This week, I have concentrated on Brannan's fascinating text, 'A First Course in Mathematical Analysis'. It makes up the bulk, if not all of the sections of Analysis in the Open University course M208 Pure Mathematics, and is a significant part of the whole course.
So, getting a head start on this material, much of which is new to me, will help to ease any mid-course calamities.
Most O.U courses, as of 2012, will run from October until June each presentation. This is 9 months of study which is then followed by a rest period of 3 -4 months, before the start of the next module. However, I have decided to use the dead time, to get a head-start on the material. This will hopefully help implant the knowledge, into the long term memory, as I will approach the material twice; once before the course starts and then later on during the module.
My only worry, is that I finish M208 with an exam week that runs from October 16th which overlaps with my next module's start date, being M337 Complex analysis, that starts early October 2012. I plan to remedy this by pre-studying the first unit of Complex Analysis before Xmas this year, and then to recap just prior to the course starting in October 2012.
Anyway, here is this week's study. Total time spent: 18hrs
Brannan - Analysis
- Solving and proving inequalities p.10 - 19 including all exercises.
- Least Upper Bounds and Greatest Lower Bounds p.22 - 30 Including some exercises.
- Monotonic Sequences p.37 - 42 including all exercises.
Velleman - How to Prove It
- Operations on Sets p.34 - 54
Maths Skills Practice exercises. 80 exercises in total
- Irrational numbers
- Quadratic Equations and complex numbers
- Discriminant
- Root Coefficient relationships
I think you are right to focus on Brannan for success in M208 (Says he prematurely as I haven't sat the exam). Analysis is the hardest part of M208 and the sooner you understand it the better. It will stand you in good stead whatever other courses you do.
ReplyDeleteHi,
ReplyDeleteI'm just going into my 4th year of a Physics MSci and thought that I'd offer some words of encouragement and support. I think this is an excellent project and certainly achievable, at least as far as taught courses go, in the time-frame you set.
I recently stumbled across a website written by a distinguished theoretical physicist in which he sets out a 'roadmap' for a self-learner to reach the edges of current knowledge in that field. It provides what I think are by far the most valuable aspects of a taught degree - a clear structure, a complete booklist and comprehensive lecture notes - all in one place and at no cost. I am sure the OU provides something of the same, but it seems to 'cut out' earlier and perhaps does not provide so clear a map of the lengthy and sometimes perilous, but very rewarding route you've chosen to follow.
Here is the website, in any case, I hope you find it helpful: http://www.staff.science.uu.nl/~hooft101/theorist.html
My only other comment is that, while in my experience undergrad taught courses do not really need a brick university, it will be very hard to do research other than at least part-time at a university. You would presumably be eligible for PhD funding at the end of your OU education provided you get a 2.1 or better, but stipends are in the >£13k bracket full-time (albeit tax free), so I'm not sure about raising a family on that.
I really do hope that you manage to take it that far, however - becoming a theoretical physics PhD after leaving school at 16 would be a remarkable feat in its own right, and if worst comes to the worst, it would be far greater a thing to reach and fail than never to try. I will keep following this blog and I wish you the best of luck for the future.
Thank you mdc, for your words of encouragement and the info provided. It's always good to hear from a like minded person.
ReplyDelete