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Wednesday, October 13, 2010

M208 is done.

A rather dark side of my personality manifested itself the last two months or so. Don't worry I killed the monster. I sort of digressed to the period when I was in high school, i.e. I did not send my work on TMAs 6 and 7 to my tutor since I more or less had it with that reptilian. Goodbye wished for, hoped for distinction. More about this in another post. In this post I'll report about the exam itself.

The exam took place in The Hague. I counted four people coming in doing M208 but there could have been more. In the examination room with about 16 or so people I have seen at least three different sets of papers of which S320 was one. It was mentioned that two people did not show up. When we entered the room we got our papers and could choose a place to work for ourselves.

At 2.30 PM ( local time ) we were allowed to open the paper. Same format as MS221, i.e. two parts A and B. Part A had 12 questions with a maximum score of 70. And Part B was a 2 out of 5 set. We could choose two questions of 15 points each. From what I recall the questions in part A were about ( not in order ):
1. Graph of (2x+3) / (3-x), incl. asymptotes and axes-intercepts.
2. Solving an inequality.
3. Diagonalizing a matrix using eigenvectors.
4. Question about [{1,2,4,9,10,12}, mult mod 13]
5. Question about Homomorphism z->|z|^2.
6. Question involving R2 geometry using vectors and inner product
7. Question on series
8. Finding an integral
9. Question on a Taylor series
10. Question about permutations
11. Question about the symmetry group of the pentagon.
12. ( Forgotten )

At 4.30 I had completed 9 out of 12 questions. Last year with MS221 I continued working on part A with the result that I only completed half of a question of part B. I think it was a correct decision. I had three questions left which would take me at least 40 minutes, leaving 20 minutes for part B. I could score 18 max. Continuing with part B at this point gave me an opportunity to collect 30 points although part B questions are somewhat more difficult.
I was getting tired and somewhat stresssed. Again, I did not complete all 12 questions in 2 hours. I did not take time to read all five questions. I started to work on question 13 which was on group theory.

13. A question about some finite group with 16 elements. The Cayley Table was given, nothing else.
- Find a cyclic subgroup, call it H.
- Prove that H is normal and that group K ( given ) is not normal.
- List elements of quotient qroup G/H
- Determine the structure of the group.
- ( One more question, forgotten )

It was now 17.00, I chose the next question on Linear Algebra
14. About a linear transformation in R3.
- Find the dimension of the kernel
- What is the geometry of the kernel
- Find a basis of the image
- What is the geoemtry of the image and find an equation
- Given two sets of 3equations with 3 unknowns determine the number of solutions

I feel about the same as last year with MS221. I am fairly sure ( 99% ) of a pass.

All in all, I have learned a lot this year. About mathematics of course, but also about myself and about the effect a study like this can have on a person. Not everything has been said about this study year. More next time.


  1. Question 12 was an interval of convergence question with a convergent interval solution by the Alternating Test (minus one to the n all over n) and a divergent interval solution courtesy of the harmonic series (1 over n).

    I ran out of time, too, so didn't do 10 marks of questions (a bit of question 5 and the last bit of question 17).

    Hoping I got 85+ out of the 90 but it will be close.

    Seemed to be a lot of graph-sketching.:-/

    Wonder how many people spotted the interval for the Reimann sums - it was [0-1], while the graph asked for [-1 to 1].

    Thanks for your blog. It's been very interesting.

  2. We have to wait until late December, I suppose, before results come in.

  3. Hope you get the good mark you deserve sorry to hear about the last TMA's. Anyway level 3 courses count more for the final course. So if the other courses inspire you as I'm sure the group theory will then you will probably still get your distinction. I think the problem with M208 from what I can tell is that it tries to be all things to all people so if your main interest is in group theory and not analysis then you are bound to feel frustrated. Having a poor tutor as you obviously had probably doesn't help matters either.
    Anyway please keep blogging

    Best wishes Chris

  4. Chris, This week it's your exam, right? I'll hope everything goes well. Please share your experiences here or elsewhere. Good luck! - Maybe this helps. It takes about an hour to complete the two part B questions. If you haven't completed all 12 questions in 2 hours. Make a calculated decision about continuing / quitting A. - Good luck!

  5. Thanks Nick, the exam is tomorrow from my experience in practice. I find I tend to make silly mistkes on numerical problems such as finding closed form of recurrence relationships and especially the rather tedious Euclidian Algorithm and curve sketching (ugh). So my plan is to do the questions I find enjoyable first such as calculus, finding fixed points, eigenvalues and group theory quickly to give me
    a head start. If I get bogged down then I'll move on. I aim to get about 60% in part A and then 20 -25% in part B. So that distinction is within my grasp but I suspect I'm looking at grade 2 pass. A real problem with the structure of the exam is that by having so many short questions it's easy to drop a mark or two per question. Conversely if it had say 5 or 6 long questions then a it would give you more chance to show how you can tackle challenging questions. A final point is that the OU seems to set the bar, rather high in most universities a mark over 70% would be enough to get a first and 60-70 would be enough to get a 2i. I resent the fact that a whole years work is effectively crammed into 3 hours.

    Anyway I'll let you know how I get on

    Thanks for the support. After tomorrow like you I will be able to concentrate on the maths I really enjoy again for a few months.

    Best wishes Chris

  6. Ok as requested here are my initial impressions of MS221 2010. I'll give a more detailed breakdown in a day or two's time. Ok just like M208 there are 12 short questions and a choice of 2 out of 4 long questions.

    the short questions were

    1 recurrence relations
    2 ellipse given as parametric equation
    3 Trig identities
    4 Combinations and coefficient of Binomial expansion
    5 Affine transformation
    6 Eigenvalues eigenvectors of matrix
    7 Differentiation using product and composite rules
    8 Integration by parts and substitution
    9 Taylor series
    10 Complex numbers
    11 Division of complicated no and Fermat's little theorem
    12 Induction involving nth diffrentiation of
    (-1)n+1 (n - 1) exp(-x)

    All of these relatively straightforward but may have expressed myself badly in induction and Fermat's theorem question so a few lost marks there and also didn't get consistent recurrence relation but method correct so estimate about 60% - 66% for part 1. Answered in order 7,8,9,10
    3,6,5,4,1,2,11,12 by which time 1 had 50 minutes left for part B
    Questions were
    13 hyperbola and rotation
    14 Fixed points
    15 Calculus
    16 Group theory

    Did most of 14 and think I got most of my marks there now 5:05 and made big mistake went for calculuse question instead of 13 and got bogged down at most only 5 points from this question so overall esttimate is between 75 - 80 marks so a reasonable grade 2 pass on the cards but distinction definitely out of reach unless examiners feeling particularly generous.

    Anyway looking forward to doing maths I enjoy. Have Brannan's book on analysis which covers M208 analysis and luckily have managed to old course material for M201 an early OU course on linear analysis which goes into the subject in far more detail than M208 does. Includes things like convergence in Euclidean spaces and the strong analogy between special functions such as Bessel and Lagrange functions and vector spaces. All good background in a relatively concrete sense for my ultimate goal which is to understand Complex Hilbert spaces as a preliminary to understanding the mathematical structure of quantum mechanics.

    Also want to do some physics including a proper understanding of the Peebles calculation of the Hydrogen Helium abundance in the early universe one of the key planks in establishing the big bang. Also some quantum field theory calculations.

  7. Ah, your goals are in quantum physics! ( In these terms my goal is to one day understand the Prime Number Theorem. ) I am lost when you start about particle physics stuff. I am not sure but I think a lot of group theory ( i.e. Lie Theory ) is on your path as well.

    About the exam: it looks like a sure grade 2 pass to me, well done. A bit of superstition ( who chooses anything 13-ish?! ) might have got you the distinction. Same sort of questions like last year it seems from your description. Keep that in mind with M208. Studying past exams does help.

    So they made M208 simpler?! I read the biography of Alan Turing, in those days the students really got a LOT of math. Universities held entry exams and they accepted only the x% best or so. Even Turing failed once. The bad think that education was only accessible for the elite classes, but this is politics.

    Thanks for your report!

  8. Thank you Nilo I got the paper today and redid the calculus question straightforward if you have time to think but not under exam pressure. A group of us from this years presentation of MS221 are getting together to provide a set of solutions to the 2010 from MS221. A number of the friends I made will be doing MST209 so look out for them next year.

    My main interest is quantum mechanics and inspired by your blog I'm going to try and set up one of my own over the next week or so. My interests are Philosophy Classical Music, Mathematics and Physics and I hope to make an interesting blog outlining all my projects including my Open University courses. Watch this space.

    As for M208 being simpler I think yes they did. In the early days the foundation course covered a lot of mathematics including an introduction to analysis and second order differential equations. In the second year there were courses 3 second level courses

    1) Real Analysis based on Spivak's book Calculus

    2) Linear Mathematics based on two books

    Linear Algebra and Matrix Theory by E Nering (not as dull as it sounds the last chapter has a good introduction to group representation theory and its application to multi-mode oscillations and molecular vibrations however this wasn't covered in the linear analysis course)

    Then a book which is rapidly turning into one of my favourite books on mathematics
    An Introduction to Linear Analysis
    by Krieder, Kuller, Ostberg and perkins

    Anyway a list of the topics covered in M201 are Vector Spaces Linear Transformations Differential Equations 1st and 2nd order inhomogeneous equations, Fourier series partial differential equations and so forth. However the most interesting part is the deep analogy made between Euclidean space and vector spaces. As you are probably aware, there is a powerful analogy between function space and vector space. The simplest example being a set of funcitions defined by sin(x) and cos(x). Over a certain interval and suitable normalisation these can be defined as a set of basis vectors the analogy with the scalar product being the intergral from -pi - pi of sin(kx)*sin(mx) which is non zero only when k = m. So an integral over this pair can be seen as a scalar product of two vectors. Anyway the point is that this type of orthogonal integral can be defined for all sorts of functions which arise as a solution of various differential equations such as Bessel Functions Legendre Polynomials and so forth. The course covers Euclidean space. From there it is but a short leap conceptually to Complex Hilbert space which is the mathematical space underlying quantum mechanics. It's a real shame the OU have dropped this course. MST209 whilst covering the same ground in terms of technique doesn't really do justice to the underlying structure and so a lot of people will come away thinking that Applied maths is just a series of techniques.

    Sorry for this rambling post but i share your opinion that whilst the Open university is fine as it goes it really could and has done in the past a lot more than it is doing at present.

  9. Hello Chris,

    Great news that you are starting your own blog. Count me in as a subscriber. Very nice of you to say that my blog inspired you to do so. ( If you choose Blogger from Google as your host we can even exchange tips about gadgets and styling. )

    I don't know if you have watched any of the Abstract Algebra videos by Benedict Gross of Harvard University. In one of his lectures he said: "You can never learn enough Linear Algebra". Your point about function and vector spaces proves his point once more.

    I understand your anger. Wait until you hear my forthcoming rant about MT365. ( I want it to be my last post of 2010. ) What I want to say now is that we should not blame the Open University. Not yet anyway.

    Mathematically we are going in a different direction, one more reason I am looking forward to see your forhcoming blog evolving. I am basically fascinated by numbers and thus the prime numbers. My interest in Group Theory can be explained from that perspective. There is a deep connection between groups and the primes. ( Just think of the Lagrange's Theorem about the order of a subgroup, there are many more involving primes. ) Numbers are in our head basically, they don't occur in nature. But groups do occur in nature in the form of symmetries. (?! ... ?! ) I see the mystery about prime numbers as the Holy Grail in mathematics.

    I see it like this. We are on our own in our quest. All mathematical knowledge is within our reach thanks to the blessing of the Internet. Our Open University study is just an explanation about our doings to the uninitiated.

    Kind regards,

  10. It was via your blog that I watched a few of the lectures and bought Artin and intend to deal with that subject maybe in 2012. So once again thanks for the inspiration. I see eventually our blogs becoming complementary I'll concentrate on linear analysis to start with and work all the way up to functional analysis and you will continue to do your really inspiring stuff on group theory and number theory. I also agree that we are essentially alone in the quest and the Open University for all its faults provides a starting point. I'm just annoyed that opportunities which were there twenty to thirty years ago are no longer there. Still with a bit of luck we can piece together what we could have done. For example as well as M201 there was also M202 which was called topics in pure maths and this was based on the four books

    Halmos Set Theory
    Herstein Topics in Algebra (including Galois theory !!0
    Minsky Computability
    Medelson Topology

    So by level 2 most people would be in a much stronger position than we will be by the end of level 3. Proof surely of the dumbing down of educational standards. It's a real pleasure to find someone like your self who insists on the highest standards possible.

    I accept in a climate of cut backs it's not the Open university's fault but I really think things are beginning to seriously bite.

    Anyway I hope to set the blog up this weekend

    Thanks again for being such an inspiration.

  11. Hi Nilo

    Just to let you know I've gone live the link is

    Hope you find it interesting

    Best wishes Chris

  12. Hello guys ! am new here, considering to complete my OU Degree in Maths Honours after a gap of 17 years !!! Can anybody suggest me if it is in reach to start with M208 and learn by youself at home easily while u r working along ?? or is it really intensive and time consuming ?

  13. M208 is a 60 point course, that can ( just ) be done alongside a full-time job. M208 is not where people usually start though: it is MST121. You have to make sure that you have the credits from courses elsewhere to start at level 2. Contact the OU for that. - Good luck!


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