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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 $U$. When talking about people this might be the collection of all people. When talking about natural numbers this might be the set $\mathbb{N}$. When talking about real numbers this might be the set $\mathbb{R}$. When talking about curves it might be the set of subsets of the plane, $\mathcal{P}(\mathbb{R}\times \mathbb{R})$, etc.

The collection of objects in this case is the set of subsets of $U$, denoted $\mathcal{P}(U)$.

Suppose, for the purposes of illustration, that $U=\{1,2,3,4,5\}$.

Consider the subsets $A=\{2,3,5\}$, and $B=\{1,3,5\}$ .

in the obvious way.

### AND

Note that two objects are contained both in $A$ AND in $B$. We call the set of such objects the intersection of $A$ AND $B$, $A\cap B$: $A\cap B=\{3,5\}$.

We can represent the ambient set $U$, as well as the sets $A$ and $B$ — and the fact that they intersect — using a Venn Diagram: We can demonstrate for a general $A$ and $B$ ‘where’ the intersection is: ## 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.

## 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.

## Week 9

We made a good start on probability, talking about random variables, independence, mutual exclusivity, conditional probability, and tree diagrams.

## Week 10

We will have a lot of probability to do — reliability block diagrams, the binomial distribution, the Poisson distribution.

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.

We do not have enough probability done to have a Maple Lab until…

## Week 11 – Maple Night

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

## Week 12 – Maple Test

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

The Maple Test will be open book and you will have already received a sample test with solutions.

## Linear Algebra: 20% Test

Results pending: along with a copy of the marking scheme and perhaps some further comments.

## Week 8* Snow Day Catch Up [28 March]

In this class we finished off the chapter on statistics. This can be viewed here.

We also did Maple Lab 4. A little help on setting this up can be viewed here.

## Week 9

We will begin delving into the chapter on Probability.

*These starred week numbers are one behind CIT’s week numbers. This is because of the snow.

## Linear Algebra: 20% Test

Results should be released next week along with a copy of the marking scheme and perhaps some further comments.

## Week 7* [21 March]

We had the Linear Algebra Test.

We continued working on statistics by looking at frequency distributions.

## Week 8* Snow Day Catch Up [28 March]

In this class we should be able to finish off the chapter on statistics. This segment of the class will be recorded and published on YouTube.

We will also do Maple Lab 4

*These starred week numbers are one behind CIT’s week numbers. This is because of the snow.

## Linear Algebra: 20% Test

Takes place Wednesday 21 March, in Week 7* [21 March].

The test will take place from 19:00-20:30 but most students should be able to complete the test in about an hour. It has about 35 Marks worth of questions: five in all (with one very short, and three shortened versions of longer questions).

Anything done in the first five weeks is examinable (see “Independent Learning” below) and it is recommended that you understand what is going on with the summaries of p. 57-59.

The nine questions from p. 60 on are a good revision but not every possible question is listed there.

## Week 6* [14 March]

We started the class with one more example of Cramer’s Rule, and then started pushing into statistics, looking at everything up to and including standard deviation.

In Maple, we did Lab 3, which was really revision for the Linear Algebra Test.

## Week 7* [21 March]

The test is going to begin at 19:00 sharp and run until 20:30. Class will resume at 20:35 sharp. This seems a very short break but the test is designed so that it shouldn’t take much longer than an hour to complete, so almost everyone should have a solid enough break.

At 20:35 we will continue working on statistics by looking at frequency distributions.

## Week 8* Snow Day Catch Up [28 March]

This may or may not be a Maple night (it depend on how far we get in the previous week).

Any students who cannot make this class should email me and request that the class be recorded (I might not be able to record all of the class but most of it.

*These starred week numbers are one behind CIT’s week numbers. This is because of the snow.

## Linear Algebra: 20% Test

Will now take place Wednesday 21 March, in Week 7* [21 March].

The test will take place from 19:00-20:30 but most students should be able to complete the test in about an hour. It has about 35 Marks worth of questions: five in all (with one very short, and three shortened versions of longer questions).

Anything done in the first five weeks is examinable (see “Independent Learning” below) and it is recommended that you understand what is going on with the summaries of p. 57-59.

The nine questions from p. 60 on are a good revision but not every possible question is listed there. In next week’s Maple you will get a chance to revise these questions.

## Week 5* [7 March]

We saw how linear systems can be written as matrix equations, and (sometimes) solved using matrix inverses. Then we spoke about determinants, and their use in figuring out if homogeneous linear systems have non-zero solutions. Finally we looked at Cramer’s Rule.

## Week 6* [14 March]

We will start the class with one more example of Cramer’s Rule, and then start pushing into statistics.

In Maple, we will do Lab 3, which is really revision for the Linear Algebra Test.

## Week 7* [21 March]

The test is going to begin at 19:00 sharp and run until 20:30. Class will resume at 20:35 sharp. This seems a very short break but the test is designed so that it shouldn’t take much longer than an hour to complete, so almost everyone should have a solid enough break.

At 20:35 we will continue working on statistics.

## Week 8* [28 March/4 April]

This may or may not be a Maple night (it depend on how far we get in the previous week).

It appears that at most one student will miss the class, which isn’t too bad. So now we now go back to the poll to pick between the two nights.

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 4

We worked with matrix inverses, seeing how the Gauss-Jordan algorithm can be used to calculate the inverse of a $3\times 3$ matrix. We solved a matrix equation.

Here find a corrected Example 2 from p. 39. In class, I made a slip in the third frame. The row operations are the same.  $\displaystyle A^{-1}=\left(\begin{array}{ccc} 1 & 1 & 1 \\ 3 & 5 & 4 \\ 3 & 6 & 5\end{array}\right)$.

We also had our second Maple lab.

## Week 5

We will see how linear systems can be written as matrix equations, and solved using matrix inverses. Then we will talk about determinants, and perhaps push towards the end of Chapter 1.

## Linear Algebra: 20% Test

Will take place Wednesday 14 March, in Week 7.

## Maple Catch Up

If you have missed the first lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.

Go through the missed lab on your own, doing all the exercises in Maple. Save the worksheet and email it to me.

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.

## Maple

We will have our second Maple Lab next week (Week 4: 21 March 2018).

If you have missed the first lab you have two options: either download Maple onto your own machine or come into CIT at another time to use Maple.

Go through the first lab on your own, doing all the exercises in Maple (Exercises 1, 2, and 3). Save the worksheet and email it to me.

If you have never done Maple before you might want to do a Lab or two with me before catching up.

## Week 3

We did some examples of matrix arithmetic and looked at the concept of a matrix inverse.

We had our first Maple Lab

## Week 4

We will continue working with matrix inverses, seeing how the Gauss-Jordan algorithm can be used to calculate the inverse of a $3\times 3$ matrix.

We will have our second Maple lab. 