MATH6055: Winter 2018, Week 1

September 14, 2018 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. We saw something new with the concept of the power set of a set.

Week 2

In Week 2 we will look more at sets and set identities, and explore Cartesian Products and perhaps introduce relations.

Tutorials

Tutorials start properly in Week 2.

  • COMP1C-X: Tuesday at 15:00 in B241L
  • COMP1C-Y: Wednesday at 12:00 in B225

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MATH7019: Winter 2018, Week 1

September 14, 2018 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.

Tutorials

Tutorials, which are absolutely vital, start next week.

Week 1

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

Week 2

We will introduce Lagrange Interpolation and start talking about Least Squares curve fitting.
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MATH6040: Winter 2018, Week 1

September 14, 2018 in MATH6040 | 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 must be purchased as soon as possible. More information has been sent out via email.

Tutorials

Tutorial for BioEng2A: Thursdays at 12:00 in B180 A272 STARTS THURSDAY 20/09

Tutorial for BioEng2B: Mondays at 17:00 in B189 STARTS MONDAY 24/09

Tutorial for SET2: Mondays at 9:00 in E15 STARTS MONDAY 24/09

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. Next week, some students will receive slips detailing areas of maths that they should brush up on. The timetable is as below:

Maths/Statistics Support in the ALC (Academic Learning Centre)

Monday

1.00pm-2.00pm

D259

4.00pm-5.00pm

D259

Tuesday

1.00pm-2.00pm

D259

4.00pm-6.00pm

D259

Thursday

10.00am-12.00pm

D259

Friday

11.00am- 1.00pm

D259

Week 1

We only had one lecture but began our study of Chapter 2, Vector Algebra by studying the difference between a scalar (single number) and a vector (list of numbers).

Week 2

We will look at how to both visualise vectors and describe them algebraically. We will learn how to find the magnitude  and direction of a vector, add them and scalar multiply them. We will speak about displacement vectors and introduce the vector product known as the dot product.

Test 1

The test will probably be the Monday of Week 5: if progress with the vectors material is slow, we may push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). 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.

General Mathematical Audience Talk: The Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups

September 1, 2018 in Probability Theory, Quantum Groups, Random Walks on Finite Quantum Groups, Research, Research Updates | Leave a comment

Slides of a talk given at the Irish Mathematical Society 2018 Meeting at University College Dublin, August 2018.

Abstract Four generalisations are used to illustrate the topic. The generalisation from finite “classical” groups to finite quantum groups is motivated using the language of functors (“classical” in this context meaning that the algebra of functions on the group is commutative). The generalisation from random walks on finite “classical” groups to random walks on finite quantum groups is given, as is the generalisation of total variation distance to the quantum case. Finally, a central tool in the study of random walks on finite “classical” groups is the Upper Bound Lemma of Diaconis & Shahshahani, and a generalisation of this machinery is used to find convergence rates of random walks on finite quantum groups.

On Parallel and Perpendicular Lines

June 5, 2018 in A1 Leaving Cert Maths, General, Grinds, Leaving Cert Maths | Leave a comment

The purpose of this post is to briefly discuss parallelism and perpendicularity of lines in both a geometric and algebraic setting.

Lines

What is a line? In Euclidean Geometry we usually don’t define a line and instead call it a primitive object (the properties of lines are then determined by the axioms which refer to them). If instead points and line segments – defined by pairs of points P,Q – [PQ] are taken as the primitive objects, the following might define lines:

Geometric Definition Candidate

A line, \ell, is a set of points with the property that for each pair of points in the line, P,Q\in \ell,

[PQ]\cap \ell=[PQ].

In terms of a picture this just says that when you have a line, that if you take two points in the line (the language in comes from set theory), that the line segment is a subset of the line:

line

Exercise:

Why is this objectively not a good definition of a line.

Once we move into Cartesian\Coordinate Geometry we can perhaps do a similar trick. We can use line segments, and their lengths to define slope, (slope = rise over run) and then define a line as follows:

Algebraic Definition Candidate

A line, \ell, is a set of points such that for all pairs of distinct points P,Q\in\ell, the slope is a constant.

This means that if you take two pairs of distinct points in a line \ell, and then calculate the slopes between them, you get the same answer, and therefore it makes sense to talk about the slope of a line, m.

line2

This definition, however, has exactly the same problem as the previous. The definition we use isn’t too important but I do want to use a definition that considers the line a set of points.

The Equation of a Line

We can use such a definition to derive the equation of a line ‘formula’ for a line of slope m containing a point (x_1,y_1).

Suppose first of all that we have an x\text{-}y axis and a point P(x_1,y_1) in the line. What does it take for a second point Q(x,y) to be in the line?

line4

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MATH7021: Spring 2018, Week 12

April 30, 2018 in MATH7021 | 4 comments

Student Feedback

If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

 

Week 12

On Monday we finished the module by looking at triple integrals.

The Wednesday 09:00 lecture will be a tutorial. In this class and your usual tutorial we will look at the P.182, P. 192, P. 163, & P.116 exercises. If these are completed you will be recommended to revise either by trying Chapter 1 & 2 exercises or perhaps by looking at the Summer 2017 paper.

As next Monday is a bank holiday, we will begin the Summer 2017 Paper (in your notes) revision on Thursday.

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MATH7021: Spring 2018, Week 11

April 26, 2018 in MATH7021 | Leave a comment

Student Feedback

If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

Assignment 2

Assignment 2 has been corrected and your results emailed to you.

Week 11

We spent three lectures looking at double integrals, in particular their application to second moments of area. We set of integration over a cylinder by looking at polar coordinates.

In the Wednesday tutorial we worked on the p. 163 (primarily) and p. 182 exercises.

Week 12

On Monday we will finish the module by looking at triple integrals.

We will therefore have three tutorials where we will look at the P.182, P. 192, P. 163, & P.116 exercises. If these are completed you will be recommended to revise either by trying Chapter 1 & 2 exercises or perhaps by looking at the Summer 2017 paper.

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MATH6038: Spring 2018, Week 11

April 26, 2018 in MATH6038 | 2 comments

Student Feedback

If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

Week 11

We looked at the normal distribution.

In Maple looked at Binomial and Poisson random variables.

Week 12 – Maple Test

The Maple Test should take no more than one hour but I am giving ye extra time. For various reasons, I have decided to schedule next week’s class as:

  • 19:05 – 20:25: Sampling and Control Charts
  • 20:25 – 20:45: Break
  • 20:45 – 22:00: Maple Test

The Maple Test will be open book. You have a sample Maple Test (this is also in the notes) with solutions (*the first with(Statistics) should be with(LinearAlgebra)). The Maple Test will not include anything from Chapter 2 (Lab 4).

We will speak about sampling in more detail and also introduce control charts.

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Some Leaving Cert Applied Maths Notes

April 23, 2018 in Leaving Cert Applied Maths | Leave a comment

For those planning on focusing on questions one to five and ten:

Applied Maths some Notes

MATH6038: Spring 2018, Week 10

April 19, 2018 in MATH6038 | Leave a comment

Week 10

We did a lot of probability — reliability block diagrams, the binomial distribution, the Poisson distribution.

Those who missed the class I recorded some of it here.

Ironically I recorded the same lectures in 2016 as you can see here.

 

Week 11 – Maple Night

We will look at the normal distribution and talk about sampling.

In Maple we will look at Binomial and Poisson random variables.

Week 12 – Maple Test

We will speak about sampling in more detail and also introduce control charts.

The Maple Test will be open book. You have a sample Maple Test with solutions (*the first with(Statistics) should be with(LinearAlgebra)). The Maple Test will not include anything from Chapter 2.

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