I have now completed TMA06 and just have to write it up neat. There weren't any nasty surprises in this TMA and it all pretty much fell into place. One thing I found, though, was that the answers to the exercises for the AB books tended to make more assumptions about continuity and the behaviour of limits. I wanted to follow this example but found that I wasn't always happy making these assumptions. In the end I decided to add an appendix to my answers where I proved some of the assumptions I was making. Not surprisingly some of these proofs were nearly as long as the answers themselves, which probably explains why assumptions have started to creep into the text.
Wanting to get all the course work out of the way I have started TMA07. The first question was a bit of a tease which surprised me a bit, but I saw the light in the end.
I have started reading a few books now that I have more time. One is "Einstein, A Life in Science" by John Gribbin and Michael White and the other is "The Millennium Problems - the seven greatest unsolved mathematical puzzles of our time" by Kevin Devlin. The Einstein book is a biography and I enjoy these type of books. It is clear that the young Einstein didn't like authority, tended to avoid lectures at University and only wanted to study things that interested him. It is fortunate for us that this didn't ultimately affect his career!
The Millennium Problems interest me. In 2000 the Clay Mathematics Institute decided to offer seven $1 million prizes for those who could solve seven of the most currently difficult outstanding problems of current mathematical research. This was a bit like the 23 problems outlined by David Hilbert in 1900. One of the Millennium Problems, the Poincare Conjecture, has already been solved by Grigori Perelman but he rejected the prize! The problem that interests me the most is the Riemann Hypothesis because this is related to prime numbers.
Saturday 19 May 2012
Thursday 10 May 2012
The End
I have reached the end of the text for M208, so that's quite a milestone reached, and I won't have to tackle any new material from now on. I started working on M208 back in mid February 2011 and so it has taken me a year and three months to read through what should really take eight months, so I have been going at roughly half speed. I haven't done the further exercises yet, but I have read and worked through nearly every proof and, believe me, that was quite a chore. On the last book I gave up with reading the very last optional proof as I just couldn't be bothered!
I enjoyed AB4 on Power Series. It was a nice amble through Taylor polynomials, Taylor's Theorem, Taylor Series and manipulating power series. Nothing too difficult and all fairly straightforward, so it maybe a topic to choose in the exam.
So what now? Well, there is TMA06 and 07 to do. That will be my first priority. Then I will be keeping things ticking over for a while by doing the further exercises. I plan to do these at random, so that I have to practise working from different parts of the course at the same time. I will also just try and work from the Handbook and see how I get on. I suspect that at this stage I will be adding a few extra notes to this where I think there isn't enough information to get me going on a question. Then sometime around late August I will start turning my attention to past exam papers and practise getting questions answered quickly and honing those skills ready for the exam in October.
I have already started think about what I might do next and this probably won't involve the OU for now. I intend to start another blog about my own explorations into prime numbers. I have also thought that I might begin trying to understand some chapters from 'An Introduction to the Theory of Numbers' by Hardy and Wright. Then another avenue for me is, perhaps, to get to grips with Special Relativity which I felt I never really did when I was a physics undergraduate. The thing is there are so many choices of things to do that I will probably not know where to start! I still have all my undergraduate text books and it is tempting to delve into Quantum Mechanics again, or Electromagnetism, or perhaps finally sit down to 'Gravitation' by Misner, Thorne and Wheeler!
I enjoyed AB4 on Power Series. It was a nice amble through Taylor polynomials, Taylor's Theorem, Taylor Series and manipulating power series. Nothing too difficult and all fairly straightforward, so it maybe a topic to choose in the exam.
So what now? Well, there is TMA06 and 07 to do. That will be my first priority. Then I will be keeping things ticking over for a while by doing the further exercises. I plan to do these at random, so that I have to practise working from different parts of the course at the same time. I will also just try and work from the Handbook and see how I get on. I suspect that at this stage I will be adding a few extra notes to this where I think there isn't enough information to get me going on a question. Then sometime around late August I will start turning my attention to past exam papers and practise getting questions answered quickly and honing those skills ready for the exam in October.
I have already started think about what I might do next and this probably won't involve the OU for now. I intend to start another blog about my own explorations into prime numbers. I have also thought that I might begin trying to understand some chapters from 'An Introduction to the Theory of Numbers' by Hardy and Wright. Then another avenue for me is, perhaps, to get to grips with Special Relativity which I felt I never really did when I was a physics undergraduate. The thing is there are so many choices of things to do that I will probably not know where to start! I still have all my undergraduate text books and it is tempting to delve into Quantum Mechanics again, or Electromagnetism, or perhaps finally sit down to 'Gravitation' by Misner, Thorne and Wheeler!
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