Category Archive

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Scanned Notes

Go to Canvas -> MATH6004 -> J.P. McCarthy to find some of the notes scanned. I want to scan all the notes but one of your classmates has gone AWOL with my notes.

Quizzes 5

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 11:05-11:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Week 12

We had our quiz on Monday, and after this we will finished our material and then had some extra tutorial time. We did not cover the Gauss-Jordan algorithm for finding the inverse of a square matrix.

Week 13

In the ordinary lecture and tutorial slots we will have classes. In the lectures I will be doing revision by doing this paper:

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

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

Student Feedback

If you would like to give fully anonymous feedback on this module and my teaching please go here.

Usually I use the student feedback to get ideas to improve my delivery of a module. As I have referred to numerous times this semester, there are obvious ways to improve my delivery of MATH6004 (e.g. edit out the so-many typos, have more exercises in the manual, etc.), and I know myself how I can improve my delivery for next year.

Now, maybe you might give my ideas I haven’t thought about, but to be honest the main reason I am giving the fully anonymous feedback mechanism to ye is to give you a chance to have your say, and have me listen to you, and if that includes being very critical so be it. It is important to me not just that your voice is listened to but that you have a voice and you are given this opportunity to say your bit.

Scanned Notes

Go to Canvas -> MATH6004 -> J.P. McCarthy to find some of the notes scanned.

Quizzes 4 and 5

Quiz 4 will be based on what we covered in Week 10 and will take place Monday 24 April in the usual lecture venue, 15:05-15:20.

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 11:05-11:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Weeks 11

One thing that is not in the MANUAL is the transpose of a matrix. We covered this on Monday. Two things you want to know:

(1) The transpose of a matrix is a matrix formed by swapping the rows and columns of , e.g.

(2) If is an matrix then is an matrix.

We started looking at matrix inverses, and the formula for calculating the inverse of a 2×2 matrix. We learned that not every matrix has an inverse, and how the determinant can be used to determine if a matrix has an inverse. We saw how matrix inverses can be used to solve matrix equations, and how (linear) simultaneous equations can be written as a matrix equation (a linear system), and if the matrix of coefficients has an inverse, the solution of the linear system is unique. We learned that linear systems can also have no solution, or infinitely many solutions, and we saw how Gaussian elimination can be used to see if a linear system that does not have a unique solution has no solutions or infinitely many solutions.

Week 12

We have our quiz on Monday, and after this we will finish Chapter 3 with the Gauss-Jordan algorithm, and then hopefully have some extra tutorial time.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

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

20% Test and Quiz 3 Results

The 20% Test results were released in a Canvas announcement, and students can view their script in this week’s labs. The solutions are now in the same announcement if you wish to view these.

I hope to have Quiz 3 corrected by the end of the week.

Quizzes 4 and 5

Quiz 4 will be based on what we covered in Week 10 and will take place Monday 24 April in the usual lecture venue, 09:05-09:20.

Quiz 5 will take place Wednesday 3 May in the usual lecture venue, 10:05-10:20. If this clashes with something, it is your responsibility to contact me. I could move it to Tuesday 2 May in that case.

Quiz 5 will be four quizzes in one: it will be (fairly different) versions of Quizzes 1, 2 (harder), 3, 4, and you pick the one you want to do.

Your 10% quiz grade will be the best four quizzes that you complete from the five opportunities.

Week 9

We will had Quiz 3 20 March at 3 pm in the usual lecture venue. It was based on argument and inference. The timing was not great considering would go on to have a full week of tutorials on argument an inference. However, to balance things out, Quiz 2 was probably too easy, and we are going to have a Quiz 5 in Week 13, and you will be marked out of your four best quizzes. See below.

Week 10

We started the final chapter on Linear Algebra. We had some discussion of vectors, then linear maps, and finally matrices. We are doing matrix arithmetic and the standard matrix representation of a linear map.

Why do we multiply matrices like that?

Weeks 11-12

We will finish the final chapter. We will probably be doing new material right up to the end of Week 12.

I had planned on having a catch-up lecture because I missed a Monday in Week 8. Unfortunately there is no time that suits everyone so that class will have to be cancelled. My apologies.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

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

COMP1B-Y tutorial in Week 8

In Week 8, Thursday March 16, the COMP1B-Y tutorial will be held at 10:00 in A243L rather than 11:00 in C128.

Quiz 3

We will have Quiz 3 20 March at 3 pm in the usual lecture venue. It will be based on argument and inference.

Week 8

I was sick for Monday’s lecture. We will catch up on this in time.

We spent the Tuesday and Wednesday lectures, and the tutorial, on argument and inference.

Argument and inference is difficult: and we will be spending all week trying to get a better handle on it.

Week 9

We will have Quiz 3 20 March at 3 pm in the usual lecture venue. It will be based on argument and inference.

Argument and inference is difficult: and we will be spending all week trying to get a better handle on it.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

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

COMP1B-Y tutorial in Week 8

In Week 8, Thursday March 16, the COMP1B-Y tutorial will be held at 10:00 in A243L rather than 11:00 in C128.

Week 7

We started talking about argument and inference. We had additional tutorial time again on Tuesday and our 20% on Wednesday evening.

Week 8

Argument and inference is difficult: and we will be spending all week trying to get a better handle on it.

Week 9

We will have Quiz 3 20 March at 3 pm in the usual lecture venue. It will be based on argument and inference.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

Week 13: 2.5% Quiz 5

Your quiz score will be best four of five.

70% Terminal Exam

Student Resources

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

20% Test in Week 7

There will be a 20% Test based on the material we covered in the first five weeks.

• Wednesday March 8th, 6-7pm, Melbourn Hall

For those enrolled on Maths Online, there are some videos here. Please let me know if this link does not work.

Week 6

On Monday we continued working on logic, doing more examples with logical equivalence. Either simplifying compound propositions, or showing that two compound propositions are logically equivalent. On Tuesday, we had a tutorial-lecture, looking at p.41. I also gave out the following table. On Wednesday we started talking about argument and inference.

In tutorials you worked on p.41 also.

Week 7

We will do more argument and inference. We will have additional tutorial time again on Tuesday.

COMP1B-Y tutorial in Week 8

In Week 8, Thursday March 16, the COMP1B-Y tutorial will be held at 10:00 in A243L rather than 11:00 in C128.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

70% Terminal Exam

Student Resources

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

Quiz 2

The second 2.5% quiz will be 15.05 pm (SHARP), Monday 27 February in B217. The quiz will be projected on the screen, and you will write your answers on a sheet I hand out at the start of class.

The quiz will be bases on sections 2.1, 2.2, and 2.3. You will need to know what a proposition is, you will need to understand the basic logical connectives (but not the material implication nor biconditional). You will also need to be able to complete and construct truth tables.

20% Test in Week 7

There will be a 20% Test based on the material we covered in the first five weeks.

• Wednesday March 8th, 6-7pm, Melbourn Hall

Watch this space (or Canvas) for more information.

Week 5

We continued working on logic, defining the logical equivalence of compound propositions and by:

• when is a tautology, we say that and are logically equivalent, and we write

We had a whole collection of “laws of logic”, which are common logical equivalencies. Your idiot lecturer has some typos here that we will correct on Monday (after Quiz 2). Like with the laws of sets, we can use these laws of logic to simplify compound propositions. Another question type is to show that two compound propositions are logically equivalent, . We can use these laws of logic, or show using truth tables that is a tautology.

On Tuesday, we had a tutorial-lecture, looking at p.36. In tutorials you worked on exercises (p.36, 41).

Week 6

We will do more simplifying using laws of logic (after Quiz 2). We will have more tutorial-lecture time on Tuesday. Then we should start argument and inference on Wednesday.

COMP1B-Y tutorial in Week 8

In Week 8, Thursday March 16, the COMP1B-Y tutorial will be held at 10:00 in A243L rather than 11:00 in C128.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

70% Terminal Exam

See Canvas for more:

Student Resources

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

Quiz 2

I am going to try the projection of the quiz again but in B217.

The second 2.5% quiz will be 15.05 pm (SHARP), Monday 27 February in B217. The quiz will be projected on the screen, and you will write your answers on a sheet I hand out at the start of class.

The quiz will be bases on sections 2.1, 2.2, and 2.3. You will need to know what a proposition is, you will need to understand the basic logical connectives (but not the material implication nor biconditional). You will also need to be able to complete and construct truth tables.

Week 3

Well, Week 3 was a disaster with the cyber attack.

Week 4

We continued talking about logic. We had some extra tutorial time on Wednesday, and we will probably have this on Tuesdays in future.

This is what we have done thus far in logic:

• You should know that a proposition is a statement that can be assigned a truth value: either true (T) or false (F).
• Given a proposition you can form a proposition , the negation, which is true whenever is NOT true.
• Given propositions you can form the proposition , the disjunction. This is a proposition that is true when either OR (or both) are true.
• Given propositions you can form the proposition , the conjunction. This is a proposition that is true when both AND are true.
• A truth table for a compound proposition, a proposition consisting of basic propositions , gives all the possible truth assignments of , and the corresponding truth value of the compound proposition.
• Given propositions you can form the proposition , the material implication. Said “if then ”, or implies , it is false only if is true and is false.
• Given propositions you can form the proposition , the biconditional. Said “ if and only if “. It is true when the truth values of and are EQUAL.
• Given a compound proposition , a proposition consisting of basic propositions , we say that is a tautology if it is true for all truth values of .Given a compound proposition , a proposition consisting of basic propositions , we say that is a contradiction if it is false for all truth values of .

Week 5

We will continue our work on logic.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

70% Terminal Exam

See Canvas for more:

Student Resources

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

Quiz 1

The first 2.5% quiz will be 11.05 am (SHARP), Wednesday 8 February in F1.2. The quiz will be projected on the screen, and you will write your answers on a sheet I hand out at the start of class.

The quiz will be a single question with three parts, worth 1%, 1%, and then a harder part (that will require independent thought) worth 0.5%.

It will be a 15 minute quiz, and the contents of Section 1.1 will be examined. Relevant exercises:

• Supplemental Exercises, p.3, Q.1-9
• Manual, p.14, Q.1-7.

Starred Exercises are harder than will be examined in the quiz.

Manuals

You need to purchase the manual. See here for details.

Week 2

In Week 2 we looked at arithmetic and geometric sequences in more detail, before going on to do some mathematical modelling using recurrence relations.

We started the chapter on logic.

Week 3

We will continue diving into logic.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

Week 3: 2.5% Quiz 1

Week 6: 2.5% Quiz 2

Week 7: 20% Test

Week 9: 2.5% Quiz 3

Week 12: 2.5% Quiz 4

70% Terminal Exam

See Canvas for more:

Student Resources

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

Manuals

COMP1B are required to purchase an academic manual for MATH6004. This contains a lot of the lecture notes and exercises for the module. The lecture notes contain gaps that we fill in during class. I will have notes for you for the first week but after that you must purchase the manual: the sooner the better.

The manuals can be purchased from Reprographics\Copy Centre beside the Student Centre. Note that this is a cash-free area so you will need to put the appropriate amount of funds — €8.50 — on your student card.

I will be writing in various colours, so maybe  a four colour pen would be useful.

Week 1

After first-day introductions, we started talking about sequences and sequences defined by a recurrence relation. We met a famous example, the Fibonacci sequence. We started talking about the sum of a sequence.

In tutorial we worked on recurrence relations, Q.1-9 on p.14. The following additional exercises to p.14 are important:

• Q. 2 write F(1000) in terms of F(998) and F(997)
• Q. 3 write C(1000) in terms of C(998) and C(997) (which includes something with just C(998))
• Q. 4 write V(1000) in terms of V(998) and V(997) (which includes something with just V(998))

Week 2

In Week 2 we will look at arithmetic and geometric sequences in more detail, before going on to do some mathematical modelling using recurrence relations.

Academic Learning Centre

Have you heard about Maths Online on Canvas? It’s full of helpful Maths and Stats resources, notes, quizzes and videos to help you throughout the whole year. 

We also use the Maths Online module on Canvas to offer Maths and Stats support to you and answer as many student questions as possible. 

Please log on to Maths online to book a maths appointment, book a place in a supported maths study session or request a workshop Links to an external site..

 If you have any other question about our Maths and Stats supports email us on Academic.Learning@mtu.ie 

Assessment

See Canvas for the assessment plan and schedule. We will probably have a quiz in Week 3. Watch this space.

Student Resources

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