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.


I am afraid I am a little on the busy side and ye might be waiting until around March 8 for your results. Just to clarify, I had intended for ye to prove rather than show in question 1; however I wrote show. Therefore if you used Theorem 1 or 2 to answer you will have to get full marks. However at the same time some people understood show as prove. By and large these people are looking at almost 100% but if they drop marks elsewhere, I will give a bonus mark to students who proved in question 1 rather than showed.


Please find the Homework. Before you open it don’t be too alarmed: you only have to do ONE of the SIX options. All of the options are about dynamical systems & complex numbers in different areas of math:

  1. Discrete Mathematics, Number Theory & Abstract Algebra
  2. Probability
  3. Differential Calculus
  4. Integral Calculus
  5. Linear Algebra
  6. Complex Numbers

Therefore, if you are good at differential calculus, for example, you should have a look at option 3.

All of these questions are unseen to you and — with the exception of Q.6 — all require some knowledge of modules you are doing now or have done before. Although we have been concentrating on real-valued functions on the set of real numbers (i.e. f(x), etc.), a lot of the theory carries over into more general sets and functions, and this is the main learning outcome of this homework.

I am not going to pretend that this is an easy assignment, but I will say that clear and logical thinking will reveal that the solutions and answers aren’t ridiculously difficult: a keen understanding of the principles of dynamical systems and a good ability in one of the options should see you through.

The final date for submission is 12 April 2013 and you can hand up early if you want. You will be submitting to the big box at the School of Mathematical Science. If I were you I would aim to get it done and dusted early as this is creeping into your study time and is very close to the summer examinations.

Note that you are will be free to collaborate with each other and use references but this must be indicated on your hand-up in a declaration. Evidence of copying or plagiarism (although this is unlikely as these are original problems by and large) will result in divided marks or no marks respectively. You will not receive diminished marks for declared collaboration or referencing although I demand originality of presentation. If you have a problem interpreting any question feel free to approach me, comment on the webpage or email.

Ensure to put your name, student number, module code (MS 3011), and your declaration on your homework.

Tutorial Venue

I have applied to get this changed to WGB G03… I didn’t get everything. The timetable is

  • This week coming 28 February LL2
  • 7 March LL2
  • 14 March WGB G03
  • 21 March WGB G03
  • 28 March WGB G03

Week 6

We finished describing what a chaotic dynamical system is and began our study of the tent mapping

What next?

We won’t be long finishing off our work on the tent mapping and then we will commence our third special study: of the doubling mapping.


Exercises for Thursday 28 February are to look at the following. Not a whole pile of new stuff covered so some revision.

Autumn 2009 Q. 2(b), 4

Summer 2008, Q. 1(a), 2(a), (b), 3, 6