## Wednesday, 12 October 2011

### M208 and M337 Exams Debriefing

Well what a day I started with M337 I have to say it was a fair exam even though I probably wont get higher than grade 3.
Part 1 has 8 questions the topics were

1) Allegedly simple questions on algebraic manipulation of complex numbers. However the last part was a fiendish raising a number to a complex power. In general for a complex number z
$$z^{\alpha} = exp(\alpha Log z)$$
where Log z = log|z| + iArg z

So it should have been simple to work out but I got bogged down

2) Sketching some sets and their difference and deciding whether or not the sets are regions, compact etc
Straightforward but I froze and for the life of me couldn't after about 2 attempts sketch the difference between the two sets.
It took me about 1/2 an hour to do these questions which should have been a simple warm up was not feeling very happy.

Then the core 3 questions on Complex Integration my favourite topic think I managed to do justice to all three parts and finished these in the next half hour so calmed down and felt a bit better,

Question 6 involved Rouche's theorem which is a method of finding zero's of a complex function within a given interval managed to get the first part out which is quite straightforward but unable to answer the last part as you had to work out how many of the zero's lay in the upper half and I couldn't see how to do it.

Question 7 was a standard one on fluid flows and their complex potentials and sketching the stream lines
I got the complex potential but couldn't sketch the stream line as it involved a complicated circle and I couldn't remember where the centre of a circle of the form

$$x^2 + y^2 + y = c$$ was

Question 8 was a question on Complex Iteration and determination of whether or not a point lay in the Mandelbrot set got about 3/4 of this question out

Part II there were 4 questions
9 Part 1 was on the Cauchy Riemann conditions which I think I managed to answer more or less correctly
Part II was on curves and the effects of a transformation. Normally the curves are quite straightforward but this time they weren't and so only managed to answer about 1/2 of the second part

Then my last question 10 should have been a straightforward derivation of a Laurent Series for the function

$$\frac{z}{1-cosz}$$

however I couldn't get it out all the usual tricks didn't work and I couldn't see how to proceed

I abandoned this and was able to answer a question on the Complex Integration of the series as they gave the answer. The second part was about the singularities of the function but by this time my brain was frazzled so I gave up.

So about 1/2 of part 2 answered. So not a satisfactory paper. I've done enough to pass probably grade 3
but certainly no more.

M208 This went much better
1 Sketch of a graph.
2 Exercise on proof involving the converse of a statement
3 Question on whether or not two sets were groups
4 Another question on groups and their cosets
5 A question on row reduction
6 A question on basis for a linear transformation I did not answer this as I hadn't revised this so left it
7 A question on the solution to an inequality
8 A question on whether or not two sequences were convergent or not
9 A question on the symmetry groups of a hexagon
10 A question on homomorphisms
11 A question on L'Hopital's Rule
12 A question on showing that an Integral was less than a certain value
Think I got most of this correct
So apart from question 6 managed to give reasonably full answers to most of the questions but may have lost one or two marks here and there

13 A question on the diagonalisation of a 3x3 matrix. Seemed to come out so confident that I got most of the marks for this question
17 A question on the Taylor polynomial of a function which I got most of

A question on the epsilon delta definition of continuity. By this time it was the last 15 minutes and I was feeling quite tired. Also as I did not write out a sample problem of this type in my handbook unlike some people I didn't phrase the answer properly so will probably only get a few marks for this question.

Still having answered most of part 1 and 3/4 of part 2 I think I've done enough to get grade 2 and if the examiners are feeling generous might get distinction.

Some people might think I'm being perverse in refusing to annotate the handbook. My argument is that the exam is a test of how much you know without any crutches. Not an ability to spot model answers to a question and then simply copying them out. There was much heated debate on this in the forum. In my opinion annotation should not be allowed however no doubt other people will think differently.

So a bit disappointed by my performance on M337 but reasonably satisfied with my performance on M208
Will try and review both courses in the next week or two and also how I plan to use down time productively.

1. Sounds like a fair go at both, Chris.
I really don't envy the thought of two pure maths exams in one day.
So, well done, given the immensity of yesterday as a whole.
No giant Cayley table in part 2?
Will you be taking a bit of down time, or cracking straight on with Calculus of Variations, etc for MS324?

2. Thanks
I'll start looking at a past paper for MS324 to see how much I can do
Also I want to finish the work on Big bang cosmology I started in August, Get back into Galois theory and Get back into the Cambridge computing projects. Just for starters.
Good luck for MST209 next week

3. Chris,

You must have a really good memory to remember what the questions were, after the exam. I find I leave exams and can only remember fragments. Post-traumatic Stress probably!

Well Done.

Dan

4. No there was no big Cayley table question otherwise I would have been tempted by that instead it was a permutation question.

There was also a question on testing functions for continuity and finding the least upper bound of a function. Felt more confident about the Taylor series one so went for that.

The other group theory question was on the counting theorem which I told myself I wasn't going to answer. I hate trying to visualise rotations of flags and or chessboards.

5. Hope you've done well, Chris. Really enjoying your blog, and the odd encounter I have with you on the OU forums. (This will increase when we both shortly start on M336 and M338 in the new year).
I'm completely with you on the non-annotation of Handbooks. It seems a bit of a cheat to me. In fact some of the Handbooks seem to have too much hand-holding information in them. But I guess in the real world, mathematicians can't remember every little detail, and so they must have to look things up on occasion, so in that respect, having a handbook is not to bad - but annotating with model answers? Thats not really for me!

6. Yes, it was a bit of a mixed bag. Though it sounds like you had a better experience with it than I did.

I can go either way on annotations. The main ones I put in were for things I've got a blind spot on (ie; differentation of a couple of specific functions. I can't see the point of wasting time working them out when that's not the point of the question (Taylor series and remainders for example)).

7. On Annotating the handbook: Interesting subject. I agree that annotating is questionable.

Unfortunately though, I fear that when you hand your degree profile to a prospective employer and it shows lower marks caused by not choosing to annotate, than someone who made full use of annotating their handbooks; One may have the moral high ground, but not necessarily the job, at the end of the process.

As the OU don't give out grades with an attached supplement stating (with / without handbook anotation), one is at risk of severe disadvantage, as you are competing against those that have annotated.

In previous art-history exams, I never took the opportunity to annotate and although I scored well, there were others who 'aced' those exams, who did annotate.

I have the moral high ground by not doing it, but they would probably get that prized PhD spot over me, if I had gone on to compete with them, based on grades.

It's a strange system, but one that I think needs to be played, if you are doing your degree for future career moves.

8. well I'm not really doing it for career moves as my career is pretty well established more for enhancing my own interest.

It's really a question of training yourself after all Cambridge Oxford Imperial and Kings don't even allow handbooks in their exams. If you make it to research you will realise there is no previous past question to guide you with a model answer prepared because it's by definition research. For my own ambitions all I need is grade 2 on average for each course My putative grade 3 on Complex analysis may put a small doubt on my ability to do the MSc but if it's at the high end Mid 60's then given that I've averaged 80% for the TMA's I'm sure they will let me on. Anyway thats in two years time.
I'm intrigued that handbooks were allowed in your Arts courses for my Psychology module and Philosphy course we were not allowed handbooks at all. Also some of the physics courses you aspire to Quantum mechanics etc only give a formula sheet based on the few past papers I've seen.

Sorry if thats a bit harsh I see where you are coming from but to be quite frank your main compettion will come from Russell Group students who got a first unaided by handbooks rather than other Open university studernts. If you get the MSc in maths then will supercede any results of your degree and I'm not sure if the MSc allows handbooks.

Chris

9. Did you say that you had a difficult time finding the center of a circle having the form:
x2+y2+y=c? (where I assume c>= -1/4)

10. Yes I just couldn't remember it during the pressure of an exam