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**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

## Transposition Survey

If you would like to help us more with the Transposition Project, please take this survey.

## Mathematics Exam Advice

- The first piece of advice is 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.
- For equations, check your solution by substituting your solution into the original equation. If your answer is wrong and you know it is wrong: write that on your script.

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

- have I answered the question that
__was asked__? - does my answer make sense? If no, say so, and then try and fix your solution.
- check your answer (e.g. if you are looking at a general true, 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, say so, and then try and fix your solution.

## Student Feedback

You are invited to give your feedback on my teaching and this module here.

## CA Results

Have been emailed to you.

## Sample Papers

I have not one but two sample exams for ye.

We will go through MATH6055 Sample 1 in Week 13 (I will give you a paper copy of this on Monday) and here is an additional Sample Exam 2 for you.

Both Sample Exams should be considered under the following understanding:

__This sample has been drafted to give you an idea of the NEW MATH6055 LAYOUT and is no indication of the specifics, difficulty or length of any individual questions. __

## Week 12

We finished our study of Graph Theory by looking at connectedness, degree, walks (Monday), and trees. Eulerian graphs (Tuesday), Hamiltonian graphs, and Dirac’s Theorem (Friday).

## Week 13

We will have three review lectures, and tutorials as normal.

I have drafted a sample paper and we will go through this exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Usual class times and locations.

Tutorials on Week 13 at the usual times and venue. As long as there are not too many people in a tutorial (max 18), you can attend both tutorials if you want.

## 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, exam papers etc.

## Student Feedback

You are invited to give your feedback on my teaching and this module here.

## Test 2

I hope to get the Test 2 results, your collated CA results, and the Test 2 Marking Scheme out to you by the end of next week.

## Sample Papers

I have not one but two sample exams for ye.

We will go through MATH6055 Sample in Week 13 (I will give you a paper copy of this on Monday) and here is an additional Sample Exam for you.

Both Sample Exams should be considered under the following understanding:

__This sample has been drafted to give you an idea of the NEW MATH6055 LAYOUT and is no indication of the specifics, difficulty or length of any individual questions. __

## Week 11

In Week 11 we explored Network Theory, or rather Graph Theory, in more depth. In particular we put Graph Theory on a firm set-theoretic foundation.

Test 2 was on Friday.

## Week 12

We will finish our study of Graph Theory by looking at connectedness, degree, walks, and trees. Eulerian graphs, Fleury’s Algorithm, Hamiltonian graphs, and Dirac’s Theorem.

## Week 13

We will have three review lectures, and tutorials as normal.

I have drafted a sample paper and we will go through this exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Usual class times and locations.

Tutorials on Week 13 at the usual times and venue.

## 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.

## Transposition Project – Part II

October 22 you took a quiz as part of the Transposition Project that the Mathematics Department is undertaking in an effort to improve our teaching.

You will have another 15 minute quiz on Monday.

If you do not have an internet ready device, or did not do the first quiz, you may leave class early.

Thank you again for your participation.

## Test 2

Test 2, worth 15% of your final grade, based on Chapter 3: Algebra, will take place on Friday 30 November in the usual lecture venue of B214.

All Chapter 3 material is examinable, but the test will be similar to the sample test.

There will also be a question on the growth rate of functions: the relevant info to answer these questions are on p. 81, and they are exercises 18, 19 on p. 79.

Here is a sample test.

The sample is to give you an idea of the length of the test. You know from Test 1 the layout (i.e. you write your answers on the paper). You will be allowed use a calculator for all questions.

I strongly advise you that, for those who might have done poorly, or not particularly well, in Test 1, attending tutorials alone will not be sufficient preparation for this test, and you will have to devote extra time outside classes to study aka do exercises.

## Week 10

We introduced and studied the properties of uses of logarithms. We began the chapter on Network Theory by looking at the Bridges of Konigsberg Problem.

## Week 11

In Week 11 we will explore Network Theory, or rather Graph Theory, in more depth. We will look at digraphs, connectedness, degree, walks, and trees.

Test 2 will be on Friday.

## Test 2

Test 2, worth 15% of your final grade, based on Chapter 3: Algebra, will take place on Friday 30 November in the usual lecture venue of B214.

Here is a provisional sample test. If we don’t cover something by 20 November inclusive it won’t be on the test: this is so you will have two full tutorials before the test. This will be clarified on Tuesday 20 November.

The sample is to give you an idea of the length of the test. You know from Test 1 the layout (i.e. you write your answers on the paper). You will be allowed use a calculator for all questions.

I strongly advise you that, for those who might have done poorly, or not particularly well, in Test 1, attending tutorials alone will not be sufficient preparation for this test, and you will have to devote extra time outside classes to study aka do exercises.

## Week 9

In Week 9 we finished talking about quadratics, and studied exponents; with a first look at exponential equations and exponential functions.

## Week 10

We will introduce and study the properties of uses of logarithms.

## Test 2

Test 2, worth 15% of your final grade, based on Chapter 3: Algebra, will take place on Friday 30 November in the usual lecture venue of B214.

Here is a provisional sample test. If we don’t cover something by 20 November inclusive it won’t be on the test: this is so you will have two full tutorials before the test.

I will give you a copy of the sample today, Friday 9 November. The sample is to give you an idea of the length of the test. You know from Test 1 the layout (i.e. you write your answers on the paper). You will be allowed use a calculator for all questions.

I strongly advise you that, for those who might have done poorly, or not particularly well, in Test 1, attending tutorials alone will not be sufficient preparation for this test, and you will have to devote extra time outside classes to study aka do exercises.

## Week 8

In Week 8 we finished talking about equations and started studying quadratics.

## Week 9

In Week 9 we will finish talking about quadratics and begin studying exponents.

## Week 7

In Week 7 we started delving more into algebra and started talking about equations.

## Week 8

In Week 8 we will finish talking about equations and start studying quadratics.

## Transposition Project

On Monday you will be sent a 20 minute quiz that you will take on a mobile internet device — such as your mobile phone — during Monday’s lecture. You will have another quiz again after we finish studying algebra.

These quizzes do not affect your MATH6055 grade but are part of a larger project the Mathematics Department is undertaking in an effort to improve our teaching.

If you do not have an internet ready device you may leave class early.

## Test 1 Results

Have been emailed to you. I will have your scripts with me in tutorials and will send out the marking scheme next week.

## Reading Break, etc.

Classes will be going full steam ahead on Monday and Tuesday 22/23 October as well as Wednesday and Friday 31 October and 2 November. I will call the next two weeks by Week 7.

## Week 6

In Week 6 we had our first test and finished our our study of functions and their properties. We started looking at algebra by looking first at number sets. We learnt, for example, that division by zero is undefined. See here for more.

## Week 7

In Week 7 we will start really getting to grips with algebra.

## Test 1

Test 1, worth 15% of your final grade, will take place in the usual D160 lecture venue at 10:00 on Tuesday 16 October. You have been sent a sample paper. The names of Laws of Sets on the sample is the same as how they will be named on the test and final exam.

Test 1 will cover the contents of Chapter 1 and the sample will give an idea of the layout and length of the test. The following *types* of questions are examinable:

- Stuff on the sample test
- P.20, Q. 1, 3 [note is a typo: it should be ], 4, 6-7, 9, 13-14
- P.26, Q. 1-4
- P.30, Q. 2
- P. 36, Q.1-3

Questions like those exercises not listed here will not appear on your exam paper but are still useful to help your learning and understanding. For example, working with truth tables should help your understanding of the Laws of Sets.

I have also sent on some additional exercises on equivalence relations via email.

## The Lee Fields Medal — CIT Maths Challenge

Maths Competition on next Wednesday with cash prizes. Poster below.

## Week 5

In Week 5 we continued our study of functions and their properties. We considered the composition of functions — and inverse functions. We started looking at examples of functions.

## Week 6

In Week 6 we will complete our study of functions.

## Week 4

In Week 4 we finished Chapter 1 by looking more at relations and their properties. We started our study of Chapter 2: Functions. A function is a special type of relation.

## Week 5

In Week 5 we will continue our study of functions and their properties.

## Test 1

Test 1, worth 15% of your final grade, will take place in the usual D160 lecture venue at 10:00 on Tuesday 16 October. I will email a sample paper in the next week. The names of Laws of Sets on the sample is the same as how they will be named on the final exam.

Test 1 will cover the contents of Chapter 1 and the sample will give an idea of the layout and length of the test. The following *types* of questions are examinable:

- P.20, Q. 1, 3 [note is a typo: it should be ], 4, 6-7, 9, 13-14
- P.26, Q. 1-4
- P.30, Q. 2
- P. 36, Q.1-3

Questions like those exercises not listed here will not appear on your exam paper but are still useful to help your learning and understanding. For example, working with truth tables should help your understanding of the Laws of Sets.

I have also sent on some additional exercises on equivalence relations via email.

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