91–100 of 106 posts
X = 0.acdabcdabcd... Y = 10000 * 0.abcdabcdabcd... = abcd.abcdabcdabcd...
Y - X = abcd.abcdabcd... - 0.abcdabcdabcd.. = abcd (without the pesky decimals)
I too learned this in high school and was fascinated by it.
Personally, I just liked solving all sorts of puzzles and math problems and other sorts of contests. There's nothing like the adrenaline rush of competing against other people in a mental challenge under time pressure. I had some books with math problems, and I liked reading those, and I did well in the contests, and that's all it really takes. You don't need a team. But I enjoyed it.
Obviously if you like competing in math contests and you are good at it then it's a good thing to do. I'm not sure how good of an idea it is to "force it" and try to get good at something that you really aren't that into.
If you're a smart person, there must be something intellectual you can really get into, right? Hopefully?
Earlier quoted context omitted.
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.
Great, honest-sounding description of this college application grind, doing things he wasn't interested in, and suggesting that most of the other mathletes also weren't interested in math. Now that he's 15 years into a tech career, I'm wondering what he thinks if/when interviewing applicants, and sees or doesn't see similar grind on the resume. I imagine that some, if they got their position by virtue of the hoop-jum…
I would want to find applicants more like the one mathlete who was still doing mathematics past school years because he found it deeply interesting. Then transferring that innate problem solving drive and aiming it towards the problems and challenges facing the company.
After hiring couple of those people I've become quite vary of them.
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…
For every distinct prime factor p (so, of 9 is a factor, use 3 not 9), only (p-1)/p of the natural numbers ≤ n are relatively prime to it. Pime. This overcpunts nothing, since prime factors are relatively prime to each other. (Proving this requires some analysis of remaimders / modular arithmetic. But working an example shows the pattern).
This gives a formula, phi(n = Sum (p_i ^ e^i)) = n • Product ((p_i -1)/p))
This also shows how OP (and maybe the coach) missed the point of math team.
Earlier quoted context omitted.
> Trying to come up with everything from scratch could take a lot longer and be very frustrating If that is frustrating instead of thrilling to you then you probably shouldn't do these competitions.
I’m trying to put myself into the shoes of the blog’s author. I just finished my math degree. It wasn’t at an elite school. I enjoy math for recreation though I’ve never been a contender in contest math. I think I can understand why the author complains about drilling for math contests. I think it’s the same reason high level chess players complain about opening book. Drilling is not fun and it reduces the creative e…
OP says in the article that he didn't understand what he was doing, but was just trying to imitate people who did to try to appear brilliant. And he claimed that most students in club were like this, due to parenting and teaching that was focused on resume building for ignorant Admissions Offices, instead of focused on learning.
Earlier quoted context omitted.
What's especially fascinating is that the core of the problem is a generalization of the totient computation, so understanding the inclusion-exclusion construction of totient is very helpful to the problem, while simply memorizing the formula is a misdirection. OP missing this point shows that he really was doing this for all the wrong reasons. He should have done FIRST or science bowl instead.
Completely agree, I also liked the problem and thought it was conceptual as far as these things go. Asking for N mod 1000 was another cute twist that was meant to get you thinking about the divisibility properties of the totient function - "hmm, so (p-1) always divides \phi(n) for all prime factors p of n, how convenient..."
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 impos…
It really shows that admissions is a crapshoot. Also, this story happened 20 years ago. Regarding your kid: There are 4million US high school graduates each year. MIT admits about 2000. Sorry for being abrasive, but why is your child crushed that he isn't the very best? Why is it sad that he isn't better than everyone else? Being upset about not being in the 0.1% as a teenager is tacky. 99.9% of us aren't.
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 impos…
I don’t know that this is a problem specifically of the US or higher education, just humans. Humans want to have the best, to be the best. There’s only so many “bests”. When competing with millions or billions of other people, the odds you are the best are very low indeed. I think it was less painful pre-internet, pre-globalization, where you only had to be the best in your town, or your state, and that was pretty da…
Earlier quoted context omitted.
I’m trying to put myself into the shoes of the blog’s author. I just finished my math degree. It wasn’t at an elite school. I enjoy math for recreation though I’ve never been a contender in contest math. I think I can understand why the author complains about drilling for math contests. I think it’s the same reason high level chess players complain about opening book. Drilling is not fun and it reduces the creative e…
Except for the intense speed pressure to create artificial rankings for competition, "drilling" is "practice for understanding". OP says in the article that he didn't understand what he was doing, but was just trying to imitate people who did to try to appear brilliant. And he claimed that most students in club were like this, due to parenting and teaching that was focused on resume building for ignorant Admissions O…
It really isn’t. The essay makes this point as well. The acquaintance of his who was most interested in math dropped out of the contest team. He went on to become a mathematician because he was actually interested in understanding higher math and how things fit together.
Drilling is just practicing computational tricks to be able to execute them by heart. This would be true regardless of the amount of time pressure or lack thereof. I’ve taken many math courses that had exams in this style and I always hated them. I much prefer trying to figure out a proof I’d never seen before. For any real work, those computations would be done by a computer anyway.