Steps to Conquering the Math Canon?

[Steven Hines]

Let me first start out by saying that I've been following the advice from http://www.qbwiki.com/wiki/How_to_becom ... nce_player to quite some success in all the categories besides theoretical math. I've taken many advance courses in math (including some analysis, abstract algebra, topology, and both ordinary and partial differential equations), but unfortunately, the canon for high school quizbowl doesn't seem to focus on those areas. If a tossup comes up on things like compactness, continuity, or something tailored to those areas I can usually first clue it. The problem is that tossups on those subjects rarely come up (if they come up at all), but rather I often find myself in the situation where I'm being beat to a prime numbers tossup because that subject hasn't really come up in my classes.

So..how can I learn the math canon (if not from my math classes) - what is it that I'm missing in my approach?

Also, is the problem I'm encountering really only in the high school canon (should my classes help me more when I get to the collegiate level)?

Lastly, I've just started to keep a notebook for quizbowl - is there any special thing a science player should be doing differently than normal in regards to said notebook?

Anyways, thanks for any help given!

[Mewto55555]

A common thing seems to be that advanced math people, once they complete high school math, keep chugging onward into upper level stuff (it sounds like you've basically hit up all the next rung of college classes). One of your big problems is going to be that high school questions are generally not written with people like you in mind: a tossup on compactness will go dead in basically every room, so writers will instead tossup something like "squares". The stuff you're probably seeing that you're most unfamiliar with (I could be wrong, I'm just guessing you haven't had a ton of background in these areas) is going to be in accessible but interesting elementary math (combo, NT, geo, etc). There's a ton of recently-written high school math questions in this thread that might give you an idea of what some of the things tossed up in high school tend to be.

I can't speak much for college level, but in high school, very basic knowledge of upper level stuff like linear/abstract combined with my contest background is enough that I usually know most of the clues in a given question.

[samus149]

There's nothing wrong with your approach, it's just that the topics you study are not applicable to the high school canon. There's really no way a regular difficulty tournament can toss up anything related to topology or abstract algebra and expect a high conversion rate. That's why you always see tossups on primes, Fibonacci numbers, Euler, and the like. These questions use math more from the high school competition "canon", which is all those theorems that come up on the USAMO and usually aren't part of a math curriculum in school.

My recommendation is that I would give to anyone else trying to get better in a subject: read old packets and Protobowl science in a private room. Yes, it's learning stock clues, but it gives you an idea of what comes up at normal tournaments. I think the best sets to read for math clues are LIST, which has some of the most original math tossups I've heard, and IMSANITY, whose math is some of the hardest I've seen. Now, that's not to say you shouldn't learn everything you can, it's just a way to get familiar with all the firstlines (I swear, if I see one more Weierstrauss function firstline...). However, you probably won't find exactly what you're looking for reading high school questions. Your knowledge of real math will definitely help in college, where the canon gets a lot more expansive. They love to ask about the things you've learned there, because that's what most math majors study.

Same rules apply for science, though you seem like you have a really strong base in that too. AP classes get you most things fairly early, but there are some things that are just stock, unless you're a masochist (you wanna real knowledge the Cabibbo-Kobayashi-Maskawa matrix, be my guest). Protobowl helps here too, just be wary of associating a word to an answer.

Oh yeah, and as for the notebook, just write down any law/term/person you hear in a question and look them up. You'll find some awesome things on Wikipedia.

[Mewto55555]

I think the true masochists are the ones who subject themselves to mindlessly memorizing names from Protobowl and thus never rise above the level of a middling high school generalist.

(EDIT: If my post is unclear, the response to seeing CKM in a tossup on weak force should not be "when you say CKM, I say weak force!" like Sean has incorrectly posited a number of times, but rather "CKM matrix is a Thing of some sort, time to go learn what it is" -- doing the latter should be described with words like "smart" instead of "masochistic")

[Stained Diviner]

In addition to what has already been said, if you want to see a lot of high school math questions, go through the Masonic sets. The categories are labeled, so you can just ctrl-f math.

[conquerer7]

Most of the stuff you're missing is combinatorics / number theory; I've done pretty well based on competition experience and generally hearing "math lore" at places like Mathcamp and MOP. There's also a self-reinforcing aspect: competition people, like Max, tend to write questions based on that stuff, and then competition people like me love it! (if NAQT accepts me, I guess I'll do the same)

Another thing that I'd rather not admit is very useful is wasting time on r/math or mathexchange. It's fun, and it's full of the kinds of cool things that people like writing about!

I don't want to start the whole argument about real knowledge all over again; if you two want to have another go, revive my thread? :P

[touchpack]

On a somewhat unrelated note, the CKM matrix is pretty easy to understand if you have elementary knowledge of linear algebra (which I will assume you do have, since this is a thread about learning math). Wavefunctions are just vectors, man!

[DoubleAW]

From my experience I would say that Wikipedia is a pretty solid resource for learning all this random math canon information. I definitely found a lot of obscure but fairly interesting things from just absentmindedly browsing around, but a good amount of them ended up coming up often. Good example: one time I looked up the Riemann sphere for some reason, and it got me a tossup at PACE that year (sphere) and HSNCT the next year (Riemann). It only took a second to discover but it came in handy later. So I would suggest kinda browsing around aimlessly for a while; you're sure to find something useful, just so long as you remember it.

[Steak and Kidney Pie]

This is one of the few areas where I have some amount of experience. As Max said, in high school there is a reasonable amount of "elementary mathematics" (nt, combo, euclidean geometry), like the kind that shows up on competitions.I'm not really sure how to learn beyond actually doing a lot of independent problem solving type stuff (e.g. work through Paul Zeitz' The Art and Craft of Problem Solving), or going to a math program such as MathCamp or AwesomeMath.

In more difficult college scripts (and tournaments like NASAT, and, to a lesser extent, HSNCT), they will ask more questions relying on multivariable calc, real and complex analysis, and linear or abstract algebra. However, the issue is that in college there are other people who have had those classes. And, in addition, just from taking a standard undergrad class, you won't necessarily be able to first-line everything. (Like at NASAT there was a question on Polynomials with 1st line about Noetherian Rings, and second line about Galois theory, I don't think either of those subjects would be in a intro abstract algebra course, I could be wrong though b/c my education in algebra has been pretty nonstandard). But if you're interested in math, as you definitely seem to be, you'll learn stuff beyond what you see in class, and be able to answer these kind of questions.

[The ChatSack Triple-Play]

This is one of the few areas where I have some amount of experience. As Max said, in high school there is a reasonable amount of "elementary mathematics" (nt, combo, euclidean geometry), like the kind that shows up on competitions.I'm not really sure how to learn beyond actually doing a lot of independent problem solving type stuff (e.g. work through Paul Zeitz' The Art and Craft of Problem Solving), or going to a math program such as MathCamp or AwesomeMath.

In more difficult college scripts (and tournaments like NASAT, and, to a lesser extent, HSNCT), they will ask more questions relying on multivariable calc, real and complex analysis, and linear or abstract algebra. However, the issue is that in college there are other people who have had those classes. And, in addition, just from taking a standard undergrad class, you won't necessarily be able to first-line everything. (Like at NASAT there was a question on Polynomials with 1st line about Noetherian Rings, and second line about Galois theory, I don't think either of those subjects would be in a intro abstract algebra course, I could be wrong though b/c my education in algebra has been pretty nonstandard). But if you're interested in math, as you definitely seem to be, you'll learn stuff beyond what you see in class, and be able to answer these kind of questions.

Seconded Zeitz. Art of Problem Solving has some pretty good stuff too, although it splits the same stuff up (so that you have to pay more for it I guess) but they do have a problem archive, as far as that goes for quizbowl purposes.

(As the abstract algebra question goes, the first UG textbook I found on Amazon has some stuff about Galois theory, but nothing on Nullstellensatz/Noether, which kinda makes sense.)

[Euler's Constant]

Seconded Zeitz. Art of Problem Solving has some pretty good stuff too, although it splits the same stuff up (so that you have to pay more for it I guess) but they do have a problem archive, as far as that goes for quizbowl purposes.

I've only heard of Zeitz in passing, but I can vouch for the Art of Problem Solving textbooks as being very good both for math contest prep and for quiz bowl. That said I feel like there's been a trend high school quiz bowl towards contest material and away from basic high school course work that's making math questions less accessible than the rest of the canon, as I think we're overestimating how many people are involved in both, especially once we move away from the top tier teams. (*The intersection between the quiz bowl and math contest circuits in Indiana is very small, so it might just be that I have a bad view of things nation wide)

While I didn't get the polynomial question at NASAT, the abstract algebra course I took at ND basically focused on Galois Theory for much of the second semester and we covered the Hilbert's Basis Theorem, Noetherian rings, and Hilbert's Nullstellensatz as well, so I don't think those clues were too hard, given the set was around regular college difficulty.

Edit: For my abstract algebra course we used Artin

[Sima Guang Hater]

Dropped in to third the Art of Problem Solving curriculum as a very good source. Also I don't have the competition ability of Max or Kevin, but I use those things as clue as much as I can.

[jonah]

So did this advice help?

[Cheynem]

He certainly took the "read old packets" to heart.