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## Week 2

You are advised to to spend **seven** hours per week on MATH6055. This should comprise of however long it takes to watch the lectures, and then the rest of time should be spent doing exercises, emailing questions, and submitting work. At the time of writing, the mechanism for submitting work is not yet set up.

### Lecture

Schedule about three hours to watch these two hours of lectures. I recommend about 50% extra time as you will want to pause/rewind.

- Laws of Sets and Illustrations of DeMorgan’s Laws (25 minutes)
- Inclusion/Exclusion Principle; and some difficult notational stuff (14 minutes)
- Cartesian Products (21 minutes)
- Tuples: Passwords and Bit Strings (7 minutes)
- Relations (22 minutes)

Here is the first tranch of notes if you have not purchased nor printed off a manual

- Relations: Examples and Reflexivity (27 minutes)

### Exercises

I recommend spending four hours on this week’s exercises.

I do not at the time of writing have the mechanism in place for submitting work.

You can (carefully) take photos of your work. If possible, convert the images to a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

Ordinarily I would encourage you to ask questions via email at any time but at present this mechanism is not in place.

Do/attempt:

**p. 32, Q. 10-11****p. 33, Q. 12-14****p. 38, Q. 1-5****p. 39, Q. 6****p. 43, Q. 1-2**

**Additional/Harder Exercises:**

**p.34, Q. 26****p. 39, Q. 7-8****p. 43, Q. 3-6**

## Week 3

In Week 3 we will finish Chapter 1 by looking more at relations and their properties. We will start our study of Chapter 2: Functions. A function is a special type of relation.

## Academic Learning Centre

I would urge anyone having any problems with material that isn’t being addressed in the tutorial communication to use the Academic Learning Centre. If you are a little worried about your maths this semester you need to be aware of this resource. You will get best results if you come to the helpers there ith *specific *questions.

## Assessment

At the time of writing, the assessment schedule has not been finalised, but we are considering two 50% tests.

## Student Resources

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

## Facetime

Some Facetime with me: click here.

## Manuals

The lectures are being delivered via pre-recorded lectures. As you will see, the lectures use a manual that contain all the lecture material, via gaps that are filled in during lectures, and exercises. I tend to use a number of colours during lectures, and pencil, so you might want to consider ordering some of these:

In a sliding scale from best to worst, in my opinion, here are your options for using this manual. There are other options but I cannot recommend them. If you do option one you have all your notes in one place and can follow the lectures as if you were in the classroom.

- Email copy.centre@cit.ie and tell them you want to order a bound copy of
*MATH6055 Manual Winter 2020*. The manuals can be collected from Reprographics beside the Student Centre. Note that this is a cash-free area so you will need to put the appropriate amount of funds on your student card. At the time of writing I do not know the cost but it will be of the order of €13. This seems like a lot of money for a manual but with all the materials (including exercises, summaries, etc) it comes to 165 pages and provides a comprehensive resource for this module. - Print off the manual at home or somewhere else. Click here to find a copy.
- I am going to scan and email the completed slides. You can keep these somewhere for your notes. You could print these or keep digital copies. Here is the first tranch of notes.

## Week 1

You are advised to to spend **seven** hours per week on MATH6055. This should comprise of however long is recommended to watch the lectures, and then the rest of time should be spent doing exercises, emailing questions, and submitting work. At the time of writing, the mechanism for submitting work is not yet set up.

We tell four tales of De Morgan.

In each case we have something that looks like AND, something that looks like OR, and something that looks like NOT.

## Sets

### The Collection of Objects

Consider a *universe of discourse*/universal set/ambient set . When talking about people this might be the collection of all people. When talking about natural numbers this might be the set . When talking about real numbers this might be the set . When talking about curves it might be the set of subsets of the plane, , etc.

The collection of objects in this case is the set of subsets of , denoted .

Suppose, for the purposes of illustration, that

.

Consider the subsets , and .

in the obvious way.

### AND

Note that two objects are contained both in AND in . We call the set of such objects the *intersection *of AND , :

.

We can represent the ambient set , as well as the sets and — and the fact that they intersect — using a Venn Diagram:

We can demonstrate for a general and ‘where’ the intersection is:

## 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.

## Week 12

We will finish our study of Graph Theory by looking at Eulerian graphs, Hamiltonian graphs, and Dirac’s Theorem.

We had the test on Tuesday.

On Friday we had a look at this graph, a Chapter 4 question:

## Student Feedback

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

## Test 2

Test 2, worth 15% of your final grade, based on Chapter 3: Algebra, and will take place on Tuesday 3 December in the usual lecture venue of D160.

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.

If you go into Canvas, and go into MATH6055 and the ‘Algebra’ unit, you might see online practise questions for Test 2.

## Week 11

On Monday we half-finished the Examples of Functions (we will finish this off on Friday) mini-chapter before starting the final chapter, the easy chapter, on Network (Graph) Theory.

## Week 12

We will finish our study of Graph Theory by looking at Eulerian graphs, Hamiltonian graphs, and Dirac’s Theorem.

The Test is on Tuesday.

## Transposition Project – Survey

With regard to *TRANSPOSITION** *(pages 86-97 of the manual), please fill out this survey.

## Transposition Project – Part II

October 14 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, and will take place on Tuesday 3 December in the usual lecture venue of D160.

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.

## Exercises on Canvas

If you go into Canvas, and go into MATH6055 and the ‘Algebra’ unit, you might see online practise questions for Test 2.

## Week 10

We worked with logarithms and started a quick look at Examples of Functions (which we needed Algebra to talk about).

## Week 11

On Monday we will finish the Examples of Functions mini-chapter before starting the final chapter, the easy chapter, on Network (Graph) Theory.

## Test 2

Test 2, worth 15% of your final grade, based on Chapter 3: Algebra, and will take place on Tuesday 3 December in the usual lecture venue of D160.

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 equations (and quadratic equations) and began studying exponents. We saw at the very end of Friday’s lecture that if we define a function:

,

by , then we define as an inverse function:

.

## Week 10

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

## Week 8

In Week 8 we will start talking about equations. On Wednesday we had a catch up lecture where we looked ahead to quadratic equations and quadratic functions.

## Week 9

In Week 9 we will finish talking about equations (and quadratic equations) and begin studying exponents.

## Reading Week

“*If you have time to look at MATH6055 over the Reading Break, may I suggest that you look at the Functions Exercises:*

*P. 61, Q. 1-11, 13*

*P. 54, Q. 1-4*

*P. 46, Q. 1-5*

*P. 41, Q. 1-2, 3 (a), 4, 5 (a)*

*If you have any questions please email me, perhaps with a photo of your work.*

”

## Catch Up Lecture

13:00 this coming Wednesday 6 November, in B217.

## Week 7

In Week 7 we started delving more into algebra

## Week 8

In Week 8 we will start talking about equations.

## Catch Up Lecture

We will not have MATH6055 class next Friday, 09:00, 25 October.

I would like to catch up on this after the reading break. Please click here and fill out your preference between the times. I know ye are all free at this times and it is just a case of picking the most popular time.

## Week 6

We finished Chapter 2 with a Concept MCQ on Functions Theory, and moved onto Algebra.

## Week 7

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

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