## Math Monstrosity - Specific Question Discussion

CPiGuy
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### Math Monstrosity - Specific Question Discussion

Hello.

This is the place to discuss specific questions, errors, errata, and to scold me for clue repeats.
Conor Thompson (he/him)
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CPiGuy
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### Re: Math Monstrosity - Specific Question Discussion

A few notes on specific questions...

At least three answerlines (long line, Banach-Mazur game, bivectors) have never come up in quizbowl before (at least not in any set in the packet search), whether as an answerline, bonus part, or clue.

I think my favorite tossup in the set was the Bridges of Konigsberg one; my favorite "academic" tossup was probably the Monster group.
Conor Thompson (he/him)
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### Re: Math Monstrosity - Specific Question Discussion

Now that I've had a chance to skim the packets, I'll comment a bit on the question content. The criticism will be a bit lengthy so it'll probably be divided into several posts.

Packet 1:

1. Brouwer fixed point theorem probably had a bit of an easy power. I would have probably put the Sperner's lemma clue inside of 15 and taken at least the words "Borsuk-Ulam theorem" and placed them outside of power. Minor criticism but Brouwer and Borsuk-Ulam are typically studied in the same lecture in your typical topology class.

2. prime - what other properties are Fermat numbers supposed to possess or not possess? That seems fairly easy and could go later in the question. Definitely wasn't expecting that to be dropped there.

3. tossups on products, Erdos number, direct sum, Russia, Bourbaki, compressed sensing, knot polynomials, Latin squares either are or appear to be excellent. Totient function was fine. [I say appear to be for those I don't know anything about - obviously my commentary is relatively worthless on those.]

4. Fourier transform - Plancherel's formula could have been named toward the end of that clue for the sake of better pyramidality.

5. Connectedness tossup was a bit easy. The topologist's sine curve is a pretty canonical example showing connectedness. The tossup would have been better off with a slightly (although not incredibly) more exotic example there and some power ending like An example of an object which has this property, but not locally, is known as the topologist's (*) sine curve, or something.

6. The Krull-Schmidt theorem is a general group-theoretic statement, so buzzes of "group theory" or "abstract algebra" being negged there would produce quite a bit of frustration. Representation theory is a pretty specific answerline, so it's good to be generous with prompts. [That doesn't apply to my particular playing experience - I picked out the wrong Krull theorem in my head and buzzed with ring theory. Whoops.]

7. On the closure tossup the clue about the compact manifold seems to be a little easier than the clues that follow.

8. The differential equations tossup was too easy for the set.

Packet 2:

1. polyomino is an excellent idea but could have used some specific antiprompts for moderators who are not as experienced with the material.

2. The D_6 clue and the subsequent clue should probably be swapped.

3. The normality lead-in definitely pretty much states the definition of normal with respect to matrices. That C*-algebras were mentioned just added to the "is this somehow just a tossup on normality" factor and added a bit of confusion.

4. Fatou's lemma being mentioned in the first line of a Lebesgue integration tossup seems a little easy, but it definitely belongs before the LDCT, so good job on that.

5. Kuratowski's theorem is super notable.

6. Laurent series are very notable. Including them as the last clue in power wouldn't have been so bad, though.
Jake Sundberg
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### Re: Math Monstrosity - Specific Question Discussion

Packet 3:

1. In addition to the previously discussed "Argand" clue, namedropping holomorphism inside of power is probably also a bit generous at this level.

2. the idempotence tossup was a hard-ass tossup.

3. Namedropping a play from ancient Greece probably narrows the answerline pool down to at most three. Try to avoid making the answerline space that narrow so early in a question.

4. Fractal might have a little bit of fraudability within power.

5. distribution tossup is entirely too easy for this set.

6. Be careful when using "s" as your argument for things involving the Riemann zeta function. It's pretty much the most notable function that historically takes "s" as an argument.

7. a repeat of things on fixed point theorems

8. given that an adjoint is a conjugate transpose, the first clue in the Hermitian tossup is pretty fraudable. The tossup would have been great if you deleted this clue.

Packet 4:

1. The Konigsberg bridges tossup seems to be fine except that you namedropped the name of a bridge (notably by saying "bridge") inside of power. What else could this be?

2. Nobody is going to have memorized which specific passage of Elements deals with the fundamental theorem of arithmetic.

3. Nothing about the ring tossup is challenging.

Packet 5:

1. probably should move the power mark on the Elements tossup right before "Bible"

2. the tossup on Fermat's little theorem is a bit easy.

3. Gelfand's theorem is a pretty easy leadin for transcendental numbers.

4. Tartaglia is pretty famous for his work on solving polynomial equations, I'm fairly certain.

Packet 6:

1. The convergence tossup leadin is notably easy.

2. Dirac's comb could have been moved a little later inside power.

3. Power could have probably been moved to right before "Newton-Cotes" on the integration tossup.
Jake Sundberg
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### Re: Math Monstrosity - Specific Question Discussion

Packet 7:

1. The Faa di Bruno clue comes up as a repeat later in the packet. You could have probably rewritten that clue as "The nth derivative of an expression defined by this operation can be calculated using Faa di Bruno's formula" for a bit more clarity. I negged this with differentiation when you namedropped "Faa di Bruno" but that's me being bad at math quizbowl for an instant.

2. You wrote a lot of excellent tossups in this tournament. The taxicab metric tossup was probably the most creative of all of those. A+. As noted earlier, the Monster group tossup is also excellent.

3. You should probably move the power mark on the alternating groups tossup to right before "simple" but that's probably just me.

Packet 8:

1. That demonic formula for 1 / pi could have been replaced by much more substantial clues.

2. The Hurewicz theorem provides an isomorphism between homology groups and the quotient space of homotopy groups modulo their abelianizations, so being negged here when I buzzed with homology groups was upsetting.

3. Name-dropping Feit-Thompson before the substance of the clue was revealed was probably not a good idea here. The more you write, the more you should get accustomed to not doing this. "Every finite group of odd order has this property by the Feit-Thompson theorem" is a much better way to write this sort of thing.

4. Same thing for the decomposition tossup. Putting the description first is a good idea.

5. If you are going to write out integrals, make sure you don't forget dx!

Packet 9:

1. Tossing up Japan whilst including a Japanese word in every line past the power marker is probably not a good idea.

2. Matiyasevich is a bit more quizbowl famous than Pell's equation and the Hasse principle.

3. The star-convexity clue is probably deserving of a spot inside of power for convexity.

4. Most people can't read tensor notation.

5. "Gauss's theorem says that a polynomial described by this term" - this clue confused me quite a bit. Why not just say "Gauss's theorem says that a polynomial with coefficients in this number system" or something like that?

6. Gerschgorin circle theorem is a very common quizbowl clue for eigenvalues at this level - perhaps it can be left inside of power but does not serve as a good leadin.

7. The fields tossup was very easy.
Jake Sundberg
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### Re: Math Monstrosity - Specific Question Discussion

Packet 11:

1. Gimbal lock is a very common buzzword for quaternions.

2. Mascheroni is an Italian mathematician. Mascherano is a notable Argentinian soccer player beloved by Diego Armando Maradona.

3. Leaving two of the three statements of the Sylow theorems inside of power is probably not a good thing for this sort of tournament.

4. The tossup on math textbooks was probably not the best idea. Tossing up a specific one is a much better idea.

Packet 12:

1. "Fitting" is a person so his name should be capitalized in the subgroups question.

2. The lead-in on the order question is not very good. It's best not to lead in with definitions if at all possible.

Tiebreakers:

1. The ideals tossup gets very easy very fast around the second clue.

2. Kruskal's algorithm is a very notable greedy algorithm.
Jake Sundberg
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### Re: Math Monstrosity - Specific Question Discussion

Some comments, attempting to keep them mostly disjoint from Jake's:

Packet 1

1. One issue with comp math tossups is a lot depends on the speed of the reader. I was playing in a room with someone who was slowed down by the TeX, so I managed to 15 this by integrating 1/(x^2) from 1 to 2 before we hit the power mark, but that wouldn't have happened if Conor had been reading.

4. Not sure I love clues like "Cantor was born in this country"; is that really testing any sort of math knowledge? The Euler clue is fine, on the other hand.

6. This Erdos number tossup is excellent, although the Tompa and Barr clues are probably harder than Casper Goffman.

9. Compressed sensing seems like one of the harder answerlines for the tournament, although it might be quizbowl famous and I don't realize it. I liked the question, though.

17. I like the idea of tossing up representation theory, but looking up the Krull-Schmidt theorem, that's a hose; the statement of the theorem makes no reference to a representation, and "group theory" or "module theory" should be acceptable. ("Ring theory" is still a neg, though.) And Maschke's theorem is a bit of a difficulty cliff; anyone who has non-fraudulent knowledge of representation theory ought to know that clue. Maybe something like Young tableaux could go there instead?

Packet 2

3. Really like this sieve theory tossup.

9. A Bach pun in the lead-in might be a little too easy for a GEB tossup in this tournament.

11. The Fisher-Tippett-Gdnenko clue is fine here, but as long as you're using it I'd take the extreme value theory clue out of the later tossup on distributions.

13. INTERCAL is a weird choice for (IIRC) the only programming language to toss up, but I won't say it's not fun.

14. Kuratowski is too early, and "this thing has a categorical product" is a non-clue; I'd use the zig-zag product instead, and maybe move that clue before Kuratowski.

Packet 3

5. The Miller-Rabin clue should probably be rewritten to be internally pyramidal, something like "A probabilistic one of these relies on the GRH for correctness; that one of these is named for Miller and Rabin." Also, "sieve of Eratosthenes" is kind of a repeat clue.

7. The lead-in should be internally pyramidal; I heard "Roth's theorem" and immediately knew the answerline would be either algebraic numbers or something related to number-theoretic density/additive combinatorics.

8. Neither this question nor the later origami tossup got very far in the rooms I played, but I'd make sure that "you can double the cube/trisect the angle in origami" isn't a repeat clue. Maybe use something else that lets you solve cubics here?

11. Like Jake said, way too easy, the lead-in kind of mystified me since I'd just heard "Fisher-Tippett-Gdnenko" last round, and Student's t should in no way be inside power.

12. What Jake said about "s," plus Riemann's functional equation for the zeta function is incredibly famous and IMO too easy for a lead-in in an all-math tournament; the zeta function is one of the best-studied objects in math, so there's no excuse for not finding a harder clue.

13. "Floor planning" was one of the few answerlines that went dead in our room all tournament; I don't know anything about this topic, though, so maybe it's fine.

15. I mean, maybe you can get away with tossing up Brouwer's fixed-point theorem and fixed points generally, but don't use the first answerline as a clue in the second tossup! Maybe something about fixed-point combinators instead?

More later...
Harrison Brown
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### Re: Math Monstrosity - Specific Question Discussion

Packet 4

4. The Cauchy-Riemann TU is really fraudable from the first clue -- I wonder what set of equations satisfied by a complex function this could be? :thinky face emoji:

5. Why a finance clue on basis points in the middle of a perfectly good math tossup? Also, the Grobner basis clue is not internally pyramidal.

7. Well, I liked this tossup, and I'm not sure saying "bruecke" really counts as saying "bridge"

12. Hume's consideration of the problem of induction is a lot more famous than Laplace's work, so those clues might be misplaced relative to each other. This was a creative answerline that I liked, though.

18. Yeah, this tossup on rings needs harder clues.

Packet 5

1. This tossup is pretty fraudable, and the Bible clue is probably a mite too easy to be inside power.

2. FLT is generalized by Euler's totient theorem, or alternatively a specialization of it; FLT is not a generalization of the totient theorem.

5. I don't know anything about Ito outside of his work in stochastic calculus, but saying "there's an axiom of [some treatment of] ZFC named after this" as your lead-in is a good way to hose people. Also, this is the first of two tossups with answerline "the empty set"? Both tossups are pretty good but there should really only be one of them.

11, 15. The tossups on Flatland and teapots were great.

Packet 6

1. I mean, I'm not sure about tossing up both the surreals and the hyperreals in the same set, but if you must do so, don't have a clue in one .

4. Disappointed that the book on the Navier-Stokes equations isn't by Cioran.

6. Like a lot of the book answerlines in this tournament, this Principia tossup is very fraudable.

8. Too obvious/easily fraudable. Hm, it's an ancient guy who lived near Rome and built cool shit. :thinky face emoji again:

11. This was probably my favorite answerline of the tournament, and it's a very well-constructed tossup. Good job.

12. The fact that the Franklin graph is 6-chromatic is interesting but might be a better clue if you gave some reason why the Franklin graph was constructed (e.g. "this is the chromatic number of the Klein bottle").

15. I didn't like this answerline; I knew what was being clued from "Ken Keeler" but had no idea how I was expected to describe it. (Fortunately the moderator was generous enough to give it to me when I babbled something including the words "Futurama" and "body switching.") It was a fun idea, though.

18. Don't use the Lo Shu as a clue twice in the same packet.

19. This was a fun and creative tossup on OEIS.

More tomorrow...
Harrison Brown
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"No idea what [he's] talking about."
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### Re: Math Monstrosity - Specific Question Discussion

Fond du lac operon wrote:Packet 6

1. I mean, I'm not sure about tossing up both the surreals and the hyperreals in the same set, but if you must do so, don't have a clue in one .
This would make it worse.
Jonah Greenthal
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### Re: Math Monstrosity - Specific Question Discussion

jonah wrote:
Fond du lac operon wrote:Packet 6

1. I mean, I'm not sure about tossing up both the surreals and the hyperreals in the same set, but if you must do so, don't have a clue in one .
This would make it worse.
I don't think anyone has ever (intentionally) attempted the empty tossup, although I may be mistaken.
Jake Sundberg
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### Re: Math Monstrosity - Specific Question Discussion

Of course that should have read "Don't have a clue in one saying 'It's not [the other]'"...

Packet 7

2. This is a cool tossup, although IMO it would have been even cooler if it were entirely group theory clues (ending, I guess, with "the order of the fourth symmetric group").

6. Nullstellensatz might be a bit early here. Also there's not a lot of internal pyramidality, although that's pretty tricky for an answerline like this.

8. Should probably at least prompt on answers like "hailstone problem" --- I said Collatz but if I'd negged with hailstone I would have been CHEESED

14. This is pretty fraudable; how many sequences of groups are there?

Packet 8

2. That infinite sum clue is horrible, but also, "mock theta functions" is probably not the giveaway for Ramanujan.

5. This is transparent in a way that I'm not sure can be corrected; when you're talking about a mathematical family across several generations including contemporaneously to Euler's granddaughter, who else could it be but the Bernoullis?

10. The cubic equation given as the second clue is way too easy to solve just by looking at it.

15. This was a cool tossup!

19. "Fourth power case" is a little too obvious a little too early. Maybe discuss details of a proof of Waring's theorem? (Like the Schnirelmann density one in Khinchin!)

Packet 9

2. This is a good tossup.

5. The first clue is a straight-up hose for "quadratic equations," and I nearly buzzed on the second clue with "Egyptian fractions." Sad!

6. POWER SET

8.
Answer: iterated prisoner's dilemma [prompt on prisoner's dilemma, accept answers that consist of repeatedly saying the words prisoner's dilemma]

10. Feel like "Newton was Master of the Mint" is too well-known to straddle the powermark.

12. I'm not a machine learning expert but the first clue seems bad, since LeCun has published papers using convnets to recognize everything.

14. Kinda think "glider" should be either a neg or an antiprompt the whole way through (and "knightship" should be treated the same way IMO ). Nobody calls the 17c/45 ship a glider.

19. This is a cool tossup.

20. These clues are too easy.
Harrison Brown
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"No idea what [he's] talking about."
CPiGuy
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### Re: Math Monstrosity - Specific Question Discussion

Well, that's a lot of feedback -- thanks! I'll try to respond to some specific ones here, now that I've gone through and edited the set somewhat.
Jake wrote:polyomino is an excellent idea but could have used some specific antiprompts for moderators who are not as experienced with the material.
Yeah, I personally antiprompted on answers like "pentomino" and that should have been in the answerline.
Jake wrote:Be careful when using "s" as your argument for things involving the Riemann zeta function. It's pretty much the most notable function that historically takes "s" as an argument.
this is true, but I decided to not change the argument because I figured adding "s" as an argument would just be another clue, and recognizing the Riemann functional equation at game speed is still pretty difficult.
Jake wrote:The Konigsberg bridges tossup seems to be fine except that you namedropped the name of a bridge (notably by saying "bridge") inside of power. What else could this be?
Only if you speak German!
Jake wrote:Tartaglia is pretty famous for his work on solving polynomial equations, I'm fairly certain.
I mean, that's what he's most famous for, but the Tartaglia-Cardano contests seem pretty unknown, unfortunately.
Jake wrote:That demonic formula for 1 / pi could have been replaced by much more substantial clues.
I've done this to save the moderators.
Jake wrote:Tossing up Japan whilst including a Japanese word in every line past the power marker is probably not a good idea.
And yet, literally every time I have read this tossup, it's gotten negged with China (all but one time on "abacus". Come on, people, cultures other than China used abaci!)
Jake wrote:Mascheroni is an Italian mathematician. Mascherano is a notable Argentinian soccer player beloved by Diego Armando Maradona.
Oooooof, that's embarrassing. Edited.
Jake wrote:"Fitting" is a person so his name should be capitalized in the subgroups question.
Huh. TIL.
Harrison wrote:Not sure I love clues like "Cantor was born in this country"; is that really testing any sort of math knowledge? The Euler clue is fine, on the other hand.
I mean, not explicitly, but that's why it's the math history distribution -- likewise, the clue about Cardano and Tartaglia's cubic fights doesn't actually test knowledge of how to solve cubic equations.
Harrison wrote:Compressed sensing seems like one of the harder answerlines for the tournament, although it might be quizbowl famous and I don't realize it. I liked the question, though.
Well, I wrote this question after looking up various "hot topics" in applied math. It's probably too hard; I probably assumed too much real knowledge on behalf of people who do not work in signal processing (I have no real knowledge of this stuff...).
Harrison wrote:Riemann's functional equation for the zeta function is incredibly famous and IMO too easy for a lead-in in an all-math tournament; the zeta function is one of the best-studied objects in math, so there's no excuse for not finding a harder clue.
yeah, but there's a difference between "knowing things about the functional equation" and "recognizing an equation at game speed".
Harrison wrote:"Floor planning" was one of the few answerlines that went dead in our room all tournament; I don't know anything about this topic, though, so maybe it's fine.
This also seems to have been too hard, since actual electrical engineer Cody Voight didn't get it (unless I misinterpreted him).
Harrison wrote:The fact that the Franklin graph is 6-chromatic is interesting but might be a better clue if you gave some reason why the Franklin graph was constructed (e.g. "this is the chromatic number of the Klein bottle").
right, but I put that clue early because I only wanted people to get it if they knew what the Franklin graph was.
Harrison wrote:(Fortunately the moderator was generous enough to give it to me when I babbled something including the words "Futurama" and "body switching.")
Good, that's literally all you needed to say. I left the answerline vague on this one for a reason.
Harrison wrote:Kinda think "glider" should be either a neg or an antiprompt the whole way through (and "knightship" should be treated the same way IMO ). Nobody calls the 17c/45 ship a glider.
So, that's the way this was originally. Then I ran this at MSNCT, Cody had a sweet buzz on the first clue but said "glider", I antiprompted him, and he couldn't pull spaceships. I thought at that point that requiring "spaceship" might be too hard. I have since reverted that tossup to antiprompt on "glider".
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### Re: Math Monstrosity - Specific Question Discussion

CPiGuy wrote: At least three answerlines (long line, Banach-Mazur game, bivectors) have never come up in quizbowl before (at least not in any set in the packet search), whether as an answerline, bonus part, or clue.
Bivector appears to have been an answer to a non-mathy bonus in Chicago Open 2015, Round 11, maybe?
Last edited by scholarhillery on Sat Jun 24, 2017 10:43 am, edited 4 times in total.
Jon Hillery
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### Re: Math Monstrosity - Specific Question Discussion

In regards to repeated clues: Another clue that was still repeated several times by the NSC running of this tournament was that the smallest non-abelian group is the dihedral group of order 6. I think it was used as a clue in two questions with answers relating to dihedral group (maybe?) and was a clue for the question whose answer was "6".

Packet 7: 16. I'm pretty sure everything in this sentence is true of all polygons, not just quadrilaterals: "The tangential kind of these objects is distinguished by
possessing an incircle, and the area of a tangential one of these objects is equal to the inradius times the semiperimeter"

Packet 12: 1. This is probably just me, but I buzzed with "pitch classes" on the question with answer "music" right when it started talking about David Lewin (2nd sentence, before the title drop though) because I own the book that was mentioned and have read a fair portion of it. This answer also fits with the first clue, which talked about pitch-class set theory (which imo is actually a really good first clue in retrospect, but I wasn't thinking of music-related things at all at the time), but when I was prompted (only because of the knowledgeable moderator) I couldn't figure out the desired answer.

Concerning the Argand plane clue: One reason it might be used in lower difficulties, but you guys haven't heard about it is that from my experience the term is tossed around a lot in the high school math competition world in relation to solving Euclidean geo problems using complex coordinates, but I've never heard the term used in the world of complex analysis, etc.

PS: I loved the clue about the Klein Four a cappella group. Sadly, I told everyone in the room about that clue before the match started because they were asking about our team name (Finite Simple Group of Order Two). Also, I was disappointed to not here a clue about the ring isomorphism form of the Chinese Remainder Theorem
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