George Oppen: Stephen's Questions

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George Oppen: Stephen's Questions

Post by t-bar » Sun Feb 22, 2015 7:43 pm

I wrote the physics and “other” science for this tournament. This was my first time writing a substantial number of questions at this level, so I’m curious how I did. Unfortunately, I wasn’t able to make it to a tournament site, so I couldn’t see the questions in action, but I’m eager for any feedback that people care to offer.

First, I’d like to thank the following people: Aaron Rosenberg playtested every physics question and provided a whole lot of very useful feedback. Neil Gurram, Bryce Hwang, and Julian Fuchs of the MIT team played many of the other science questions and offered helpful advice as well. I’d also like to thank Auroni for giving me an opportunity to work on this set.

As people have noted, my questions probably ended up a good bit easier than Auroni’s. I hope nobody felt like they got screwed by the variability here.

In the physics, I tried ask about things that, as a physicist, I find important and exciting. Where I thought it was appropriate, I included clues on cool recent research: the leadin to the superconductors tossup, the bonus on Hofstatder’s butterfly, and the bonus on Nima Arkani-Hamed all arose from this approach. I also wrote a few bonus parts that, while not strictly computational, asked you to produce a quantity rather than the name of something: I’m thinking of the bonus part on sqrt(g/L) in the Euler-Lagrange bonus, the part on N! in the Gibbs paradox bonus, the part on 2f in the focal length bonus, and the computer science bonus part asking you for the runtime of Dijkstra’s algorithm. I know that these sorts of questions have been used plenty of times before—I’m curious how people thought these particular examples played out.

I know far less about most of the other sciences, in particular earth science. I picked things that I thought looked significant and askable, and I hope that I succeeded for the most part.

For what it’s worth, I also wrote about half the trash, specifically the tossups on Galaxy Quest, Steve Buscemi, ricin, Brooklyn Nine-Nine, and [three questions in the last few packets that I'll let people read on their own before posting about here], as well as the bonuses on Donnie Darko, The Breakfast Club, Martin Starr, Passion Pit, The Hollies, and [two more bonuses]. Feedback on these questions is also welcome.
Last edited by t-bar on Sun Feb 22, 2015 7:55 pm, edited 1 time in total.
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Re: Stephen's Questions

Post by t-bar » Sun Feb 22, 2015 7:44 pm

Responses to specific things mentioned already:
vinteuil wrote: It "felt" like there was a lot of cosmology and astrophysics in this set, but I could be wrong.
You’re probably right on this. When I initially planned out my subdistributions for the tournament, I allotted 1/1 for stuff on relativity, 1/1 for GR, and 3/4 of the “other” science for astronomy. Since I was mostly writing on things I was confident I could write well, the pure astro may have ended up more astrophysics-y, and lumped together with the 2/2 astro-y physics made up a pretty big chunk of the physical science.
vinteuil wrote: (e.g. that representation theory bonus where you more or less had to have taken a class on that to get more than 10)
I’m actually a little surprised by this, though it may be an entirely reasonable criticism. Here’s the bonus:
In Round 1, I wrote:Identify the following tools that you might use if you were interested in representation theory, for 10 points each.
[10] Since rep theory concerns itself with matrices of different dimensions, you would use this matrix operation a lot. It equals the sum of the diagonal elements of a matrix, and it also equals the sum of its eigenvalues.
ANSWER: trace
[10] This function assigns to each element of a group the trace of its matrix in a given representation. Its values are often compiled in tables, with one row corresponding to each irreducible representation.
ANSWER: character [do not accept "characteristic"]
[10] This theorem asserts that every representation of a finite group over a finite-dimensional vector space is a direct sum of irreducible representations.
ANSWER: Maschke’s theorem
Both character tables and Maschke’s theorem were discussed in my introductory abstract algebra class, with character tables being given a particularly thorough treatment. I thought they were something that people might have been exposed to without taking a class specifically devoted to representation theory, but I could be wrong.
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Re: Stephen's Questions

Post by vinteuil » Sun Feb 22, 2015 8:37 pm

t-bar wrote:Responses to specific things mentioned already:
vinteuil wrote: (e.g. that representation theory bonus where you more or less had to have taken a class on that to get more than 10)
I’m actually a little surprised by this, though it may be an entirely reasonable criticism. Here’s the bonus:
In Round 1, I wrote:Identify the following tools that you might use if you were interested in representation theory, for 10 points each.
[10] Since rep theory concerns itself with matrices of different dimensions, you would use this matrix operation a lot. It equals the sum of the diagonal elements of a matrix, and it also equals the sum of its eigenvalues.
ANSWER: trace
[10] This function assigns to each element of a group the trace of its matrix in a given representation. Its values are often compiled in tables, with one row corresponding to each irreducible representation.
ANSWER: character [do not accept "characteristic"]
[10] This theorem asserts that every representation of a finite group over a finite-dimensional vector space is a direct sum of irreducible representations.
ANSWER: Maschke’s theorem
Both character tables and Maschke’s theorem were discussed in my introductory abstract algebra class, with character tables being given a particularly thorough treatment. I thought they were something that people might have been exposed to without taking a class specifically devoted to representation theory, but I could be wrong.
Interesting. Our intro abstract course didn't cover that, although it was completely over-the-top in terms of thoroughness (we covered all of chapters 1-12 and a big chunk of 17 in Dummit and Foote), but I suppose that people's courses could be differently thorough. "Character" is definitely something I've heard of and that I know is supposed to be important, though (maybe a tie-in with the "homomorphism from a group to the multiplicative group of a field" character would work better?).

That said, we 30d this bonus, because Basil took a rep theory course last semester, so it was definitely not entirely impossible.
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Re: George Oppen: Stephen's Questions

Post by kayli » Sun Mar 15, 2015 11:24 pm

I got here a little late, but even if you encounter 'Maschke's theorem' in algebra, there's a non-zero chance that you don't know it even has a name. For example, Fulton and Harris, which is a fairly traditional first book in representation theory doesn't give it a name and you could probable go your entire career in mathematics without having that name in your working memory. This I think is representative of a broader trend within quizbowl writing about mathematics (also economics but that's a different story) which I think is miguided which is that we tend to focus on names more so than content. An equivalent and perhaps better way to test the same knowledge would be to say that according to Maschke's theorem every representation of a finite group can be decomposed into this operation on distinct irreducible representations. That's perhaps not perfect but I think we should be alert to when theorems with names might not have those names used very often and instead test the underlying concept.
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Re: George Oppen: Stephen's Questions

Post by Adventure Temple Trail » Sun Mar 15, 2015 11:34 pm

Alpha Phi Gamma wrote:I got here a little late, but even if you encounter 'Maschke's theorem' in algebra, there's a non-zero chance that you don't know it even has a name. For example, Fulton and Harris, which is a fairly traditional first book in representation theory doesn't give it a name and you could probable go your entire career in mathematics without having that name in your working memory. This I think is representative of a broader trend within quizbowl writing about mathematics (also economics but that's a different story) which I think is miguided which is that we tend to focus on names more so than content. An equivalent and perhaps better way to test the same knowledge would be to say that according to Maschke's theorem every representation of a finite group can be decomposed into this operation on distinct irreducible representations. That's perhaps not perfect but I think we should be alert to when theorems with names might not have those names used very often and instead test the underlying concept.
I agree with this sentiment fully. I'm not as much of a math wizard as Kay by any stretch, but I was definitely very confused the first time I heard a bonus part on "Cayley-Hamilton" or "Clairaut's theorem" even though I had learned the basic concepts underlying both in classes.
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Re: George Oppen: Stephen's Questions

Post by vinteuil » Sun Mar 15, 2015 11:37 pm

Matthew Jackson wrote:
Alpha Phi Gamma wrote:I got here a little late, but even if you encounter 'Maschke's theorem' in algebra, there's a non-zero chance that you don't know it even has a name. For example, Fulton and Harris, which is a fairly traditional first book in representation theory doesn't give it a name and you could probable go your entire career in mathematics without having that name in your working memory. This I think is representative of a broader trend within quizbowl writing about mathematics (also economics but that's a different story) which I think is miguided which is that we tend to focus on names more so than content. An equivalent and perhaps better way to test the same knowledge would be to say that according to Maschke's theorem every representation of a finite group can be decomposed into this operation on distinct irreducible representations. That's perhaps not perfect but I think we should be alert to when theorems with names might not have those names used very often and instead test the underlying concept.
I agree with this sentiment fully. I'm not as much of a math wizard as Kay by any stretch, but I was definitely very confused the first time I heard a bonus part on "Cayley-Hamilton" or "Clairaut's theorem" even though I had learned the basic concepts underlying both in classes.
I agree to a certain extent (definitely with Clairaut's theorem), but there are definitely some theorems that are ALWAYS learned by name (Cayley-Hamilton, I would have thought, fits this actually). Still, Kay's point about actually testing if people know what the theorems say (rather than vaguely recognizing the statement) is great, and people should do this more.
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Re: George Oppen: Stephen's Questions

Post by Mewto55555 » Mon Mar 16, 2015 9:06 pm

Matthew Jackson wrote: I agree with this sentiment fully.
Jacob wrote: Still, Kay's point about actually testing if people know what the theorems say (rather than vaguely recognizing the statement) is great, and people should do this more.
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