MATH7019: Winter 2019, Week 3

September 26, 2019 in MATH7019 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Assessment 1

Assessment 1 has been emailed to all of you.

Start ASAP.

The hand in date in Friday 11 October 2019. Work handed in late shall be assigned a mark of zero. The hand in time is presently 13:00 but this may be extended to later in that day.

Telegram App

For those who have already contacted me, I hope to have this set up for Monday.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

Tutorials

The “your choice” split worked well last week and we will continue it this week.

You choose to attend either tutorial:

  • 11:00 in A243L
  • 12:00 in A213B
Tutorials are the most important thing in your learning.

Week 3

We had a tutorial for the Monday lecture — on linear least squares.

Then we finished looking at Chapter 1, and started looking at Chapter 2: Differential Equations — with a particular emphasis on Beam Equations.

Week 4

We will probably not have a tutorial on Monday, but instead plough into chapter two: we will hopefully start looking in particular at simply supported beams.

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MATH6040: Winter 2019, Week 3

September 26, 2019 in MATH6040, MATH6040 - Day | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Test 1

Test 1, worth 15%, takes place from 16:00 to 16:50 sharp, Monday 14 October in the Melbourne Hall (rows I-K). I have emailed your 15:00-16:00 lecturers so that they will leave you plenty of time to get to the Melbourne.

There is a sample on P.46 of the notes to give you an idea of the length and layout only.

Almost everything in Chapter 1 is examinable. Additional practise questions may be found by looking at past exam papers (usually vectors are Q. 1, sometimes Q. 2).

You will want to be familiar with all the concepts in the Vector Summary, P. 42-45.

Telegram App

For those who have already contacted me, I hope to have this set up for Monday.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

Diagnostic Test

I will be in touch with those who have taken the diagnostic test.

Academic Learning Centre

If you are a little worried about your maths this semester, perhaps after the Quick Test or in general, I would just like to remind you about the Academic Learning Centre. Most students received slips detailing areas of maths that they should brush up on. The timetable is here.

Week 3

We started working with the cross product and looked at the applications of vectors to work.

We had some active learning time with a Concept MCQ: Vector or Scalar?

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MATH7019: Winter 2019, Week 2

September 22, 2019 in MATH7019 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Manuals

The manuals are available in the Copy Centre. Please purchase ASAP. More information has been sent via email.

Telegram App

I am exploring the possibility of setting up a classroom group chat that would have the functionality of WhatsApp without having your phone number made public.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

Tutorials

There are two tutorial slots for MATH7019 this semester
Both Fridays:
  • 11:00 in A243L
  • 12:00 in A213B
Provisionally, you will be allowed attend either tutorial. The problem with this is that if everyone chooses to attend the 11:00 tutorial, this tutorial will be too full and you will not get the one-to-one help you need.
My hope is that some students recognise this and attend the 12:00 tutorial and perhaps we have something a large tutorial of perhaps <20 students at 11:00 and a smaller tutorial of perhaps <10 students at 12:00.
The students in the smaller tutorial will get more help.
We will try this for two weeks. This Friday might be a disaster (maybe not), and if next Friday is too I will do a split, and have the split alternative between 11/12 and 12/11.
I hope that is kind of clear. Tutorials are the most important thing in your learning.

Week 2

We introduced Lagrange Interpolation and Least Squares curve fitting. We spoke about the Pearson correlation coefficient. We started looking at non-linear models:

Y=a\,\theta_1(X)+b\,\theta_2(X)

Week 3

We will continue looking at non-linear models.

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MATH6055: Winter 2019, Week 2

September 22, 2019 in MATH6055 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Manuals

The manuals are available in the Copy Centre and are required for Monday’s lecture.

Week 2

We looked more at sets and set identities and looked at truth tables.

Week 3

In Week 3 we will look at the Laws of Sets and move onto Cartesian Products and Relations.

Telegram App

I am exploring the possibility of setting up a classroom group chat that would have the functionality of WhatsApp without having your phone number made public.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

We might talk about this again next week.

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MATH6040: Winter 2019, Week 2

September 19, 2019 in MATH6040, MATH6040 - Day | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Manuals

The manuals are  available in the Copy Centre (at a cost of €14) and are required for Monday’s lecture.

Test 1

The 15% Test 1 will be held in the Melbourne Hall, 16:00 Monday 14 October, Week 6. Ye all have lectures at 15:00 but I will request from your lecturers that ye be left go on time.  There is a sample test in the notes.

Telegram App

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

Diagnostic Test

If you haven’t already, you are invited to take the following ‘Diagnostic Test’:

       click here

This ‘Test’ does not go towards your grade, but allows me to give you some feedback on where you are in terms of material you have seen before that will be used in this module.

Academic Learning Centre

If you are a little worried about your maths this semester, perhaps after the Quick Test or in general, I would just like to remind you about the Academic Learning Centre. Most students received slips detailing areas of maths that they should brush up on. The timetable is here.

Week 2

We continued working with the dot product and then introduced the cross product.

Week 3

We will look at the applications of vectors to work and moments. We might begin Chapter 2: Matrices.

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MATH6055: Winter 2019, Week 1

September 13, 2019 in MATH6055 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Week 1

We had one lecture and after listening to me go on about the importance of mathematics to your programme we started the first chapter on Sets and Relations by looking at some number sets. We saw something new with the concept of the power set of a set. We also took the quick test.

Week 2

In Week 2 we will start the first chapter proper. We will see something new with the concept of the power set of a set, and set identities, and we’ll explore Cartesian Products and perhaps introduce relations.

Telegram App

I am exploring the possibility of setting up a classroom group chat that would have the functionality of WhatsApp without having your phone number made public.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

We might talk about this again next week.

Tutorials

Tutorials start properly in Week 2.

  • COMP1C-X: Tuesday at 15:00 in B241L
  • COMP1C-Y: Wednesday at 12:00 in B143

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MATH7019: Winter 2019, Week 1

September 13, 2019 in MATH7019 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Manuals

The manuals are available in the Copy Centre. Please purchase ASAP. More information has been sent via email.

Telegram App

I am exploring the possibility of setting up a classroom group chat that would have the functionality of WhatsApp without having your phone number made public.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

We might talk about this again next week.

FAO: Erasmus Students — Calculators

The Student Resources tab above contains some information about calculators.

Here is a list of some allowed and not allowed calculators.

If you have to purchase a calculator, my recommendation is that you purchase something like a Casio fx-83GT PLUS. This might be available in the CIT shop.

Tutorials

Tutorials, which are absolutely vital, start next week. There may be a split but this might not occur until Week 3.

Week 1

In week one we had one and a half classes. One half class was given over to a general overview of MATH7019 and we spent about an hour introducing the topic of Curve Fitting including Lagrange Interpolation.

Week 2

We will start talking about Least Squares curve fitting.

Quick Test: Academic Learning Centre

I would urge anyone having any problems with material that isn’t being addressed in the tutorials to use the Academic Learning Centre. If you are a little worried about your maths this semester, perhaps after the Quick Test or in general, you need to be aware of this resource. The timetable should be up some time next week.

You will get best results if you come to the helpers there with specific questions. Next week, some students will receive slips detailing areas of maths that they should brush up on.

Assessment 1

Assessment 1 will have a hand-in date the Friday of Week 5, 11 October. The Assignment is in the manual but I must also send on your personal data sets next week.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.

Student Resources

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

Periodicity of Random Walks on Finite Quantum Groups

September 12, 2019 in Quantum Groups, Random Walks on Finite Quantum Groups, Research Updates | Leave a comment

In the case of a finite classical group G, we can show that if we have i.i.d. random variables \zeta_i\sim\nu\in M_p(G), that if \text{supp }\nu\subset Ng, for Ng a coset of a proper normal subgroup N\rhd G, that the random walk on G driven by \nu, the random variables:

\xi_k=\zeta_k\cdots \zeta_1,

exhibits a periodicity because

\xi_k\in Ng^{k}.

This shows that a necessary condition for ergodicity of a random walk on a finite classical group G driven by \nu\in M_p(G) is that the support of \nu not be concentrated on the coset of a proper normal subgroup.

I had hoped that something similar might hold for the case of random walks on finite quantum groups but alas I think I have found a barrier.

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MATH6040: Winter 2019, Week 1

September 12, 2019 in MATH6040, MATH6040 - Day | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Diagnostic Test

If you haven’t already, you are invited to take the following ‘Diagnostic Test’:

       click here

This ‘Test’ does not go towards your grade, but allows me to give you some feedback on where you are in terms of material you have seen before that will be used in this module.

Telegram App

I am exploring the possibility of setting up a classroom group chat that would have the functionality of WhatsApp without having your phone number made public.

If this is something you might be interested in, please download the Telegram app and set yourself up with an @ handle.

We might talk about this again next week.

Manuals

The manuals are  available in the Copy Centre (at a cost of €14) and should be purchased as soon as possible.

Tutorials — Subject to Change — Keep an Eye on Your Timetable

Tutorial for BioEng2A: Wednesdays at 10:00 in B149

Tutorial for BioEng2B: Mondays at 17:00 in B189 (starts this Monday 16 September)

Tutorial for SET2: Mondays at 9:00 in B180 (starts Monday 23 September)

Week 1

We began our study of Chapter 2, Vector Algebra. We looked at how to both visualise vectors and describe them algebraically. We learned how to find the magnitude  and direction of a vector.

Week 2

We will continue working with the vectors and hopefully learn how to add them and scalar multiply them, about displacement vectors,  the vector product known as the dot product and perhaps then introduce the cross product.

Test 1

The test will probably be the Monday of Week 5. Official notice will be given in Week 3. There is a sample test in the notes.

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.

The Ergodic Theorem for Random Walks: from Finite Groups, to Group Algebras, to Finite Quantum Groups

September 6, 2019 in Quantum Groups, Random Walks on Finite Quantum Groups, Research | Leave a comment

Slides of a talk given at Munster Groups 2019, WIT.

Abstract: It is a folklore theorem that necessary and sufficient conditions for a random walk on a finite group to converge in distribution to the uniform distribution – “to random” – are that the driving probability is not concentrated on a proper subgroup nor the coset of a proper normal subgroup. This is the Ergodic Theorem for Random Walks on Finite Groups. In this talk we will outline the rarely written down proof, and explain why, for example, adjacent transpositions can never mix up a deck of cards. From here we will, in a very leisurely and natural fashion, introduce (and motivate the definition of) finite quantum groups, and random walks on them. We will see how the group algebra of a finite group is the algebra of functions on a finite quantum group. Freslon has very recently proved the Ergodic Theorem in this setting, and we present ongoing work towards an Ergodic Theorem in the more general finite quantum group setting; a result that would generalise both the folklore and group algebra Ergodic Theorems.