Andy's Math/CS page

Wednesday, April 16, 2008

A simple plan to improve your graduate program

It's just this: Food is key. We need more food. (In what follows, I'm speaking not just for MIT theory students, but for all students everywhere.)

Cancel the subscription to 'Journal of Timed Networked Multithreaded Aqueous Automata', and a few others. You've just saved about $20,000.

Use the money to provide copious snacks for students and faculty. Weekly receptions help, but really we're hungry all the time. To elaborate on that point:

-The student center is a tiresome 5-10 minutes away.

-Graduate students are low on cash. We work strange hours that discourage grocery shopping (and may not own a car). Some of us are newly weaned from the meal plans of our undergrad days, and we're only slowly learning to provide for ourselves. The food around here is expensive.

If department budget is truly an issue, there is another way, practiced with admirable success by UC San Diego's CSE department: recruit grad student volunteers to maintain a stocked snack-room, with foods purchased cheaply in bulk and paid for on the honor system. Of course, a snack-room should also be a social space.

Candy and tasty treats help, but it's too easy to over-rely on them and come crashing down. At some point we all wish there were less of these around the office. Consider in their stead:

-apples and bananas
-peanuts and peanut butter

...all cheap, real-tasting, and calorific.

That's it! An easy, cost-effective intervention that will keep students and faculty working happily in their offices on their next theorem or patentable device.


Friday, April 04, 2008

Some babies grow in a peculiar way

Today I bumped into an order of growth I hadn't seen before, and thought I'd share it for a modest bit of mental aerobics.

Readers may well have seen functions of form

f(n) = (log n)^c,

known as 'polylogarithmic'. These are important in, e.g., query complexity, where we like the number of queries to be much smaller than the input size n when possible. Also emerging from such studies are the 'quasipolynomial' functions, of form

g(n) = 2^{(log n)^c}.

As a warmup--how fast do these things grow?

OK, now the main course tonight is the following:

h(n) = 2^{2^{(log log n)^c}}.

What do you make of these? And what questions need answering before we understand such a growth rate 'well enough'? I'm unsure and would love to hear your thoughts.