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.

## Assessment 1

Assessment 1 will be on the Wednesday of Week 4, 5 October 2016.

The following  group will sit the assessment at 17:15 (arrive around 17:05):

• COMP1B-X

The following group will sit the assessment at 18:15 (arrive around 18:05)

• COMP1B-Y

Keep an eye on your CIT Blackboard and email for the latest and definitive assessment information.

## Week 3

We started the Assessment 2 material by looking at VAT, Income Tax and Interest.

## Week 4

We will continue our work on Chapter 2.

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.

## Test 1

The first 15% test will take place at 9 am Tuesday 18 October in B149 (Week 6). You can find a sample in the course notes, after the section on rates of change I think… actually I am not 100% where it is. It is a test that could arguably take 42 minutes but I’ll give ye from 09.05 — 10.00. You will be given a copy of these tables. Don’t worry I’ll scribble out the “UCC”!

Note that the format will be the same of this.

1. Differentiation from First Principles
2. Tangent Lines
3. Differentiate by Rule
4. Differentiate by Rule
5. Differentiate by Rule
6. Rates of Change
7. Rate of Change/ Geometry of Graph,

but this is dependent on our progress in lectures.

## Week 3

In Week 3 we covered everything in the notes up to the quotient rule.

## Week 4

In Week 4 we will talk about another way of combining functions — composition — and how to differentiate them — the Chain Rule.

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.

## Assessment 1

Assessment 1 has been emailed to all of you. The hand in date in Thursday 13 October. Work handed in late shall be assigned a mark of zero.

• I want you to read the first page carefully. When you start getting down to actually doing the assignment, read the problems carefully
• the purpose of this assignment is to help with your understanding of the material and hopefully this will end up with you being proficient in its use and able to do well in the final exam
• you should start right now because you only have two weeks to complete the assignment.
• yes you can ask me questions about the assignment before, after and sometimes during class (if ye are working on a problem). Also you can ask me questions via email.
• if you are having problems using Microsoft Excel then you are to email me ASAP and arrange to visit me in my office. You will bring your work on a memory key and we will sort it out
• The assignment is worth 15%. The question on the final paper will be worth 25% of the 70% — which is 17.5% — on offer on the final paper. Do a good job with this assignment and you should do well on Q.1 on the paper and you might just have 32.5% in the bag before we go onto more technical stuff.
• MOST IMPORTANTLY — you are welcome to work together. All of you have different data so none of you will have the same answers. Therefore you cannot copy each other. The best way to learn is by teaching.
• Work submitted after 17:30 on Thursday 13 October will be assigned a mark of zero. Hand up whatever you have on time.

There is a right way to think about equations and there is a wrong way to think about equations. Let us not speak of the wrong way…

The equations I have in mind are those equations written in the form

$f(x)=g(x)$,

where the aim is to find all the real numbers $x$ that ‘satisfy’ the equation.

We aren’t always taught the logic behind solving equations. The first thing to say is that many of us are trained to believe that this ‘$=$‘ means the ‘the answer is’. This is not what equals means. This may have happened to us because while young children our textbooks had stuff like

$2+6=\dots$

written in them… the ‘answer’ of course being eight and the = sign almost suggests that we have to ‘do something’ to $2+6$. Of course, this is not what equals means, and while the pupil who writes

$2+6=8$

is correct, the pupil who writes e.g.

$2+6=11-3$,

has written a statement just as true as $2+6=8$.

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 2

In Week 2 we looked at Decimals — including long multiplication and division — Ratio & Proportion and approximation. We have just began to look at percentages.

## Week 3

We will finish off the section on percentages and then look at error. This will conclude our study of the Assessment 1 material. After this we will look at tax and interest.

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 2

In Week 2 we covered linear least squares.

## Week 3

We will investigate how to handle 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.

## Week 2

In Week 2 we learned how to differentiate from first principles and also how to differentiate sums of differentiable functions.

## Week 3

In Week 3 we will continue talking about the duality between algebra & geometry and perhaps begin to talk about differentiating some more functions.

# Introduction

In Ireland at least, we first encounter fractions at age 6-8. At this age, because of our maturity, while we might be capable of some conceptional understanding, by and large we are doing things by rote and, for example, multiplying fractions is just something that we do without ever questioning why fractions multiply together like that. This piece is aimed at second and third level students who want to understand why the ‘calculus’ of fractions is like it is.

Mathematicians can in a rigorous way, write down what a fraction is… this piece is pitched somewhere in between these constructions — perhaps seen in an undergraduate mathematics degree — and the presentation of fractions presented in primary school. It is closer in spirit to a rigorous approach but makes no claims at absolute rigour (indeed it will make no attempt at rigour in places). The facts are real number axioms.

# Defining Fractions

We will define fractions in terms of integers and multiplication.

To get the integers we first define the natural numbers.

### Definition 1: Natural Numbers

The set of natural numbers is the set of counting numbers

$\mathbb{N}=0,1,2,3,4,\dots$,

together with the operations of addition (+) and multiplication $\times$.

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 Reprographic/Copy Centre. You will need these notes for next week.

## Week 1

We studied basic arithmetic, in particular we looked at the various number systems and the arithmetic of fractions in particular.

## Week 2

In Week 2 we will look at Decimals — including long multiplication and division — Ratio & Proportion and probably percentages too.

## Tutorials

Tutorials start properly in Week 2. See your timetable.

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 Reprographic/Copy Centre. You will need these notes for next week.

## Week 1

In week one we spoke about the questions that the derivative was originally formulated to answer. Namely how do we find the tangent to a curve.

## Week 2

In Week 2 we will look at calculating some derivatives.

## Tutorials

Tutorials start properly next week:

• Monday 17:00 in B189
• Friday 09:00 in B185

As discussed on Tuesday, you must make at least ONE of these classes every week.