systems of Differential Equations (Links to an external site.); important for next year, won’t be examined this semester but will get ye the notes and lectures before the end of year (so as to have them as a reference for next year).

Assignments

35% Assignment 1 on Chapter 1 — due end of Week 5, 28 February.

15% Assignment 2 on Chapter 2 — due end of Week 7, Sunday 14 March

35% Assignment 3 on Chapter 3 — due end of Week 11, Sunday 25 April will be released soon

15% Assignment 4 on Chapter 4 — due end of Week 13/14/15, (7/14/21 May) tbd

Student Resources

Please see Student Resources (Links to an external site.) for information on the Academic Learning Centre, etc.

Abstract

An exposition of quantum permutation groups where an alternative to the ‘Gelfand picture’ of compact quantum groups is proposed. This point of view is inspired by algebraic quantum mechanics and posits that states on the algebra of continuous functions on a quantum permutation group can be interpreted as quantum permutations. This interpretation allows talk of an element of a compact quantum permutation group, and allows a clear understanding of the difference between deterministic, random, and quantum permutations. The interpretation is illustrated with the Kac-Paljutkin quantum group, the duals of finite groups, as well as by other finite quantum group phenomena.

Arxiv link here.

Easter might provide extra time to put into Chapter 3.

Matrices Test — Corrections

I have a bit of a backlog of corrections but hopefully I can get these to ye before Easter Sunday.

Week 9

Lectures

Final two sections of Chapter 3:

Here are last year’s lectures of the same material:

Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises. 

Try:

  • p. 143, Q. 1-5 [Note these exercises are interleaved – there are questions here from earlier sections in Chapter 3]
  • p. 150, Q. 1-6 [Note these exercises are interleaved – there are questions here from earlier sections in Chapter 3]

Additional Exercises: p. 143, Q. 6, p. 151, Q.7-8, 9-10

Submit work for Canvas feedback by Sunday 28 March for video feedback after Monday 29 March.

Outlook

I will be providing learning support over Easter.

Looking further ahead, to after Easter, a good revision of integration/antidifferentiation may be found here. Here is some video of revision of antidifferentiation.

Week 10 

Perhaps of the order of 1.5 hours of lectures on starting Chapter 4 on (Further) Integration with a revision of antidifferentiation, and a look at Integration by Parts. We will use implicit differentiation to differentiate inverse sine.

Week 11

Perhaps of the order of 1.5 hours of lectures on completing the square, and work.

Week 12

Perhaps of the order of 1.5 hours of lectures on centroids of laminas and centres of gravity of solids of revolution.

Assessment Schedule

Week 11  – 25% Differentiation Test (Zoom Tutorial in Week 10, after Easter)

Week 14 – 25% Integration Test (Zoom Tutorial in Week 13)

Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

Student Resources

Please see Student Resources for information on the Academic Learning Centre, etc.

Assessment Corrections

I cannot promise at this point when these will be completed. It is my intention to have these corrected before the end of Week 9. Watch this space.

Assessments 3 and 4

I will give proper notice for VBA Assessment 2 by the end of Week 9 and for Written Assessment 2 during Easter.

Week 9

Lectures

There is a longer, more in-person (old, last year) version of the above material: 

Lab 7

See VBA Lab 7

Theory Exercises and Q & A

Q&A on Tuesday as normal:

p.97, Q. 1,2 and p. 98 exercises

Week 10

I have linked here to last year’s videos but will be recording fresh videos. How different they will be I am not too sure.

Outlook

Week 11 and 12

Lectures

None. Perhaps additional tutorial time in Week 11 for Written Assessment in Week 12.

Labs

We will do our last lab, Lab 8 in Week 10. VBA Assessment 2 in Week 11.

Assessment

This is provisional and subject to change.

  1. Week 6, 25% First VBA Assessment, Based (roughly) on Weeks 1-4
  2. Week 7, 25 % In-Class Written Test, Based (roughly) on Weeks 1-5
  3. Week 11, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9
  4. Week 12, 25% Written Assessment(s), Based on Weeks 6-10

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

Student Resources

Please see Student Resources  for information on the Academic Learning Centre, etc..

You have to put regular time to work on Chapter 3:

  1. because without doing so you could be very, very lost on 35% Assignment 3, and
  2. because if you are going into Level 8 Structural Engineering it will be assumed that you are competent with the Chapter 3 material

You need to get cracking on Chapter 3.

Assignment 1 & 2 Corrections

I am experiencing a hardware issue at the moment and it is making it difficult to get corrections done.. My promise is to complete corrections of both Assignment 1 and Assignment 2 before the end of Week 9. Sorry for the delay.

Week 9

Lectures

No lectures in Week 9. If you are behind please put big time into Chapter 3, catching up.

Exercises

If you are up to date on the Week 7 exercises, put some time into:

  • p.127, Q.1-11

Additional exercises p.130, Q.12-19.

Submit work for Canvas feedback by Monday 29 March for video feedback after Tuesday 30 March.

Outlook

In Week 10 you will also spend all your time doing Chapter 3 Exercises/Assignment 3. It is my intention to continue providing learning support throughout the Easter break.

Section 3.5 Systems of Differential Equations. is important for next year but I have messed up and so it will not be examined. I will record lectures and fill in the notes for ye though during Easter once I am caught up on corrections.

Weeks 11 and 12 are given over to Chapter 4. Perhaps of the order of 2 hours of lectures on Double Integrals in Week 11 and of the order of 2 hours of lectures on Triple Integrals. If I see that students have submitted Assignment 3 early I may record these earlier than Weeks 11 and 12 (or student could look at the old lectures, the ones that say “integrals” here)

Assignments

35% Assignment 1 on Chapter 1 — due end of Week 5, 28 February.

15% Assignment 2 on Chapter 2 — due end of Week 7, Sunday 14 March

35% Assignment 3 on Chapter 3 — due end of Week 11, Sunday 25 April will be released soon

15% Assignment 4 on Chapter 4 — due end of Week 13/14/15, (7/14/21 May) tbd

Student Resources

Please see Student Resources for information on the Academic Learning Centre, etc.

Things are definitely getting more difficult now folks. I am happy with the work a lot of ye are putting in but from now on everyone will have to work hard if they want to succeed. The good news is that Easter might provide extra time to put into Chapter 3.

Week 8

Lectures

Two sections of Chapter 3:

If you are interested in a very “mathsy” approach to curves you can look at this. I have live video of some of the above material here.

Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises. 

When you are finished with the material for Test 2 (Weeks 4-6) you can try:

  • p. 120, Q. 1-3
  • p. 128, Q. 1-5 [Note these exercises are interleaved – there are questions here from earlier sections in Chapter 2]

Additional Exercises: p. 121, Q. 4-7, p. 130, Q.5-7

Submit work for Canvas feedback by Sunday 21 March for video feedback after Monday 22 March.

Week 9

We will look at partial differentiation and its applications to error analysis.

Looking further ahead, a good revision of integration/antidifferentiation may be found here.

Assessment Schedule

Week 5 – 25% Vectors Test

Week 8 – 25% Matrices Test (Zoom Tutorial in Week 7)

Week 11  – 25% Differentiation Test (Zoom Tutorial in Week 10)

Week 14 – 25% Integration Test (Zoom Tutorial in Week 13)

Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

Student Resources

Please see Student Resources for information on the Academic Learning Centre, etc.

Assessment Corrections

I cannot promise at this point when these will be completed. I am having a hardware issue at the moment which means that I might have to get the ball rolling for ye by correcting the Written Assessment first. Watch this space.

Week 8

Lectures

Some theory background for Chapter 2:

Intro to PDEs and Laplace’s Equation (39 minutes)

The first part of this on finite differences is important for the rest of the semester. The second, a handwaving derivation of Laplace’s Equation. It should give you an idea of what a PDE is, should help consolidate some “thermo”-type stuff, but is theoretical background.

There is a longer, more in-person (old) version of the above material: Intro to PDEs (less than 20 minutes), and Derivation of the Laplace Equation (40 minutes).

Theory Exercises and Q & A

You might want to focus on labs that you didn’t get to look at yet (as well of course as Lab 6)

Week 9

I have linked here to last year’s videos but will be recording fresh videos. How different they will be I am not too sure.

Outlook

Week 10

Lectures

Perhaps of the order of 1.5 hours of lectures on the Heat Equation. We will then be finished the lecture material.

Labs

We will do our last lab in Week 10.

Assessment

This is provisional and subject to change.

  1. Week 6, 25% First VBA Assessment, Based (roughly) on Weeks 1-4
  2. Week 7, 25 % In-Class Written Test, Based (roughly) on Weeks 1-5
  3. Week 11, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9
  4. Week 12, 25% Written Assessment(s), Based on Weeks 6-11

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

Student Resources

Please see Student Resources  for information on the Academic Learning Centre, etc..

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