TMA06

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.