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Thursday, February 3, 2011

M381 TMA01 progres

Completed another question today. "Prove that the last digit of a triangular number cannot be 2,4, 7 or 9".

1. Hi Nilo this isn't strictly relevant but I thought you and all
your followers might be interested in the following letter on the
maths course choice forum about the
proposed replacement for the 3 third level courses
M336 Group theory
M338 Topology
M381 Number theory

The idea is to merge it into a 60 point course. I have mixed feelings
but I should be able to complete M338 and M336 next year so it doesn't really affect me. It would seem that the geometric aspects of group theory and topology are being dropped also continuity is going to be explained in sequences rather than open sets which is the mainstay of most of the books on topology and functional analysis I have on my book shelf. On the other hand the fact that a module on rings and fields is going to be introduced is good news. In an ideal world they would keep the current 3 courses with maybe some slight updating and introduce the module on rings and fields as a separate unit. Interesting they don't mention Galois theory so may be they just take you half way up the hill and leave the rest up to you.

As one of the individuals currently trying to shepherd the proposal
>for M303 (working title: Further Pure Mathematics) through the OU's
>Byzantine approvals process, I can give you some idea of what the content
>of M303 is likely to be.
>
>The module will consist of 6 books in the following order:
>
>Numbers I
>Groups
>Numbers II
>Metric Spaces I
>Rings and Fields
>Metric Spaces II
>
>Numbers I and II will be based on the numbers half of M381 and the
>content is not expected to be drastically different, although there will
>be two units of new material introducing rings (using number theory as
>motivation).
>Groups will be a (proper) subset of M336, Groups and Geometry (4 units
>worth: Groups, Abelian and Cyclic Groups, Finite Groups, Sylow's
>Theorems)
>Metric Spaces I and II will be heavily based on M338 but will exclude
>topological spaces and the block B material on geometric topology. There
>is likely to be a little new material on metrics in groups. The emphasis
>will shift from discussing continuity in terms of open sets to discussing
>continuity in terms of sequences as a consequence of working only with
>metric (rather than topological) spaces. This will probably be the most
>changed of the preexisting material.
>Rings and Fields is new and will develop the theory of rings and fields
>and show how it is used both in public key cryptography and in
>understanding `ruler and compass constructions' (eg: why can you not
>trisect an arbitrary angle using only a ruler and compass).
>
>Overall about two-thirds of the material in the module will be drawn from
>M336, M338 and M381, although some of it will be heavily revised.
>
>There will also be material on the historical context of the topics:
>currently we think this will be in the form of an extra chapter/appendix
>in each book discussing the history of the subject matter but the detail
>of this is still to be settled.

2. I was hoping to take M336 next year, and potentially M338 (not least of which because I like the tutor I'd likely be working with for one or both.) After 120 credits at Level 3 this year, I was hoping for a quieter time, but I really was hoping to do both courses in their entirity.

As an aside, how are you both finding M381 so far? (Chris, I think you might be in my Tutor group actually :))

- Kevin

3. I am busy as it is with 60 (...) at level 3 But as I have explained, getting a degree is the last of my goals. My goals are no secret, they are on the top of my blog.

To the point. Your question about M381. I think it is a great course. The logical stuff has jaw dropping theorems and although I had already studied most of the NT topics elsewhere, after studying a topic in M381 I feel as though I own it. - I would certainly recommend this course.

4. I'd definitely agree on recommending M381 as a course. It's probably been, all in all, the most challenging course I've taken with the OU - you're right about the jaw-drop moments with some of the results, especially for me in Number Theory. I've had a few late nights scribbling away on the white-board trying to go through proofs, and it's really a good feeling to actually cement some of it in my mind.

For me, the degree isn't so much as important as the journey towards it. I think I'm just finding these days that with potential course cuts, I'm trying to fit in a lot of courses before they possibly go away. I think with an unlimited amount of time I'd happily sit and go through the entire curriculum if I could.

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)