I gave a talk to the Quantum Groups & Interactions Workshop in Glasgow.

Abstract: Woronowicz proved the existence of the Haar state for compact quantum groups under a separability assumption later removed by Van Daele in a new existence proof. A minor adaptation of Van Daele’s proof yields an idempotent state in any non-empty weak*-compact convolution-closed convex subset of the state space. Such subsets, and their associated idempotent states, are studied in the case of quantum permutation groups.

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I gave the same talk to the Non local games seminar and C*-Days in Prague:

Abstract: The first part of the talk will give a post hoc motivation for Banica’s 2005 definition of the quantum automorphism group of a finite graph, and in doing so attempt to build a good intuition for quantum automorphism. Frucht in 1939 showed that every finite group is the automorphism group of a finite graph, and a natural  pursuit in the theory of quantum automorphism groups is to establish quantum analogues of this result.  Based  on a joint work with Banica, the second part of the talk will address this question.

The slides are subtly different: the one for C*-Days is the latest version:

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Assignment 2 – Corrections

I am now promising these be ready for 14:00 Tuesday 2 May and ye can look at your hand-ups in class.

Remarks to poorly answered questions:

Week 12

On Tuesday we looked at triple integration. Then we had tutorial time on Wednesday and Thursday.

Week 13, Review Week

We will go through an exam paper, answer questions, and have tutorial time as appropriate. The Monday is a bank holiday.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Scanned Notes

Go to Canvas -> MATH6004 -> J.P. McCarthy to find some of the notes scanned. I want to scan all the notes but one of your classmates has gone AWOL with my notes.

Quizzes 5

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 11:05-11:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Week 12

We had our quiz on Monday, and after this we will finished our material and then had some extra tutorial time. We did not cover the Gauss-Jordan algorithm for finding the inverse of a square matrix.

Week 13

In the ordinary lecture and tutorial slots we will have classes. In the lectures I will be doing revision by doing this paper:

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Assignment 2 – Submission

Please see this mornings email.

Week 11

We worked on double integration. We had about 55 minutes of tutorial time on Thursday.

Week 12

We will work on triple integration. There will possibly be two tutorials on Chapter 4.

Week 13, Review Week

We will go through an exam paper, answer questions, and have tutorial time as appropriate.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Usually I use the student feedback to get ideas to improve my delivery of a module. As I have referred to numerous times this semester, there are obvious ways to improve my delivery of MATH6004 (e.g. edit out the so-many typos, have more exercises in the manual, etc.), and I know myself how I can improve my delivery for next year.

Now, maybe you might give my ideas I haven’t thought about, but to be honest the main reason I am giving the fully anonymous feedback mechanism to ye is to give you a chance to have your say, and have me listen to you, and if that includes being very critical so be it. It is important to me not just that your voice is listened to but that you have a voice and you are given this opportunity to say your bit.

Scanned Notes

Go to Canvas -> MATH6004 -> J.P. McCarthy to find some of the notes scanned.

Quizzes 4 and 5

Quiz 4 will be based on what we covered in Week 10 and will take place Monday 24 April in the usual lecture venue, 15:05-15:20.

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 11:05-11:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Weeks 11

One thing that is not in the MANUAL is the transpose of a matrix. We covered this on Monday. Two things you want to know:

(1) The transpose of a matrix A is a matrix A^T formed by swapping the rows and columns of A, e.g.

\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}^T=\begin{bmatrix}1 & 4 \\ 2 & 5 \\ 3 & 6\end{bmatrix}

(2) If A is an m\times n matrix then A^T is an n\times m matrix.

We started looking at matrix inverses, and the formula for calculating the inverse of a 2×2 matrix. We learned that not every matrix has an inverse, and how the determinant can be used to determine if a matrix has an inverse. We saw how matrix inverses can be used to solve matrix equations, and how (linear) simultaneous equations can be written as a matrix equation (a linear system), and if the matrix of coefficients has an inverse, the solution of the linear system is unique. We learned that linear systems can also have no solution, or infinitely many solutions, and we saw how Gaussian elimination can be used to see if a linear system that does not have a unique solution has no solutions or infinitely many solutions.

Week 12

We have our quiz on Monday, and after this we will finish Chapter 3 with the Gauss-Jordan algorithm, and then hopefully have some extra tutorial time.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

15% Assignment 1 Comments

15% Assignment 2

Assignment 2 has a hand-in time and date of 11:00 20 April. Assignment 2 is in the manual.

Week 10

This was a critical week for this module: but attendance wasn’t where it should be. There is still a a chance (tomorrow, 30 March) to get in a good solid block of work.

This was a bumper week of tutorials to get you in order for Assignment 2 over Easter.

Week 11

We will work on double integration and when we finish that section we will have tutorials.

Week 12

We will work on triple integration. When finished we will have tutorial time on that topic.

Week 13, Review Week

We will go through an exam paper, answer questions, and have tutorial time as appropriate. The Monday is a bank holiday. This may or may not affect us.

Study

Please feel free to ask me questions about the exercises via email or on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

Weeks 9-10

In lectures we finished off the material. The Wednesday of Week 10 will be a tutorial for the second written assessment.

In VBA, in Week 9, students did the first part of Lab 7 (the second part, the arrays, will not be examinable).

In Week 10, some students looked at Lab 8 to help their understanding of the Heat Equation. for Written Assessment 2.

20% VBA Assessment 2

See Canvas for the assessment information.

40% Written Assessment 2

See Canvas for the assessment information.

Week 11

The two lecture slots will be tutorials.

The lab slot will be VBA Assessment 2.

Week 12

Tutorial-like class in the Tuesday lecture. The Written Assessment is 16:00-18:00. There will be no labs.

MCQ League

The final MCQ will (probably) be corrected this week and the cash-money prizes given out after Easter.

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

20% Test and Quiz 3 Results

The 20% Test results were released in a Canvas announcement, and students can view their script in this week’s labs. The solutions are now in the same announcement if you wish to view these.

I hope to have Quiz 3 corrected by the end of the week.

Quizzes 4 and 5

Quiz 4 will be based on what we covered in Week 10 and will take place Monday 24 April in the usual lecture venue, 09:05-09:20.

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 10:05-10:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Week 9

We will had Quiz 3 20 March at 3 pm in the usual lecture venue. It was based on argument and inference. The timing was not great considering would go on to have a full week of tutorials on argument an inference. However, to balance things out, Quiz 2 was probably too easy, and we are going to have a Quiz 5 in Week 13, and you will be marked out of your four best quizzes. See below.

Week 10

We started the final chapter on Linear Algebra. We had some discussion of vectors, then linear maps, and finally matrices. We are doing matrix arithmetic and the standard matrix representation of a linear map.

Why do we multiply matrices like that?

Weeks 11-12

We will finish the final chapter. We will probably be doing new material right up to the end of Week 12.

I had planned on having a catch-up lecture because I missed a Monday in Week 8. Unfortunately there is no time that suits everyone so that class will have to be cancelled. My apologies.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

15% Assignment 2

Assignment 2 has a hand-in time and date of 11:00 20 April. Assignment 2 is in the manual, and once you finish the exercises in the manual you will be in a great position to start.

15% Assignment 1

These have been corrected and I will bring them with me this week.

Week 8-9

In Week 8, we had good tutorial time on the inverse Laplace transform. Then we finished Section 3.5, the full exam questions.

Then in Week 9, we had a full week of tutorials. Attendance for the double was slack!

Week 10

This is a critical week for this module: please attend properly. This will be a bumper week of tutorials so that you are in great nick to do Assignment 2 over Easter. Students who finish the 19 exercises are invited to start Assignment 2.

Week 11

We will work on double integration and when we finish that section we will have tutorials.

Week 12

We will work on triple integration. When finished we will have tutorial time on that topic.

Week 13, Review Week

We will go through an exam paper, answer questions, and have tutorial time as appropriate. The Monday is a bank holiday. This may or may not affect us.

Study

Please feel free to ask me questions about the exercises via email or on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

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