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Math Team

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Re: Math Team

#61

Post by dexwiz »

In my High School experience I encountered two styles of knowledge competition. Quiz Bowl, which was essentially Jeopardy. And Academic Super Bowl, which was like extra school.

Quiz Bowl was full of a ton of smart kids with various interests. We "practiced," but the only skill you could really develop was being able to predict a question before it was finished so you could be the first to answer. Questions varied widely from competition to competition. One time we got to be on local TV to compete, but there really wasn't a season or tournaments. It was mostly 1 on 1 matches after school. Overall it was a ton of fun.

Academic Super Bowl was also full of smart kids, but they were more goal oriented. It was something you had to study for. Before the competition you were given some categories, you assigned categories to teammates, studied, and then competed at various events. It was literally just more memorization. I got drafted to do it one year the night before a competition, because I was The Guy for a topic they needed a teammate for. It was awful. I fumbled my way through because I didn't have near the detailed knowledge required for the specific subcategory. I probably would have done better if I had more time to prep. It was a big tournaments, and at the end there were different prizes for schools by various sizes.

The type of kids in the two were varied. Everyone wanted to get into a good college. The former seemed to love knowledge for the sake of knowledge. While the later had a ton more grit, they lacked passion in areas outside of directed study. The former would read a book, because it was mentioned offhand in another piece of media. The later would read a book because it was assigned to them.

Reading through this thread, it seems like people's experiences of Math Competitions varies from one to the other. Having grit to study and work at it gets you far, but having passion probably gets you further. The issue is grit tends to be fungible while passion is not.

Re: Math Team

#62

Post by amluto »

markisus wrote: post #34
zeitgeistcowboy wrote: post #3

In the 4th paragraph he describes “the arc of a stone falling to earth” as an exponential function. Is that true? I always thought it was quadratic.

Solutions to linear differential equations are exponentials, and this may be what the author meant. In a state space model, we can write Newton's law under gravity if we let y(t) = [x(t), x'(t)]^T, let A = [ 0, 1; 0 0], let b = [0, -g]^T, and set y'(t) = A y(t) + b. Indeed, the solution is y(t) = exp(A t) (y0 + int_0^t exp(-As) b ds). In Einstein's theory, we have a generalization which says a stone's path through sp…

> So the author is right, under this interpretation.

Huh?

You can say “state space,” invoke the general solution to inhomogeneous ODEs, and write it out with integrals and matrix exponentials, and the answer is still quadratic. Unless you consider t^n e^(0t) to be exponential. (Hint: what are the eigenvalues of A? One could start by calculating A^2.)

Which leads to one of the most important lessons from all of physics: you can take a problem, use a different technique to solve it, and you get the same answer! It’s magic.

Re: Math Team

#63

Post by julianeon »

quax23 wrote: post #28
aleyan wrote: post #5

Went to the same school, was on the same math team, but was a year ahead of the author. Quit math team in my junior year because I wasn't at a competitive level, but it was a great time while I was on it. As a SWE, I rarely get to exercise the tenacity and problem solving skills I learned on the math team, but when I do they are "transformative" to the rest of the team. > Nights were for other worthless extracurricul…

I can relate; I didn't study quite as hard as my peers, didn't get into the prestigious private colleges that they got into (still went to an excellent public school across the Bay from Stanford), studied a fair bit of math, and ended up with a decent job where I've found that my math and problem solving skills have paid dividends. I'm certainly not making tech or F-U money, but I have a comfortable life a few years…

My experience, a few decades later, is that everyone who optimized for STEM and long hours in high school made the right choice. The only downside I’ve seen is some wistfulness about lost romances and the preciousness of childhood. The upside is much higher earning power and greater opportunity later in life. I’d actually be interested in counter examples. In my circle I’m not aware of any, which is different than saying they don’t exist.

Re: Math Team

#64

Post by legerdemain »

ianbicking wrote: post #57
legerdemain wrote: post #51

I went to a combined middle/high school in a small city of 200,000 in upstate New York, and no one on our Math League team distinguished themselves in any way other than by transferring to another nearby high school that had an actual IB program. At that level of engagement, Math League was all right, just something for a nerdy, unpopular teen to do to break up the monotony of dreary upstate winter evenings. I'm more…

In my high school the order of classes was, if I remember: Algebra I, Geometry, Algebra II/Trig, Analysis. Calculus was still "after" high school at that time (early 90s), though starting to become common. So Analysis was kind of pre-calculus, a variety of different subjects that weren't quite calculus. I remember bits of algebra, probability, compound interest, etc. We didn't have Analysis I/II, but the boundaries b…

High schools in my area called the course before calculus "pre-calculus," analogously to "pre-algebra" coming before "algebra" in middle school.

Re: Math Team

#65

Post by totierne2 »

TrackerFF wrote: post #12

I'm from Scandinavia, and I always find it both fascinating and alien how much focus the US system puts on extracurriculars - and more specifically competitive extracurricular activities. On one side, it is probably good to motivate pupils to aim for something, and get good at it - but on the other side, you obviously end up with a bunch of kids that are just really good at grinding away - even if their heart is not…

I was in the British system (3 subjects, interview, effectively CV/Resume for top University, but mostly school exams, I academically stuck rigidly to the syllabus plus minor extracurricular).

My 17 year old son is in the Irish system. Top 6 subjects count for points, nothing else. Plus some minor need to pass requirements on other subjects. i.e. you cannot just specialise in science and maths at the end. (His 6th best subject will be Irish, English or French, all hard to get very top marks in.)

With dumbing down/grade inflation the skill to get ahead into a good degree is be pretty good at everything. Rather than absolutely brilliant at a couple of things.

He did a tiny bit of computers and maths extra classes, but we could not keep the maths classes going when it went back to in person after COVID, as we are on the poorer side of Dublin. Small chance he goes to Britain for undergraduate, which will be weird as he would suddenly have interviews/CV/Resume, whereas no interview/CV/Resume in Ireland.

Re: Math Team

#66

Post by inthewoods »

What I'm really curious about is how he got into Stanford, a school that famously no one gets into, given what we know about him. Not to say he's not smart or interesting - he's clearly a good writer - but I don't see what made him stand out to get into that school. I'd be interested to understand that.

I've got a freshman in high school - and he's very bright - doing AP Calc now. But he already feels like it's impossible to get into these schools so why bother. He started the conversation tonight with "I don't think I want to go to MIT anymore." Which broke my heart a little bit - not because I care whether he goes to MIT - but because it you could see his expectations being crushed by reality.

This is the system that we have built for higher education in the United States, and it's incredibly f*cked up.

Re: Math Team

#67

Post by junar »

gowld wrote: post #47
fortenforge wrote: post #39

The author mentions at one point that he was unable to solve a problem because he didn't memorize the formula for the Euler totient function in order to count the number of numbers relatively prime to 9999. ...but its actually an interesting (and not super difficult) exercise in its own right to figure this out even if you don't know the formula. Encourage you all to give it a shot. SPOILERS: 9999 = 3^2 * 11 * 101, s…

The problem (and linked solution is here) https://artofproblemsolving.com/wiki/index.php/2022_AIME_I_P... The totient formula isn't the hard part of the problem. The test has a very short time limit (for the difficulty of the problems), and has many gruelingly complicated problems,so if you dont have the formulas down cold, you'll burn out during the contest. Of course, if you don't care about silly speed-mathing con…

Agree, and to add a bit more context:

* The contest has 15 problems and a time limit of 3 hours, giving only an average of 12 minutes per problem.

* The average score is 4.83/15, from the official statistics [1].

* The statistics noted that only 5.17% of test takers answered this problem correctly, making it the second-hardest problem out of the 15 on the exam.

[1] "AIME 02/08/2022" https://amc-reg.maa.org/reports/generalreports.aspx

Re: Math Team

#68

Post by markisus »

amluto wrote: post #62
markisus wrote: post #34

Earlier quoted context omitted.

Solutions to linear differential equations are exponentials, and this may be what the author meant. In a state space model, we can write Newton's law under gravity if we let y(t) = [x(t), x'(t)]^T, let A = [ 0, 1; 0 0], let b = [0, -g]^T, and set y'(t) = A y(t) + b. Indeed, the solution is y(t) = exp(A t) (y0 + int_0^t exp(-As) b ds). In Einstein's theory, we have a generalization which says a stone's path through sp…

> So the author is right, under this interpretation. Huh? You can say “state space,” invoke the general solution to inhomogeneous ODEs, and write it out with integrals and matrix exponentials, and the answer is still quadratic. Unless you consider t^n e^(0t) to be exponential. (Hint: what are the eigenvalues of A? One could start by calculating A^2.) Which leads to one of the most important lessons from all of physic…

I consider exp(At) to be an exponential expression in A. Depending on A, you may get a matrix whose entries are quadratic in t, as in this case. For another case, you may have trigonometric entries in t, as in the case of A = [0, 1; -1, 0].

Maybe you would personally say that neither of these cases is truly or essentially exponential, since we have more recognizable closed forms. But then you should also commit to saying exp(it) = cos(t) + i sin(t) is not truly exponential. I would find that a little strange, but to each his own.

Anyway, I agree that you get the same answer in the end, as you must.

Re: Math Team

#69

Post by lusus_naturae »

carabiner wrote: post #53
lusus_naturae wrote: post #49

Earlier quoted context omitted.

I guess we’ve come far enough from being hunter-gatherers that the value of acts that ensure group cohesion and community wellbeing seem like some sort of extra effort or altruism, instead of a fundamental aspect of optimizing survival as a whole. That said, I was talking about governance and policies, not what career choices someone should or could make.

In the US at least, you're most likely to effect systemic change by having a lot of money.

Not unique to the U.S., and also is called corruption or cronyism in general terms when money mostly enables one to “effect systemic change”. The U.S. civil rights protests stand in stark contrast as one example, at least.
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