Holidays at an end

The new year started today in terms of my normal PhD routine, following my return from the christmas holidays and the three week break. With the intention of fitting in work after the main christmas period, I had packed my bags expectantly with two text books and plenty of notes; although the reality of juggling lots of people to meet meant that not as much work as I would have liked was achieved in the first two weeks, the third week of the holiday was very productive.

The last week of the holiday can not really be counted as a holiday in the truest definition of the word, because — although not in Guildford — I have been working. In truth, it's been more of a grappling process than a working one, because I have been making my way through Peter Olver's book, Applications of Lie Groups to Differential Equations, which is certainly harder in parts than anything else I have encountered. My supervisor (Peter Hydon) asked me to look at the first two chapters, which approaches symmetry from a geometric point of view (which is to say it looks at how transformations affect the "space" in which equations and the such like live), as well as going through constructs and concepts that I am familiar with from a different perspective. It was only having read through the chapters at least three times that it started to make sense, due in part to the formal "theorem-proof" approach the author employs, and only this very morning have I felt brave enough to try some of the questions set at the end of each chapter.

In terms of my development, this book has certainly presented a challenge and has proved indicative if the sort of application I will need to show such that my time as a PhD student will result in my being awarded a PhD. In a sense, it symbolises the leap of faith every student makes from A-level to undergraduate study, only the gap that has to be bridged is that much bigger. Still, it has proved an excellent start to the year.

(Incidentally, I also picked up another textbook from Amazon. This one was E. L Ince's Ordinary Differential Equations, and - although originally published in 1927 - it has proved to be very useful for brushing up on a few forgotten first-year modules. It's getting to be a bit worrying when I start reading maths textbooks for enjoyment in the evening, wouldn't you say?)