Mit Interview Secrets!! - Page 3

RobbCarr · 10-25-2005, 02:30 PM

http://www.wired-designs.net/localExtrema.pdf ...All latexified so a bit easier to read...mmm I feel rather silly now

sarang2005 · 11-03-2005, 12:21 PM

I am quite new to calculus, but can't help posting...

Isn't f(x) = x sine (1/x) where x belongs to (0,1]
and f(0)=0
such a function?

stasterisk · 11-03-2005, 12:29 PM

Definition: thread hijacking

RobbCarr · 11-03-2005, 02:53 PM

Nope Sarang, it does "oscillate" (I use quotes because it doesnt technically oscilate between two values) for a while, but its not uncountable at all you could verify this fairly quickly by looking at the derivative, or just a graph (though having the derivative might help) Actually a day or so after posting http://www.wired-designs.net/localExtrema.pdf (2 replies back) I found a similar proof of the same in a book on integration (Actually it was cited as well known and that a proof appeared in said book from a mathematics article I was reading so I found a pdf of the book).

mathwiz · 11-04-2005, 12:01 AM

How about just sin(1/x) in the interval (0,1]

Ben Golub · 11-04-2005, 01:42 AM

only countably many zeroes. easy to place them into bijection with the integers. infinite is not enough. uncountable is needed.

Ben Golub · 11-04-2005, 01:44 AM

Robb -- sorry I didn't respond right away. It seems like you sort of have the right idea, but your proof seems to assume you can isolate each maximum inside its own open interval, and this need not be possible... The idea is to cover the maxima by intervals (possibly overlapping) with rational endpoints, and there are only countably many of those.

By the time you get to college, make sure to polish up your mathematical writing. It's no use understanding it if you can't explain it lucidly to others.

RobbCarr · 11-04-2005, 02:37 AM

Yeah the mathematical writing is a bit of an issue for me. The number theory course I am taking through EPGY is pretty writing intensive so that is helping a good bit (The problem sets have been ranging from 12-16 pages...not horribly long but its a good bit of mathematical writing. I always find it funny the largest amount of time is not spent on the proof itself, or the idea, but going back and making the flow alot more coherent....eh it is really a bad habit at this point. I have 3 notebooks on my desk full of random mathematical proofs/ideas and it is incredibly disorganized and cluttered. Previously it had been something that I just do for myself so when attempting to mathematically communicate I often end up assuming everyone follows my thought process completely without taking time to explain fully out of not being accustomed to it. Meh its something I need to and am working on.

I had considered the rational endpoint idea very briefly actually, however at the time (Around 3:30 am) it did not seem like a viable approach for whatever reason.

Thank you for the advice.

ishmaelstrom · 09-19-2006, 10:13 PM

Basically bringing this up; it has some pretty good advice about the interview process. Found it on good 'ol google. Here's the link to Stu Schmill's blog entry on the new blog site: http://www.mitadmissions.org/topics/...ach_your.shtml

Good luck, everyone! My interview is on Thursday. ^^;

_Daniel_ · 09-20-2006, 01:47 AM

http://en.wikipedia.org/wiki/Table_manners

noday42 · 09-20-2006, 03:17 PM

haha.....and the above crazy math posting is one of the many reasons I WANT to go to MIT

though....if we were discussing science instead of math...I would actually be able to participate...maybe

kryptonsa36 · 09-20-2006, 05:59 PM

All righty, then.

My friend's friend was asked on her interview to explain what would happen if she was to fall through a hole bored through the center of the Earth all the way to the opposide side of the world.

Assuming that there is no air resistance and that she would not eventually be burned to a crisp, of course!

(By the way, interviewers arn't going to be displeased or anything if you politely reply that you haven't the slightest inkling of a correct (albeit theoretical) answer.)

tripNip · 09-20-2006, 06:43 PM

She would fall at a decreasing rate of gravitational acceleration proportional to the distance between her and the center of the earth. She would be going really, really fast by the time she reaches the center, at which point in time she would have no gravity acting on her for an instant. Then she would continue at a high speed, through the earth's center and toward the other side, losing speed at an increasing rate proportional to the distance between her and the center of the earth. By the time she reaches the other side, she will come to a rest, and hopefully she will hang on or someone will grab her, or else she will fall back and forth through the center of the earth forever. And oh yeah, she'll be upside down when she comes out the other end.

OutlierLove · 09-20-2006, 07:33 PM

MIT interview question of the day: Show that the union of two proper subgroups of a group cannot be the entire group.

One of my friends was asked this question in his interview. He actually solved it on his first try and the interviewer was impressed...but he still didn't get in.

o0CrazyGlue0o · 09-20-2006, 08:04 PM

My MIT interview is going to be at a library. I guess well just be whispering to each other X-D