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## Assessment 1 – Results

I will have the assignments with me tomorrow if you want to see your work.

## Assessment 2

Assessment 2 is on p.136. It has a hand-in time of 16:00 Monday 26 November.

As suggested in class, I would advise you to — if possible — complete this assignment early if you can, freeing up time in your tutorial to get work done on Chapter 3: Probability & Statistics.

## Week 8

We looked at the Poisson distribution, the Normal distribution, and started discussing Sampling.

## Week 9

We will complete Chapter 3 by looking at Sampling and Hypothesis Testing. We may have an extra tutorial during one of the lectures.

## Assessment 1 – Results

I will have the assignments with me tomorrow and next Friday if you want to see your work.

## Assessment 2

Assessment 2 is on p.136. It has a hand-in time of 16:00 Monday 26 November.

## Week 7

We finished looking at Chapter 2 by looking at the Three Term Taylor Method for approximating solutions of ordinary differential equations.

We started Chapter 3 (Probability and Statistics) by looking at some general concepts in probability and then we looked at random variables with a binomial distribution.

## Week 8

We will look at the Poisson distribution and perhaps the Normal distribution.

## Assessment 1 – Results

I am starting corrections today and will get the results to you as soon as I can. I cannot give an accurate day at this stage: it could be Monday but just as easily could be a few days after this – I can’t make any promises.

## Assessment 2

Assessment 2 is on p.136. It has a hand-in date of Monday 26 November and we have already covered everything that will be asked and so you have over five weeks to complete the assignment.

## MicDrop Project

On Monday you will be sent a 15 minute survey that you will take on a mobile internet device — such as your mobile phone — during Monday’s lecture.

This survey is part of a larger project the Mathematics Department is undertaking —  Mathematics in Context: Developing Relevancy-Orientated Problems — in an effort to improve our teaching.

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

Maths Classes will be going full steam ahead on Monday 22 October as well as Wednesday, Thursday, Friday 1, 2, 3 November. I will call the next two weeks by Week 7.

## Week 6

In Week 6 we finished looking at cantilvers and then summarised what we learnt about beams. We had one lecture as a tutorial but then looked at numerical approximations to solutions of differential equations that we cannot solve exactly.

After the storm last year I recorded some examples. If you missed some classes this week you could do worse than watch this cantilever example and this summary of beams to catch up

## Week 7

In Week 7 we will look at the Three Term Taylor Method and begin Chapter 3 on Probability and Statistics.

## Assessment 1

If you haven’t started this you seriously need to get cracking.

• The hand in deadline is 17:30 on Tuesday 16 October 2018.
• Hand it in class at 13:00 on Monday or else drop it into my office, A283. I should be here Monday 14:00-16:00, Tuesday 11:00-15:00 and 17:00-17:30.
• Hand in whatever you have done by the deadline: work handed in late will be assigned a mark of zero.
• Email me your Excel work.
• Print off a hard copy of your excel and submit this with any other written work.
• Further instructions in the manual.

## The Lee Fields Medal — CIT Maths Challenge

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

## Week 5

In Week 5 we finished looking at simply supported beams. We then looked at fixed end beams and cantilevered beams.

## Week 6

In Week 6 we will finish looking at cantilvers and then summarise what we learnt about beams but then look at numerical approximations to solutions of differential equations that we cannot solve exactly.

## Week 4

In Week 4 we started looking in particular at simply supported beams.

## Week 5

In Week 5 we will look at more examples of simply supported beams before moving onto fixed-end beams.

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 3

In Week 3 we finished Curve Fitting and started the second chapter on Differential Equations — with a particular emphasis on Beam Equations.

## Week 4

In Week 4 we will start looking in particular at simply supported beams.

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.

## Tutorials

Are now running as per your timetable.

## Week 2

We introduced Lagrange Interpolation and Least Squares curve fitting.

## Week 3

We will speak briefly about the Pearson correlation coefficient, and will begin talking about fitting curves/models that aren’t of the form

$Y=a\,\theta_1(X)+b\,\theta_2(X)$

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.

## Manuals

The manuals are available in the Copy Centre. Please purchase ASAP. More information has been sent via email.

## Tutorials

Tutorials, which are absolutely vital, start next week.

## Week 1

In week one we had one and a half classes. One class was given over to a general overview of MATH7019 and we spent about half an hour introducing the topic of Curve Fitting.

## Week 2

We will introduce Lagrange Interpolation and start talking about Least Squares curve fitting.
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“Straight-Line-Graph-Through-The-Origin”

The words of Mr Michael Twomey, physics teacher, in Coláiste an Spioraid Naoimh, I can still hear them.

There were two main reasons to produce this straight-line-graph-through-the-origin:

• to measure some quantity (e.g. acceleration due to gravity, speed of sound, etc.)
• to demonstrate some law of nature (e.g. Newton’s Second Law, Ohm’s Law, etc.)

We were correct to draw this straight-line-graph-through-the origin for measurement, but not always, perhaps, in my opinion, for the demonstration of laws of nature.

The purpose of this piece is to explore this in detail.

## Direct Proportion

Two variables $P$ and $Q$ are in direct proportion when there is some (real number) constant $k$ such that $P=k\cdot Q$.

Correlation does not imply causation is a mantra of modern data science. It is probably worthwhile at this point to define the terms correlation, imply, and (harder) causation.

### Correlation

For the purposes of this piece, it is sufficient to say that if we measure and record values of variables $x$ and $y$, and they appear to have a straight-line relationship, then the correlation is a measure of how close the data is to being on a straight line. For example, consider the following data:

The variables $y$ and $x$ have a strong correlation.

### Causation

Causality is a deep philosophical notion, but, for the purposes of this piece, if there is a relationship between variables $y$ and $x$ such that for each value of $x$ there is a single value of $y$, then we say that $y$ is a function of $x$: $x$ is the cause and $y$ is the effect.

In this case, we write $y=f(x)$, said $y$ is a function of $x$. This is a causal relationship between $x$ and $y$. (As an example which shows why this definition is only useful for the purposes of this piece, is the relationship between sales $t$ days after January 1, and the sales, $S$, on that day: for each value of $t$ there is a single value of $S$: indeed $S$ is a function of $t$, but $t$ does not cause $S$).