Tuesday, August 27, 2013

Heading back to Harvard!

I've been at home for the past two weeks after having spent the summer doing math research in Duluth, MN.  I had a fantastic time, though I'm ready to head back to school and tackle my senior year!

Here are the courses I'm thinking of taking next semester.

Math 18.315 (at MIT) -- Combinatorial Theory
Math 213a -- Complex Analysis
Math 232a -- Introduction to Algebraic Geometry I
Computer Science 121 -- Introduction to the Theory of Computation

I'll likely pick three, which seems like plenty when combined with a senior thesis and graduate school applications.

Monday, June 24, 2013

Life Update: Senior Year at Harvard, Duluth REU

I realize that I haven't written in a while.  Sorry about this!  Here's a quick update about my mathematical adventures.  Hopefully I'll be better about posting here more often.

In the fall I will start my fourth year as a math concentrator at Harvard.  I hope to write a senior thesis (though I don't have a topic or an advisor yet... a mounting source of stress in my life right now), so it's reasonably safe to say that this blog will soon become a place to vent my frustration and describe my progress.

This past year I took the undergraduate number theory sequence, the graduate algebraic topology sequence, and a course on Lie algebras.  I still don't know what I want to study long-term, but I'm leaning towards number theory for my thesis.  I still miss my Budapest days of combinatorics and graph theory, so I'm thinking about taking some courses at MIT next semester.  We'll see!

I am currently writing from Duluth, Minnesota, where I'm participating in an REU.  Hopefully this means that I will finally understand what math research is all about.  This program is supposed to imitate the process of writing a thesis; we each set our own hours to work on our own research problems, meeting with advisors as often as we feel is necessary.  Once a week we give 15 minute talks to the students and advisors in the program.  It has been a totally different experience for me, and I think I will get a lot out of it.

We do weekly write-ups of our progress, but I'll probably write up a shortened version for this blog.

Wednesday, July 6, 2011

Go Fish!

I always thought that Go Fish was a silly game. Maybe alright for summer camp in the 4th grade, but certainly not something anyone over the age of 12 should bother with.

That was, until we tried playing Go Fish with a set deck.

Hopefully you already know what Set is. If you're into pattern recognition and some friendly competition (or not-so-friendly, if you're playing with some intense mathematicians), I'd recommend picking up a deck.

Here is the basic idea. You have a deck of 81 cards. Each card has four characteristics associated with it: color, number, shading, and shape. See above image to see what I mean. 12 cards are dealt out, and everyone who's playing tries to find a "set" as quickly as possible. A set is 3 cards which, for each of the four characteristics, are either all different or all the same.

Anyways, it's pretty fun. Lots of yelling and hands slamming down on the table. But after playing a couple rounds last weekend, three of us decided that we'd rather play some normal cards. But we didn't have a normal deck. That's when we decided to play Go Fish with our Set deck.

Instead of asking asking someone "do you have any 4's?" we would say, "do you have a green, single, shaded oval?" And of course, while in normal Go Fish you try to get 4-of-a-kinds, in our game you try to make sets.

We realized pretty quickly that asking for specific cards was making for a pretty slow (read: boring) game, so we instead revert to specifying only 3 of the 4 characteristics, and asking all players, instead of just one.

The beginning of the game was pretty boring. You look at your cards, pick two, determine the (unique) card which would complete the set, and specify three characteristics which belong to this card. I suppose you could get fancy and try to make it so that these characteristics describe two (or even three!) cards which would give you a set, but I don't think any of us were that intense about it.

By the middle (/end), it was a nightmare. No one wants to try to mentally organize 60+ Set cards. Our brains definitely needed a little time to recuperate after that. Angie, Kevin and I decided: never again.

Friday, June 17, 2011

When I'm not working...

"Taimanov arrived with a full Russian entourage: a second, an assistant, and a match manager, but even with all the help, he was, nevertheless, helpless. Bobby defeated him in six straight games, the first shutout of a grandmaster in chess history.

"The crushing loss virtually ended Taimanov's chess career. The Soviet government considered it a national embarrassment and punished him for not drawing at least one game. Officials canceled his salary and forbade him to travel overseas. At the conclusion of the match, Taimanov had sadly told Fischer: 'Well, I still have my music.' "

This book is fantastic.

Tuesday, May 31, 2011

Harard academics, take two.

I guess I haven't updated this in a while! Nothing much to say, I guess. I survived freshman year (barely... I still don't know how I found the energy to spend 33 solid hours on the Math 55 take-home final exam). Finals were in mid May, and I got a week-long break before starting my summer job. I'm now in Maryland, and the weather is miserably hot. East coast people: how do you stand it?!

Anyways, the Harvard course catalog was just released and I'm thrilled to find that the math/cs classes that I had wanted to take don't conflict with each other:

Math 131. Topology I: Topological Spaces and the Fundamental Group (MWF 10am-11am)
Math 114. Analysis II: Measure, Integration and Banach Spaces (MWF 11am-12pm)
Computer Science 50. Introduction to Computer Science I (MW 1pm-2:30pm)

Now for my fourth course, I'm deciding between:

Aesthetic and Interpretive Understanding 24. First Nights: Five Performance Premieres (TTh 11am-12pm)
Culture and Belief 37. The Romance: From Jane Austen to Chick Lit (MW 12pm-1pm)

I've heard good things about First Nights, and it would be nice to take a class that's related to music for a change. But even more than taking a music class, I really want to take a class that assigns some fun literature. This is where Chick Lit comes in. I read the reading list and concluded that I HAD to take this class (Pride and Prejudice, Jane Eyre, Wuthering Heights, Rebecca, Wide Sargasso Sea, Bridget Jones’s Diary... are you pump-cited or what?!). Unfortunately, it really messes with my schedule. I'd then have class from 10am to 2:30pm on Mondays and Wednesdays, and no class on Tuesdays and Thursdays. But I'm definitely considering it!

I don't think I'll be taking an easy load, but with 55 out of the mix, things should be much more manageable.

Sunday, February 27, 2011

Probability and Midterms

My USW 26 midterm is on Wednesday. One part of it will be an "identification of terms" section. I'll be provided with 7 terms, of which I will have to choose 5 to identify and elaborate on.

The professor has provided us with a list of 44 terms, from which she will choose the 7 that will appear on the midterm

Here is where the math comes in: how many terms do I have to study to have a reasonably good chance of recognizing at least 5 of the terms which appear on the test?

I'm so excited by this problem not because it's particularly tricky or elegant, but because it is the kind of thing we're looking at in my Probability class at the moment. And because the answer will tell me how lazy I'm allowed to be while studying.

Anyways, here we go:

Suppose I learn x terms. Then we need to add up the probability that I recognize exactly 5, exactly 6, and exactly 7 of the terms presented on the test. Let p5, p6, and p7, respectively, represent these quantities.

The number of ways of choosing 7 terms such that I studied exactly 5 of them is just "x choose 5" times "44-x choose 2". The total number of ways of choosing 7 terms out of 44 is "44 choose 7".

So p5= ("x choose 5" times "44-x choose 2")/("44 choose 7")

You calculate p6 and p7 using a similar method. The binomial coefficients are going to get messy if I try to type them out, so I'll get out my paper and pen (or, if I'm being totally honest here, I'm just going to type this all into Wolfram Alpha) and report back.

The result: in order to be 90% sure of knowing at least 5 of the terms on the test, I need to study at least 36 of the 44 terms on the study sheet.

Guess I should get studying.

Tuesday, February 1, 2011

Study study study

My schedule this semester:

Math 55b: Honors Real and Complex Analysis
Math 154: Probability Theory
Astronomy 16: Stellar and Planetary Astronomy
US in the World 26: Sex and the Citizen

Maybe I'm masochistic for continuing with 55 (and now, I'm pleased to say, I am officially the stupidest person still left in the class), but it's kind of a point of pride that I finish it. I think the rest of my classes should be easy enough to provide some sort of balance, though I don't know if "balance" is actually feasible with 55 still in the mix. I suppose we'll see.

We switched rooms, so now I'm in a double which also means that my desk and work-space is in the common room. I've been having trouble studying and problem-setting due to noise (it's amazing how much sound travels in dorms), so I recently purchased industrial strength ear protectors. So now I get to be even geekier when I do my math :)

I think it's time for some quality homework-ing before dinner. Sziasztok!