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## 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.

• 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:

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.

## Student Feedback

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

## Week 9

We spoke about indices/exponentials, and then we introduced logs as inverses of exponential functions.

In tutorial, C-X looked at functions, and C-Y moved onto algebra.

## Week 10

There is going to be a bit of a turbo-charge to finish the material for the exam. Initially we will be looking at properties and computer science applications of logs.

The good news is that we will be able to skim the mini-Chapter 5 and still have everything well covered for assessment.

In tutorial, students can take a look at Sample Test 3.

## Week 11, Wk 12 Dec — Additional Tutorials

The ordinary ten-week semester has left us very short on preparation for Test 3.

Therefore there will be 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).

I spoke about the tutorial slot on Wednesday… I have realised that I made an appointment in the afternoon, so I cannot do that slot.

## 40% Test 3 – Functions Algebra

This test will take place Thursday 15 December at 4 pm. In the IT Building (Canvas announcement incoming).

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## Week 8

We drove into Chapter 4 Algebra, spending a lot of time talking about equations.

In tutorial, C-X focused on Test 2, while C-Y had a good tutorial on functions.

## Week 9

We are practically finished talking about the basics of equations. We will spend a lecture or two talking about indices/exponentials. Then we will introduce logs as inverses of exponential functions.

In tutorial, C-X will look at functions, and C-Y move onto algebra. We are very short for time for tutorials: students are advised to spend some time outside tutorials working on exercises.

## Week 10

We will spend more time talking about logs, and then we will fly through mini-Chapter 5. Ideally we will spend the last lecture doing the Sample Test 3 in the manual.

## 40% Test 3 – Functions Algebra

This test will take place Thursday 15 December at 4 pm. Probably in the IT Building (watch this space).

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## 30% Test 2 – Equivalence Relations & Graphs

Test 2 takes place 6 p.m. Wednesday 23 November in the Melbourn Hall.

We have now completed the material for Test 2. Everything in Chapters 1 and 2 is examinable, with the emphasis on transitive and equivalence relations as well as Chapter 2. You may be required to use algebra to prove that a relation is reflexive, symmetric, or transitive.

There is a sample test on p.88 of the test. This is only to give you an idea of the type of content (but not specific questions) that will be examined. The test may be a little longer and/or harder.

• Do not to congregate outside the Melbourn Hall until 10 minutes before the assessment is due to commence and do wait outside until you are ready to begin your assessment.

• Be mindful of groups already in the hall when entering the exam hall.

• Do not congregate in the waiting area of the Melbourn building when the assessment has finished as the noise can disrupt the students completing their assessment.

• Leave their bags in the shelved area just inside the exam hall doors – not on the floor in the exam hall lobby.  As we get busier, space will become scarce in the shelved area so if possible, only bring essential items (pens, calculators etc.) to the venue.

## Week 7

We finished Chapter 3, by talking about inverses, and looked at some examples of invertible functions that we will use in the chapter on Algebra… which we started.

In tutorial we focused on Test 2 material.

## Week 8

We will drive into Chapter 4 Algebra. We have nine lectures to cover Algebra and the rest of Functions (Chapter 5)

In tutorial, C-X will focus on Test 2, while C-Y will move onto Test 3: Functions & Algebra.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## No MATH6055 class Friday 18 November (once off in Week 9)

The Friday C-Y tutorial will be preponed to Thursday 17 November at 11:00 in B116.

## 30% Test 1 – Sets & Relations – Results

These have been released in an announcement.

## Week 6

We drove into Chapter 3, on Functions. We saw their definition in terms of a domain, codomain, and a set of ordered pairs. We learned that we can visualise functions with arrow diagrams (usually for small domains), and coordinate graphs (usually for functions that map reals to reals). We learned about the properties of a function: namely 1-1, onto, and bijective. We spoke about compositions.

## Week 7

We will finish Chapter 3, by talking about inverses, and look at some examples of invertible functions that we will use in the chapter on Algebra… which we will also start hopefully.

We will focus in tutorial on the Test 2 material.

## 30% Test 2 – Equivalence Relations & Graphs

Test 2 takes place 6 p.m. Wednesday 23 November in the Melbourn Hall.

We have now completed the material for Test 2. Everything in Chapters 1 and 2 is examinable, with the emphasis on transitive and equivalence relations as well as Chapter 2. You may be required to use algebra to prove that a relation is reflexive, symmetric, or transitive.

There is a sample test on p.88 of the test. This is only to give you an idea of the type of content (but not specific questions) that will be examined. The test may be a little longer and/or harder.

• Do not to congregate outside the Melbourn Hall until 10 minutes before the assessment is due to commence and do wait outside until you are ready to begin your assessment.

• Be mindful of groups already in the hall when entering the exam hall.

• Do not congregate in the waiting area of the Melbourn building when the assessment has finished as the noise can disrupt the students completing their assessment.

• Leave their bags in the shelved area just inside the exam hall doors – not on the floor in the exam hall lobby.  As we get busier, space will become scarce in the shelved area so if possible, only bring essential items (pens, calculators etc.) to the venue.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## No MATH6055 class Friday 18 November (Week 9)

The Friday C-Y tutorial will probably be preponed to Thursday 17 November at 11:00 in B116.

## 30% Test 1 – Sets & Relations – Results

Hopefully these will be released before the end of Week 6

## Week 5

We finished Chapter 2.

## Week 6

We will drive into Chapter 3, on Functions.

## 30% Test 2 – Equivalence Relations & Graphs

Test 2 takes place either 23 or 24 November (watch this space).

We have now completed the material for Test 2. Everything in Chapters 1 and 2 is examinable, with the emphasis on transitive and equivalence relations as well as Chapter 2. You may be required to use algebra to prove that a relation is reflexive, symmetric, or transitive.

There is a sample test on p.88 of the test. This is only to give you an idea of the type of content (but not specific questions) that will be examined. The test may be a little longer and/or harder.

• Do not to congregate outside the Melbourn Hall until 10 minutes before the assessment is due to commence and do wait outside until you are ready to begin your assessment.

• Be mindful of groups already in the hall when entering the exam hall.

• Do not congregate in the waiting area of the Melbourn building when the assessment has finished as the noise can disrupt the students completing their assessment.

• Leave their bags in the shelved area just inside the exam hall doors – not on the floor in the exam hall lobby.  As we get busier, space will become scarce in the shelved area so if possible, only bring essential items (pens, calculators etc.) to the venue.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## 30% Test 1 – Sets & Relations

Test 1 takes place Wednesday 18:00-19:00, October 26th, Melbourn Exam Hall, Rows A-G

We have now completed the material for Test 1. Everything up to and including equivalence relations but not including equivalence classes is examinable. You may be required to use algebra to prove that a relation is reflexive, symmetric, or transitive.

There is a sample test on p.56 of the test. This is only to give you an idea of the type of content (but not specific questions) that will be examined. The test may be a little longer and/or harder.

• Do not to congregate outside the Melbourn Hall until 10 minutes before the assessment is due to commence and do wait outside until you are ready to begin your assessment.

• Be mindful of groups already in the hall when entering the exam hall.

• Do not congregate in the waiting area of the Melbourn building when the assessment has finished as the noise can disrupt the students completing their assessment.

• Leave their bags in the shelved area just inside the exam hall doors – not on the floor in the exam hall lobby.  As we get busier, space will become scarce in the shelved area so if possible, only bring essential items (pens, calculators etc.) to the venue.

## Week 4

We finished talking about Relations and we started Chapter 2 on Networks.

## Week 5

We will aim to finish Chapter 2 and possibly start Chapter 3, on Functions. Test one is on Wednesday evening.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## 30% Test 1 – Sets & Relations

Test 1 takes place Wednesday 18:00-19:00, October 26th, Melbourn Exam Hall, Rows A-G

We have now completed the material for Test 1. Everything up to and including equivalence relations but not including equivalence classes is examinable. You may be required to use algebra to prove that a relation is reflexive, symmetric, or transitive.

There is a sample test on p.56 of the test. This is only to give you an idea of the type of content (but not specific questions) that will be examined. The test may be a little longer and/or harder.

• Do not to congregate outside the Melbourn Hall until 10 minutes before the assessment is due to commence and do wait outside until you are ready to begin your assessment.

• Be mindful of groups already in the hall when entering the exam hall.

• Do not congregate in the waiting area of the Melbourn building when the assessment has finished as the noise can disrupt the students completing their assessment.

• Leave their bags in the shelved area just inside the exam hall doors – not on the floor in the exam hall lobby.  As we get busier, space will become scarce in the shelved area so if possible, only bring essential items (pens, calculators etc.) to the venue.

## Manuals

The manuals are available in the Copy Centre (at a cost of €14.10). These are needed to participate properly in class. More information in the Week 1 summary.

## Week 3

We explored further Relations and their properties. We had a detour to algebra to give a tool to help prove that relations have particular properties.

Students present in tutorial worked on Cartesian products and relations.

## Week 4

We will finish talking about Relations and and we will start Chapter 2 on Networks.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## Manuals

The manuals are available in the Copy Centre (at a cost of €14.10). These are needed to participate properly in class. More information in the Week 1 summary.

## Week 2

In Week 2 we looked at the Laws of Sets and moved onto Cartesian Products and Relations.

Students present in tutorial worked really hard on well on the Laws of Sets exercises.

## Week 3

We will explore further Relations and their properties. We might start Chapter 2.

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.

## Manuals

COMP1C are required to purchase an academic manual for MATH6055. This contains all 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 — €14.10 — on your student card (here).

With all the materials (including worked examples, summaries, etc) it comes to 222 pages and provides a comprehensive resource for this module.

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

## Week 1

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.

## Week 2

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

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 workshopLinks to an external site..

Supported Maths Study is on every Monday from 3.30pm – 5.30pm in B231.

Supported Statistics Study is on every Wednesday from 3pm – 4pm in B231.

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.