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 jippo@campus.ie and I will add you to the mailing list.

## This Week

On Monday we had a test and on Wednesday we finished off the first part of the course titled “Discrete Dynamical Systems”.

In the tutorial we discussed the terms eventually and converges. We also discussed how to solve the following problem:

Find points $x_0$ and $x_1=f(x_0)$ such that $x_0$ is eventually periodic but neither $x_0$ nor $x_1$ are themselves periodic.

Finally we answered 2009 Q. 2(b).

## Next Week

Before I start complex numbers I am going to do 2010 Q. 3(b)(iii) and 2009 Autumn Q. 3(d), (e). Then we shall begin complex numbers. Perhaps a quick review of Leaving Cert (Ordinary or Higher Level) Complex Numbers would be a good idea for you.

I have copies of some notes that give some more in depth information on the logistic map. If you would like a copy of these drop me a line.

## Test Results

I won’t have them as fast as I’d like is all I can say. I’ll do my best.

## Homework

Now that the test is over I am trying to draft your homework ASAP. I hope to give you a choice of more than one project —all will be on topics that are extensions or generalisations of what we have covered in the class. The final date for submission is 24 April 2012 so I will definitely want to draft this homework by Monday week 5 March 2012. You will have full freedom in which one you want to do and 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 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), my name, and your declaration on your homework.

## Problems

2010 Q. 3(b)

2010 Autumn Q. 3(b)

2009 Autumn Q. 3