## Week 2

We looked at the Euler Method, and then started looking at big $\mathcal{O}$ notation, and Taylor Series. We started doing error analysis for Euler’s Method.

In VBA we started programming the Euler Method.

Read the rest of this entry »

## Week 2

We finished the Gaussian Elimination examples on Wednesday, and began to look at applications of linear systems to traffic and pipe flow (Thursday).

We had more than two classes of tutorials — Monday, a few minutes on Wednesday, and most of the Thursday double.

## Week 3

We will finish the Chapter 1 material and finish the week off with more tutorial time.

## 15% Assignment 1

Assignment 1 has a (provisional) hand-in date of  Thursday 23 February (Week 5). More information on Canvas early next week once the class list has settled down.

## 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..

## Quiz 1

The first 2.5% quiz will be 11.05 am (SHARP), Wednesday 8 February in F1.2. The quiz will be projected on the screen, and you will write your answers on a sheet I hand out at the start of class.

The quiz will be a single question with three parts, worth 1%, 1%, and then a harder part (that will require independent thought) worth 0.5%.

It will be a 15 minute quiz, and the contents of Section 1.1 will be examined. Relevant exercises:

• Supplemental Exercises, p.3, Q.1-9
• Manual, p.14, Q.1-7.

Starred Exercises are harder than will be examined in the quiz.

## Manuals

You need to purchase the manual. See here for details.

## Week 2

In Week 2 we looked at arithmetic and geometric sequences in more detail, before going on to do some mathematical modelling using recurrence relations.

We started the chapter on logic.

## Week 3

We will continue diving into logic.

## 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

70% Terminal Exam

See Canvas for more:

## Student Resources

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

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.

## Week 1

We started the first chapter on Linear Algebra. Essentially, for us, simultaneous equations. We looked at Gaussian Elimination including Partial Pivoting, which is required in the presence of rounding. We looked at four examples, but had no tutorial time.

## Gaussian Elimination Tutor

If you download Maple (see Student Resources), there is a Maple Tutor that is easy to use and will help you with Gaussian Elimination. Open up Maple and go to Tools -> Tutors -> Linear Algebra -> Gaussian Elimination.

## Week 2

We will have tutorial time on Monday, then finish the Gaussian Elimination examples on Wednesday, and maybe begin to look at applications of linear systems to traffic and pipe flow.

## Assignment 1

Assignment 1 has a (provisional) hand-in date of  Thursday 23 February (Week 5). More information next week once the class list has settled down.

## 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..

## Manuals

COMP1B are required to purchase an academic manual for MATH6004. This contains a lot of the lecture notes and exercises for the module. The lecture notes contain gaps that we fill in during class. I will have notes for you for the first week but after that you must purchase the manual: the sooner the better.

The manuals can be purchased from Reprographics\Copy Centre beside the Student Centre. Note that this is a cash-free area so you will need to put the appropriate amount of funds — €8.50 — on your student card.

I will be writing in various colours, so maybe  a four colour pen would be useful.

## Week 1

After first-day introductions, we started talking about sequences and sequences defined by a recurrence relation. We met a famous example, the Fibonacci sequence. We started talking about the sum of a sequence.

In tutorial we worked on recurrence relations, Q.1-9 on p.14. The following additional exercises to p.14 are important:

• Q. 2 write F(1000) in terms of F(998) and F(997)
• Q. 3 write C(1000) in terms of C(998) and C(997) (which includes something with just C(998))
• Q. 4 write V(1000) in terms of V(998) and V(997) (which includes something with just V(998))

## Week 2

In Week 2 we will look at arithmetic and geometric sequences in more detail, before going on to do some mathematical modelling using recurrence relations.

## 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

See Canvas for the assessment plan and schedule. We will probably have a quiz in Week 3. Watch this space.

## Student Resources

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

## Week 1

In Week 1, by briefly looking at a number of examples (many of which we have seen before), we had a review of some central ideas from approximation theory such as approximation, measurement error, accuracy & precision, iteration, convergence, meshing, error, etc.

We started looking at where ordinary differential equations come into Engineering.

In VBA we had a quick review lab, focussing on plotting data, command buttons, message boxes, input boxes, If-statements and do-loops.

If you have not completed Lab 1 (p.120), I recommend that you do at least up to the first Do-Loop exercise to get you back in the VBA groove.

The first MCQ results are on Canvas. Only two students top-scored.

Read the rest of this entry »

## Student Feedback

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

## Week 12

We looked at the Winter 2021 paper for revision. It is in the back of the manual.

We will finish Q. 4 (b) early on Friday, and will have some tutorial time then for the final exam.

We had a tutorial on Tuesday… some students focused on Chapter 3, others did some Chapter 1 revision.

## Final Exam Preparation

Your preparation for the test is doing exercises. There is an awful lot of exercises in Chapter 1 to 4. I recommend in particular:

• Curve Fitting: p. 33, 48
• Probability and Statistics: p. 160, Q. 5-7; p. 179, Q (d); p.171, Q. 1-2; p.178, Q. 1-2
• Taylor Series, p. 134, Q. 1-4; p. 191, Q. 1-4; p. 207, Q. 2-3, 5-6

After Assignment 2, students are probably as prepared as they can be for Static Beam Differential Equations… but possibly no harm to do some refresher questions. They do require practise.

If you want feedback on study, please check your work against answers in the the manual, and/or email me your work with any questions.

## Mathematics Exam Advice

• You don’t have to answer questions in order Q. 1, Q. 2, etc. If you know in advance the structure of the exam, you can decide in advance what questions you are doing first, second, etc. This is related to:
• Read questions carefully. Don’t glance at a question and go off writing: take a moment to understand what you have been asked to do.
• Don’t use tippex; instead draw a simple line(s) through work that you think is incorrect.

If you do have time at the end of the exam, go through each of your answers and ask yourself:

1. have I answered the question that was asked?
2. does my answer make sense? If no, write that on your script, and then try and fix your solution.
3. check your answer (e.g. if you are looking at something general, look at a special case; substitute your solution into equations; check your answer against a rough estimate; or what a picture is telling you; etc.). If your answer is wrong, write that on your script, and then try and fix your solution.

## Student Feedback

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

## Week 12

We looked at the Winter 2021 paper for revision. It is in the back of the manual.

We will finish Q. 3 (c) early on Friday, and will have some tutorial time then for the final exam.

Students will receive one-to-one help in tutorial, but it will be up to students to decide what they want to look at; be it Vectors, Matrices, or Further Differentiation.

## Final Exam Preparation

Your preparation for the test is doing exercises and knowing the content of the Chapter Summaries. There is an awful lot of exercises in Chapter 1 to 4. I recommend in particular:

• Vectors: p. 31, 41, 49
• Matrices: p. 76, 89, 104
• Further Differentiation: p. 188, 200, 215

After Test 2, students are probably as prepared as they can be for Integration… but possibly no harm to do some refresher questions.

There are past exam papers in the Week 11 announcement, but most of these questions appear already in the manual, either as examples we did in class, worked examples, marking schemes, or exercises.

If you want feedback on study, please check your work against answers in the the manual, and/or email me your work with any questions.

## Mathematics Exam Advice

• You don’t have to answer questions in order Q. 1, Q. 2, etc. If you know in advance the structure of the exam, you can decide in advance what questions you are doing first, second, etc. This is related to:
• Read questions carefully. Don’t glance at a question and go off writing: take a moment to understand what you have been asked to do.
• Don’t use tippex; instead draw a simple line(s) through work that you think is incorrect.

If you do have time at the end of the exam, go through each of your answers and ask yourself:

1. have I answered the question that was asked?
2. does my answer make sense? If no, write that on your script, and then try and fix your solution.
3. check your answer (e.g. if you are looking at something general, look at a special case; substitute your solution into equations; check your answer against a rough estimate; or what a picture is telling you; etc.). If your answer is wrong, write that on your script, and then try and fix your solution.

## Student Feedback

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

## 40% Test 3 – Functions Algebra

This test will takes place Thursday 15 December at 4 pm in Room IT2. More information on Canvas. The ten-week semester has left us very short on preparation for Test 3. Therefore there will be three additional classes in Week 11

• Tuesday 13 December, 14:00, B217 (usual lecture time and venue),
• Wednesday 14 December, 10:00, F1.4 (room change),
• Thursday 15 December, 09:00, F1.4 (room change).

Your preparation for the test is doing exercises (and dipping into the notes when you don’t understand what e.g. one-to-one means). There is an awful lot of exercises in Chapter 3 to 5. Here I pick out some that you could focus on (note Functions summary p.120):

• Sample Test 3, p. 196
• p. 94, Q. 1,3,5
• p. 97, Q. 1-2
• p.105, Q. 1-5
• p.114, Q.1-4, 9-11, 13
• p.141, Q. 2
• p.145, Q. 1-3, Q. 1, 3-4, 8-10
• p.155, Q. 6-9
• p.175, Q. 2-5, 8-10
• p. 189, Q. 1(a), 3, 17-19

This is what I will be recommending students work on in tutorials. If you want feedback on study but cannot make it to the additional classes, please check your work against answers in the back of the manual, and/or email me your work with any questions.

## Mathematics Exam Advice

• You don’t have to answer questions in order Q. 1, Q. 2, etc. If you know in advance the structure of the exam, you can decide in advance what questions you are doing first, second, etc. This is related to:
• Read questions carefully. Don’t glance at a question and go off writing: take a moment to understand what you have been asked to do.
• Don’t use tippex; instead draw a simple line(s) through work that you think is incorrect.

If you do have time at the end of the exam, go through each of your answers and ask yourself:

1. have I answered the question that was asked?
2. does my answer make sense? If no, write that on your script, and then try and fix your solution.
3. check your answer (e.g. if you are looking at something general, look at a special case; substitute your solution into equations; check your answer against a rough estimate; or what a picture is telling you; etc.). If your answer is wrong, write that on your script, and then try and fix your solution.

## Week 10

There was a bit of a turbo-charge to finish the material for the exam. Initially we looked at some properties and computer science applications of logs. Then we looked at algorithmic complexity. It is OK that we skipped some sections — we are on a tight schedule of ten weeks, and everything that was essential was covered, and covered for the final test.

In tutorial, students looked at Sample Test 3.