Math Team

Post by lupire » Thu, Dec 21, 2023, 2:04 AM UTC

jimbokun wrote: post #55

neilv wrote: post #52

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.

Post by amluto » Thu, Dec 21, 2023, 2:53 AM UTC

markisus wrote: post #68

amluto wrote: post #62

Earlier quoted context omitted.

> 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 sa…

Post by chrchang523 » Thu, Dec 21, 2023, 3:52 AM UTC

jhshah wrote: post #75

lupire wrote: post #73

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..."

Post by bee_rider » Thu, Dec 21, 2023, 5:00 AM UTC

julianeon wrote: post #63

quax23 wrote: post #28

Earlier quoted context omitted.

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 sa…

Post by thoughtpeddler » Thu, Dec 21, 2023, 7:20 AM UTC

lupire wrote: post #82

This story is about high school circa 2005. It is far, far harder to qualify for an elite high school math team or get into Stanford now.