Another week and apart from a miserable cold, I have managed to visit the O.U library, get a steer on what I should be studying, and adjusted my study load appropriately.
I found that I was getting too far into geometry and that I can leave some of my planned study in that subject, until next year and the year after.
I also reflected on some comments that were left on my blog this week, by a rather brilliant, learned and certainly not failed physicist, Chris. He said, tongue in cheek, that I was starting to transmogrify into a pure mathematician. I guess he based this astute comment on my recent fascination with some of the pure mathematics topics that I have recently encountered, and my lack of Open University physics courses that I plan to be examined in, over the next 3 years.
To answer this observation, I would say that my plan hasn't changed; rather, through detailed study and research, my approach has changed. Following my in-depth studies of the life and works of Rodger Penrose, and my experience of university level mathematics and physics; I feel, that to understand mathematical physics as easily as possible and with a wide range of knowledge and tools; whilst tackling the outlier abstract topics that exist; I believe that I will be best placed to succeed, by following the path below:
1. Absorb the building blocks of mathematics. E.g. not just learning the mechanics of an Einstein-Rosen Bridge, or Loop Quantum Gravity, but actually knowing how it all 'ticks' at the purist of mathematical levels.
2. Understand all undergraduate level, mathematics.
3. Learn both pure and applied mathematics at taught MSc level.
4. Then apply all of this knowledge to a theoretical physics PhD.
I believe that any plan to learn a bit of physics and a bit of applied maths at undergraduate level, will be okay; but wouldn't allow for the depth of understanding required, for a PhD in the field. Some may argue with that; but I know that I need to personally start at the basement, before moving up. One could argue that bothering with any pure maths topic is a waste of time when attempting an experiment such as mine. However, I would disagree with that assertion.
Don't get me wrong; I am not going to be neglecting physics over the next few years; rather, I will study it alongside the maths, until I know how to handle those numbers!
You only have to look at some of the most cutting edge theoretical or mathematical physics that is currently being worked on; and you will see that, to even understand it, you need a solid base of group theory, combinatorics, linear algebra, topology and a sprinkling of calculus.
If there is one thing that I have truly learnt from the first year of my experiment in perseverance by trying to convert my GCSE in Maths, into a PhD in Theoretical Physics; is that I love mathematics, I think I'm okay at it, and I can't wait to study all of the maths that I can squeeze in, over the next 10 years.
As my first-year sixth-form physics teacher once said, before his untimely death under the wheels of a lorry, 'mathematics is the language of physics; and without it, you are up S**t creek, without a paddle'.
Good old Mr. Curley.
Ok I think I can see where you are coming from to some extent we are looking through opposite ends of the telescope. I did theoretical physics as opposed to mathematical physics. The emphasis on my course and training was learning how to use stuff like quantum mechanics, electromagnetism and quantum field theory to solve concrete problems which can be compared with experiment. For that one does need a facility for Applied maths and to some extent the pure maths is secondary. So for example in particle physics one learns how to caclulate Feynman diagrams to caclulate the scattering cross sections of various reactions predicted by whatever model is currently in vogue. This is bread and butter work but enables those at eg CERN or Fermi lab to guide their experiments.
ReplyDeleteOr if one is a theoretical Astrophysicist one generally learns how to apply Einstein's theory of relativity along with statistical physics, Nuclear physics and relativistic fluid dynamics to solve problems such as what happens when galaxies collide or when stars collapse into a black hole and so forth. THere as well as analytical skills one also needs to develop computational skills and one reason why I set up the Cambridge Computing projects forum was to complement the education that OU maths and physics students get from the OU which ignores computational methods almost entirely.
For successful research in these areas one obviously needs a good grasp of mathematical techniques but not necessarily a good grasp of pure maths.
It might surprise you but most physicists would regard Penrose and Hawking and eg Ayitah Singh or Chris Isham as essentially mathematicians not physicists. Also what they do is probably considered on the periphery of physics. It is my ambition to understand eg Hawking and Penroses work on the singularity theorems of relativity or Von Neumann on the Foundations of quantum mechanics and that is why I embarked on the journey to understand some pure maths via the OU but even if I get the MSc there is still quite a gap between what the OU offers and what is needed to understand the geometric, functional analysis and topological background before having the confidence to tackle say the singularity theorems of General Relativity.
Also I want to keep my feet on the ground and get the background to understand say the calculation of the Helium abundance or the properties of the Higg's boson and for all the elegance of the work of the geometric topologists or functional analysts the results aren't really going to help in this basic work.
Anyway good luck in your quest I will take a keen interest in your progress.
Best wishes Chris