Nevertheless, M337 recently led me to my number one, all time greatest, mathematical achievement... ever. Albeit an unnecessary one. It was an equation I devised for the Laurent Series asked for in the final question of the assignment. I pieced this equation together from a few flukily spotted patterns and not a small amount of head scratching, over the last hour or so before enveloping the assignment up and rushing it to the post office. Ever since, I have found it frequently on my mind. I randomly write it up on my blackboard, or on my A4 pad, and just marvel at it. Somehow I had come up with this! Pretty sad behaviour to be fair. But still, if this is how I react to coming up with one good equation, well, how must it feel to be someone like Andrew Wiles and crack Fermat after almost 360 years?
When I got the marked version back, my tutor Alan Slomson commented thus: "This is ingenious and correct, but you didn't really need to find a formula of this kind" Yep, ingenious and correct, but totally unnecessary. Somehow that makes me feel even better. Like I went above and beyond the call of duty. Don't get me wrong, I don't think I'm some kind of expert. I'm sure many others came up with something similar or better, but it was one of those moments, all too rare, when you just know that you've devised something special. If nothing else, it's proven to me that I'm getting the hang of the 2D nature of working in the complex plane, and specifically, how useful e can be.
I'm still a long way from owning the subject of complex analysis, but I'm slowly slowly getting there. As before, the two good assignment results have inspired me to up the pace a bit, and put more effort in. But I will have to wait until tomorrow before getting back to it, as I have a job due at 1am tonight. I should have done half of it yesterday (in fact I should have done a third of it on Friday, and another third yesterday), but we know how I work in that regard. Why do today what you can put of until tomorrow? And why do today and tomorrow what you can put off until the day after that, so you have to work all day to finish in time? That's me.
Well, happy studying everyone!
Well done I got the question in the simplest form I could and then said in a parenthesis there is probably a simpler way of writing it. However my tutor just wrote Nope. Upper 90's eh I'm afraid I only got 80 so you are definitely owning the subject more than me.
ReplyDeleteThanks Chris
ReplyDeleteWell, I guess we aren't really comparing like-for-like, when I had the benefit of M208 beforehand. I'd imagine that 80% when studied alongside the prerequesite material probably translates into quite a bit higher in terms of achievement. Either way, I was glad to read in your post a few weeks back, that likewise me, things are slotting into place in this course... I'm sure we're both well on our way to M337-ownage. By the way, I just re-read the post in question to make sure my memory served, and I couldn't agree more over the second part of Question 2. Easily the hardest part of the TMA. In particular, I felt I was endlessly going round in circles with that Im(f(z)) less than or equal 0 part, (b)(iii).
Onward and upwards
Neil H
I managed to come up with a solution ofr the final part that didn't involve the condition but proving that the function was constant. Namely splitting the function into real and imaginary parts then raising the function to an exponential and taking its modulus as the imaginary part then becomes 1 you are left with
ReplyDeleteexp(-f) is a constant so going round in circles
exp(f) must also be constant and then f is constant as it's bounded. Then as the imaginary part is constant the real part must also be constant so the function is constant as a whole
Not quite on your special formula status but my supervisor seemed impressed but I only got two out of three as I didn't use the condition and to be frank I'm not sure I fully understand where it fits in.
As you say we are not competing against each other. I think parts C and D will be a bit more 'Straight forward but tedious' as the books say. As you say Onward and upwards
Cheers Chris
This is an inspiring read.
ReplyDeleteOff to look up the Laurent Series now.
Nice one, Neil.
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ReplyDeleteIntriguing Chris. I doubt I'd have got to proving it was constant that way. I managed to get the condition into it, in what I assume was the right way. Though my argument involved a cop-out geometric reasoning to get through part of it (the tutor set me right, but fortunately there was no valid reason to deduct any marks for it - it was typical me, going right round the houses, twice, to prove something that should have taken just a couple of lines). Sigh, this being intentionally vague so we can avoid giving away our answers to everyone else is quite tiresome, no? It'd be so much easier if we could just explain exactly what we did.
ReplyDeleteRight, I'm back to trying to catch up to the M337 schedule again! Good luck.
To oumaths, that's really commendable, deep in the throes of MST209 but curious enough to go and check out Laurent Series. I found them pretty interesting, a nice next-step at last from Taylor Series (which having to meet again for the third course in a row was not particularly inspiring). Hope the course is going well. Oh a new post I see..