Life isn’t a straight line.
Finding your dream career involves a lot of twists and turns, like a river.
In my search for the perfect job, I find myself constantly changing course,
because even though planning is helpful, the plans themselves are useless.
Some of you have probably noticed that I’m helping with
organizing a new contest
and are asking what exactly this is.
So far, I haven’t said much about it because so much is up-in-the-air
(and that’s still true).
However, with the first few acceptances and registrations coming out,
I’m going to post an FAQ and few quick thoughts of my own.
Just to be clear, everything here is my own personal commentary and views
and not those of my employer or OMEGA generally.
What is OMEGA?
OMEGA (Organization for Math Engagement and Growth in America)
is a new 510(c)(3) whose ambitious long-term goal
is to build great, robust math programs for thousands of students
all across the USA (whether competition-like or not).
However, that is a pipe dream, because OMEGA is also about four months old
and has a whopping four staff, many of …
During your turn, part of figuring out the best move involves looking into the
future to see what the next player will do. If they discard, will it be okay?
Is there some obvious clue that they will do? And so on.
As you get better at Hanabi, you will need to do this prediction not just for
the next player, but for an entire go-around of the table. And as you really
get good at Hanabi, you will need to do this for as far in the future as you
can reasonably predict. (Sometimes, this means 15 moves or more in the
future.)
Similar to chess, initiating a move in which you can predict the next sequence
of moves is called initiating a “line”.
In post-game reviews, we will often compare and hypothetically “play through”
two different lines …
I had a student at MOP ask me something equivalent to
“how should I study while at MOP?”There is also a question about whether you should be studying much at MOP
at all — you could also spend a lot of time making new friends, for example.
That’s a value judgment that I think is better left to individuals
and I won’t comment on it further in this post.
For those of you that don’t know, MOP
is the three-week summer camp for the USA’s team to the IMO.
At first I was going to just link my FAQ.
But then I thought about it a bit more, and I was surprised to find that
my answer was not the same as the general how-to-study FAQ.
The additional condition “while at MOP” was enough to cause me to
stay up that night writing an entirely different …
In my last semester of MIT I led a recitation (i.e. twice-a-week review) sessionFor those of you that don’t know how the system works, at MIT,
18.02 is a huge class with 400 to 500 students (mostly first-years).
In order to make sure students actually get the individual attention they
need (impossible during lecture), the math department also places each student in a
recitation section
of about 20 students each, meeting twice a week for an hour each.
for multivariable calculus (18.02) at MIT
(although the first few weeks are all linear algebra).
It’s different from many contexts I’ve taught in before;
the emphasis of the class is on doing standard procedures,
but the challenge is that there is a lot of ground covered.
That is, compared to other settings I’ve taught,
there is generally a tradeoff of less depth for more …
I was a coordinator for last year’s IMO 2024 and this year’s IMO 2025.Before, I was a coordinator for some virtual IMO during the pandemic too,
which is much less fun. And from 2017-2019 I was an observer for the USA.
Here’s some thoughts about that, contrasting my IMO 2019 post.
What is coordination?
For those of you that don’t know, coordination is the grading process for IMO.
As I describe it in my FAQ:
Basically, the outline of the idea is: before the exam, a marking scheme
(rubric) is set for each problem, to cover the typical cases of what progress
will be worth what points. Then, the leaders of each country get to see the
solutions of their country’s students, while there is a number of coordinators
from the IMO host country for each problem. Both the coordinators and the
leaders read …
I am always harping on my students to write solutions well rather
than aiming for just mathematically correct, and now I have a
pair of problems to illustrate why.
For any integer d>0,
let f(d) be the smallest positive integer that has exactly d positive divisors
(for example, f(1)=1, f(5)=16, and f(6)=12).
Prove that for every integer k≥0, f(2k) divides f(2k+1).
I like this problem, so try it out if you haven’t.
This is a problem …
During this year’s MOP,
we used the following procedure to divide some of our students into two classes:
Let p=7075374838595186541578161 be prime.
Take the letters in your name as it appears on the roster,
convert them with A1Z26 and take the sum of cubes to get a number s.
For example, EVANCHEN corresponds to s=53+223+⋯+143=16926.
Then you’re in Red 1 (room A155) if s is a quadratic residue modulo p,
and Red 2 (room A133) otherwise.
The students were understandably a bit confused why the prime was chosen.
It turned out to be a prank:
if you ran the calculation on the 30-ish students in this class,
it was …