Good lord, has it really been 8 weeks since my last post? I've had a bit of a break from all things studying for the last two months, as I had to defer my O.U module, Astrophysics, whilst I recovered from some health issues.
Before I left, I managed a couple of TMA's and also some of the research elements; and whilst I am sad to leave this interesting subject, I can't help but feel that it is probably actually for the best; as I can now, truly concentrate, on my new found love affair with pure mathematics. My degree profile will also probably look a a little more focussed, since it will contain all level 3 maths modules.
Also, in a strange twist of fate; whilst I have just effectively added another year to my level 3 study schedule; I hadn't realized that by doing Astrophysics, I would have been unable to complete Complex analysis, before moving onto the MSc. This would have been quite foolhardy, in my opinion. So, this could be a blessing in disguise.
It now means that I will take two pure maths modules in October, as planned (number theory and logic, with groups and geometry), but because I will now need to study more level 3 modules in 2014, I can now add complex analysis, to my quiver. I had planned to self study the complex analysis books, that were kindly sent to my by Chris F; but I think that Chris was quite right when he suggested, some time ago, that any future sponsor for post-graduate maths research / work, would question why one did not have such an important module.
Anyway, the study break has given me a good opportunity to start slowly re-reading some of my O.U module Units from M208, Pure Mathematics, which I completed last year. I have forgotten a fair bit, and there was some of it that I never entirely understood, the first time around (epsilon-delta, I'm looking at you!)
So, I have a rather lazy summer ahead, with some hopefully enjoyable revision of pure maths. I also plan to dust off my copies of Hardy's - Course in Pure Mathematics; Brannan's - Geometry and Spivak's - Calculus (Which should really be called Real Analysis, judging by the content of the book).
Sounds wise to me. One option you might consider is just doing M381 this year then the New maths course M303 when it comes along. It would mean you having to exclude M381 from your final degree but that way you get the best of both worlds
ReplyDeleteM381 has number theory and logic especially group theory.
M336 has abstract groups and from what I hear a
really rather pointless section on Wallpaper.
M303 has only the number theory part of 381 and the abstract group theory part of M336. But also includes an introduction to abstract algelbra rings and fields etc. And also the metric space aspects from the old topology course. Whioh would be more arrows added to your quiver.
Of course the downside is that M381 is an excluded combination with M303 but the chance to learn about Godel's theorem and logic and computability is to good to miss. As is the abstract algebra part of M303.
Anyway something to think about
Best of luck in the new courses. I will be looking forward to your blog in October as I will be starting both coures in the Autumn, once MST209 is finished, exam on Wednesday. Can not wait to be finished with applied Math, having similar sentiments to your own and relish getting back to the unadulerated abstraction of pure math.
ReplyDeleteBest Regards
DmC
Best of luck, too, DmC.
ReplyDeleteI don't know what it is about pure maths, that is so appealing. Maybe it is because it feels very clinical, when answering problems. It seems black and white, at times, which can be very warming, in a world of so many grey areas; but, I think I am about to discover, when studying Godel in October, that it isn't black and white, at all!
Dan
Hi Dan
DeleteFor me, Pure Math is to wander into the world of Platonic forms and stare in wonderment. Pure Math allows one to think in a less than rigourous way while still enjoying its Rigour. For example, I was fascinated last year when thinking about one of the heavily discussed course topics in MS208 the notion of continuity. At the begining of Real Analysis we are told about the Archimedian Denstity property if a, b are Elements of R and a < b then there is a rational no. x and an irrational no y such that a < x <b and a < y < b. i.e. between any two distinct real numbers there are infinitely many rational numbers and infinitely many irrational numbers. Which brings into question the notion of discreteness and continuity. i.e in the natural Domain all numbers are infinitely close to each other; in that 1 is "right next" to 2 i.e there is nothing betweeen the two numbers, one can proceed seamlessly from one number to the next. However every number in the Real Domain is infinitely far away from each other, making the Real numbers in some fashion "more" Discrete than the Natural numbers and vice versa. I like to think of it as a matter of prespective, we are viewing numbers in the Natural domain from the infintesmial up while we see the Real numbers from the Infinite down. Anyhoo I have this typed so will leave it as is but feel free to ignore my ramblings. Thanks for the reply, good luck with the blog and studies.
Regards
DMC
Thanks Chris,
ReplyDeleteI'm not sure I trust the O.U to present M303 next year; what with the delays already and the budget cuts. I'm sure it will go ahead, but I'm not sure I want to gamble on it.
I also share your excitement about Godel. The course is worth doing, just for that. It is unfortunate that Godel isn't examined, as I can imagine many a time pushed student, skipping it. Such a shame.
Dan
Yeah I must admit I share your scepticism probably best to get all the points you need to start the MSc when if M303 comea along you can always take a year out to fit that in. The chance to learn some abstract algebra is just to good to miss. So I think in retrospect your plan to do M381 and M366 is probably the best. Also M337 will probably be the hardest of the courses you have chosen so best to leave it till last and then spend a whole year on it. Better master that epsilon delta definiton quick as M337 uses it extensively.
ReplyDeleteHi Dan
ReplyDeleteFor me, Pure Math is to wander into the world of Platonic forms and stare in wonderment. Pure Math allows one to think in a less than rigourous way while still enjoying its Rigour. For example, I was fascinated last year when thinking about one of the heavily discussed course topics in MS208 the notion of continuity. At the begining of Real Analysis we are told about the Archimedian Denstity property if a, b are Elements of R and a < b then there is a rational no. x and an irrational no y such that a < x <b and a < y < b. i.e. between any two distinct real numbers there are infinitely many rational numbers and infinitely many irrational numbers. Which brings into question the notion of discreteness and continuity. i.e in the natural Domain all numbers are infinitely close to each other; in that 1 is "right next" to 2 i.e there is nothing betweeen the two numbers, one can proceed seamlessly from one number to the next. However every number in the Real Domain is infinitely far away from each other, making the Real numbers in some fashion "more" Discrete than the Natural numbers and vice versa. I like to think of it as a matter of prespective, we are viewing numbers in the Natural domain from the infintesmial up while we see the Real numbers from the Infinite down. Anyhoo I have this typed so will leave it as is but feel free to ignore my ramblings. Thanks for the reply, good luck with the blog and studies.
Regards
DMC