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A Mathematical Trivium (1991) [pdf]

physics.montana.edu

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Re: A Mathematical Trivium (1991) [pdf]

#3

Post by mixedmath »

Koshkin wrote: post #2

I like the (possibly, older) style of the integral sign that appears in this paper better than how it is usually typeset these days.

I've heard these called the German or Russian style integral sign. I don't know the actual history. I have seen this question [1] on the tex/latex stackexchange about making this integral sign.

I would expect a journal to not use a different font integral sign, however. Or rather, I would expect the "house style" to include font choices for integral signs as well. I'm not aware of any journal that uses this type of integral now, but I suppose I should also note that I mostly read papers from the arxiv now anyway.

[1]: https://tex.stackexchange.com/questions/170028/integral-sign...

Re: A Mathematical Trivium (1991) [pdf]

#4

Post by lordnacho »

Seems pretty reasonable to me. If you look at these questions and learn how to do them, you'll have learned a fair bit. It's not like you can learn by rote all the transformations you'll need to answer these, you're better off just learning the theory.

I would have loved to have a simple 100 known-but-non-trivial questions like this. You avoid the lottery of having to remember some particular detail (say some integral that appears in some derivation that an adhoc question might contain), but you don't avoid having to actually know how the theory works, because it's a little bit too hard to memorize.

Admittedly you might still get stuck on a trivial step but at least you've had a chance to go over the questions, and it might be relatively fresh.

Re: A Mathematical Trivium (1991) [pdf]

#6

Post by hpcjoe »

Very enjoyable! I started working a few problems in my head, and realized I'd run out of scratch ram quickly.

I especially liked his points on examination, what we call the "orals" in Physics. There, the (in his words, defenseless) student is up in front of a board, while professors throw problems at them. I had a few good questions on mine, and one which was ... poorly specified. I remember thinking I simply had to crank on that problem, showing my thinking processes to try to answer the question. At the end, the prof nodded, pointed to something before my conclusion, and said "that was as far as I got."

I remember feeling relieved yet angry. Just smiled, nodded, thanked him for the question, and moved on.

Talk about an imbalanced power dynamic.

Re: A Mathematical Trivium (1991) [pdf]

#7

Post by enriquto »

The limit in question 2 is wickedly difficult to solve by traditional means. You have to apply l'Hôpital rule about seven times, and it becomes a monster formula. Or, you expand everything by Taylor up to order eight. In any case, the computation fills several pages. There must surely be a geometrical reasoning to compute that limit.

Re: A Mathematical Trivium (1991) [pdf]

#9

Post by admissionsguy »

enriquto wrote: post #7

The limit in question 2 is wickedly difficult to solve by traditional means. You have to apply l'Hôpital rule about seven times, and it becomes a monster formula. Or, you expand everything by Taylor up to order eight. In any case, the computation fills several pages. There must surely be a geometrical reasoning to compute that limit.

https://mathoverflow.net/questions/20696/a-question-regardin...
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