Computer Science and Math

At the end of last semester, I decided to double major in computer science and math, rather than just in math. This decision was based on several reasons:

  • Practicality. As much as I love theoretical math, most of it is totally irrelevant to the real world. CS is closely related but far more useful.
  • Opportunity. Cornell has a top-rate CS department, and it would be a shame for me to not take advantage of it. I am virtually done with my math major as well, so it does not cut into that.
  • Expanding my skill set. I think CS is a strong backup in case I didn’t get anywhere with math.

The catch is, being a junior already, I need to rush the major in my remaining 3 semesters (including this one). This will require quite a bit of work, but due to my math major, I have much of the foundation done. I also have every liberal arts distribution requirement out of the way. In addition, during my sophomore year I took CS 2110, so that is another requirement done. My schedule for this semester is below.

2013 Spring Schedule

The most interesting class will be Math 7370, which is Algebraic Number Theory at the graduate level. I have some background in analytic number theory but not in algebraic number theory, so it will be interesting to see the differences. Also, the same professor is teaching 4340 and 7370, so I should have ample opportunity to ask any questions about algebra.

As for CS classes, I hear CS 3410 has a lot of work, but I am prepared. Also, given that I did decently in Combinatorics (Math 4410) last semester, CS 4820 should not be too hard. And given the knowledge from a math major, I doubt 4850 will be that difficult.

In addition, I have planned a more consistent posting schedule for this blog. There won’t necessarily be more posts, but they should be spaced more evenly. Also keep an eye on my math blog—I will continue to update it this year.

When the Snow Finally Returns: Cornell Spring 2012

For many days, the town of Ithaca was enjoying the rare and delicate specimen of winter without the winter. The next day, stuff starts dropping from the sky—hey, it’s pretty cool I guess. And the day after that, the universe as we know it is covered in snow. Such is the schizophrenic weather of this place.

The snow arrives firstly as a reality check. What is more real than snow, diving in swarms into your face and crunching your every step to your classes? Or perhaps, snow serves as the exact opposite. By making the outside world less accessible, less attractive, it has a hibernating effect. You want to stay indoors more and move less, sinking into a false reality. Who knows?

What I do know is that I haven’t blogged in a long time. In fact, it has been a really long time. Here are my thoughts so far on my classes this semester:

  • Math 6120 – Complex Analysis. This is the first math/science class I have ever taken that did not contain absurdly large amounts of review of background knowledge before diving into the course material. There was no review in fact. Granted, this is a graduate level course, and it is the first time I am taking one. It is an incredible change of pace from previous courses.
  • Math 4140 – Honors Intro to Analysis II. Significantly harder than part 1, which I took last semester, but still significantly easier than complex analysis. Then again, this is an undergraduate course, so it was to be expected.
  • German 1220 – Exploring German Contexts II. Also much harder than first-semester German, though this may be due to my rustiness at it since I practiced no German over the break.
  • Astro 1102 – Our Solar System. I’ve always wanted to take an astronomy class, as my interest in this subject stems from first grade. Plus, Cornell has a prominent role in the Mars rover project, so it was interesting hearing the professor talk about his opinions on how the rover mission should continue on the first day of class.
  • Math 4900 – Independent Research. My topic is the relation between thermodynamic formalism and complex dynamics, and my advisor is John Hubbard, who is also teaching the complex analysis class. For a layman description, we are trying to understand how one can use mathematical techniques that were originally developed to analyze fractals, to analyze thermodynamics. This seems like an interesting bridge between math and physics.

So, this is my first semester ever not taking any humanities/social science classes. It is also my first semester ever taking more than one math class. In that respect, this is really the first time since first semester of freshman year that I feel I’m doing something new. In the prior case, it was the nontrivial transition from high school to college. And now, it’s that from a general education to a more focused one. In the meantime, I’ll try to update this blog if anything interesting shows up.

One final bit of news: as of a few days ago, I am officially a math major. Cheers!

Lock Picking, and Solving Problems

Days pass by normally, and often you don’t pause to reflect on them because they’re the same day, the same old routine. The little differences that set your days apart—these start to become annoyances and tidbits, even interruptions in your daily schedule. Until you have a day that is so bizarrely different from the repeated existence that it shakes your foundations of routine to the ground.

Today (or rather, yesterday, since I am passing the midnight mark as I am typing this) was one of those days: it was the day of the Cornell homecoming game, and I suppose attending a sports event was something I had not done for over half a year. But besides that, the intriguing part happened when a fellow trumpet player and I left a bit after half time, only to find the band room locked on all exits.

For the next part, I will let other people remain anonymous, though I doubt the Cornell police are reading this. And if you are, you need not be alarmed as there was neither criminal intent nor damage done.

The person with me is quite good at knowing how things work, so he naturally assembles a makeshift lock-picking set from some handy materials. This includes a trumpet lyre, a Cornell Homecoming pin button, and an iPhone. The iPhone was used solely as a flashlight (this was at nearly 9 pm), the lyre was used as a “torsion wrench,” and the pin from the pin button was used as a pick, i.e. the thing that any lock-picker in a movie uses to poke into the keyhole.

After perhaps 15 minutes of attempts, it is clear that the lock is too sophisticated. He mentions how he could only set the first “tumbler” in place but that the lock had five tumblers. Heck, I didn’t even know those things in locks were called tumblers.

While this was going on, I reflected on the nature of problem solving, and realized that the problems I solve in classes, whether they be physics questions that assume surfaces are frictionless, or math questions that deal with uncountably infinite sets—I realized that such problems didn’t help the slightest bit when I faced this real world problem of a locked door. Even the highest levels of theoretical math and physics wouldn’t help now.

I even joked at how, if this were some action movie, one of us could climb through the ventilation system and pop down inside the room and open it from the inside. Unfortunately, it is an old building and there is not a ventilation shaft to fit into.

That physical locked door in front of me was the ironic manifestation of the hypothetical locked door. Neither my friend nor I had the key. And without the key, there was no getting past it.

I exit the building temporarily to go to the Statler, and on my way out, I see some other familiar band people coming in. I tell them we tried to lock pick the door, and continue walking. When I came back a few minutes later, a remarkable thing had occurred: the door was open! My friend and the other band people were inside, and yet none of us had a key.

It turns out that one of the people I ran into on my way to Statler had done the impossible: he climbed through a ridiculously small opening in the top corner of the room where some utility pipes passed through, and successfully landed and opened the door from the inside. Of course, in the room where we spend so long lock-picking, there just happened to be a ladder.

Cornell Fall 2011

Cornell Tower

It’s been a nice semester so far. The weather is so much better than in Austin, where temperatures are still surpassing 100°, and it feels great not being a freshman—I actually know where things are!  Classes I’m taking:

  • Math 4130 (Honors Introduction to Analysis I): Mostly review so far. It’s only been a week, I’m pretty sure it will get harder as the semester goes on. But I definitely think Math 2230/2240 are great preparation.
  • Phys 1116 (Mechanics and Special Relativity): Also mostly review.
  • Gerst 1210 (Exploring German Contexts I): Intense immersion learning. I feel like I’ve learned more German in the past week than I learned in my first month of Spanish in middle school. This makes perfect sense, since college is quite a step up from middle school.
  • Econ 3010 (Microeconomics): We’re covering some of the underlying theory of economics, which is intrinsically heavy on math. Particularly, a lot of what I learned in Math 2230 last year is coming into use. Having independently studied some game theory over the summer, I found this introduction very interesting; things are clicking already.
  • CS 2110 (Data Structures and Object-Oriented Programming): Almost all review. In yesterday’s section we covered linked lists, which seemed to baffle at least half the group. The 25-hour assignment due next week does not look fun though.

Of course, I am also in the band, which has started up. Once again I am impressed by the speed at which it learns the show. Everyone seems ready for performance after a mere one rehearsal.

My residence for this year is 14 South Avenue, which is on the southwest corner of campus. This is a total change from last year, when I was on the northeast side of campus. The change of perspective is certainly nice.

Here is my schedule from Schedulizer:

My Mirror Behavior

One of the coolest things about college is all the new and fascinating people you meet. This probably has greatly to do with the diversity of American universities. The Cornell freshman class, for instance, has students from every state except Montana. Obviously a pretty important state, right?

It may disappoint you, however, that this article is not about any new or fascinating people who I have met at Cornell, though I certainly know many of them. It is also not about fascinating people whom I have known for a long time in Austin. In fact, this post is about a person who is, for most readers of this blog, neither new nor fascinating.

It is about me.

I noticed the strangest thing yesterday about myself. Well, maybe not strange, but certainly something I hadn’t noticed before. It’s that in any conversation, I act as a mirror. That is, when I chat with someone, I essentially acquire the attributes of that person.

It starts with the topic of the conversation. Yesterday, after my history class, I had the most extended profound discussion with someone, who is also quite a new and fascinating person: Elliot Casparian. It started out when he talked about our class as not learning history but learning about history, that the course was heavy on how history was done, that it was almost like the philosophy of history. We talked for perhaps an hour, including lunch. We ended up covering the following topics (don’t ask me what the transitions were, I don’t remember):

  • History and meta-history
  • The surprisingly advanced state of modern-day technology, including medical, space, electronic, and acoustic
  • The Internet and IPv4 exhaustion
  • Existence and the meaning of life: does it matter?
  • The multiverse, many-worlds, and simulation theories
  • Theoretical physics vs philosophy
  • Knowing and certainty
  • Mathematical proofs and the incompleteness theorem

The underlying thing is that every one of these topics has some philosophical undertone that we brought up in conversation. So unconsciously, we took the initial philosophical topic and ran with it for as far as we could. How this relates the my mirror aspect is that Elliot started the conversation, and I adjusted myself to philosophy right away.

Whether a conversation I have lasts ten seconds or an hour, and whether it is about philosophy, movies, books, computers, or whatever, I seem to always mirror the topic of discussion.

But that isn’t the interesting part.

What’s interesting is that in what I say in a conversation, the mirroring occurs not only in the content, but in the form as well.

I noticed this at first in online chats. If the person I’m chatting with tends to write proper English, i.e., capitalizing the first letter of each sentence and ending sentences with periods, I tend to do the same (thought there are exceptions).

if on the other hand the other person uses a more “normal” internet chat style, i find that i do the same

Also, if the other person uses CAPS a lot, I tend to use it as well, thought it’s usually like LOL, never an ANGRY MESSAGE.

It’s easy to notice online. But I found this occurs in real conversations just as well. For instance, I almost never curse. But if the people around me use profane language, I have a much higher chance of doing so too.

If someone is speaking very dryly and/or using elevated language, I usually do the same. If I am speaking to a person who is very argumentative, I tend to argue as well.

If people are being clever, I try to make witty retorts. If people are making puns, I go on a pun rampage. And of course, if people are being sarcastic, well, I’m already pretty sarcastic, so that makes it even worse (or better, as the case may be).

And there’s a lot more about speech that I can’t quite put into words—you know, all the subtle things that go on in a conversation. So I concluded that in conversation, I’m basically like a mirror.

But wait, there’s more?

I find that my mirror behavior doesn’t end with conversation. It extends to my daily life. And again, it’s a lot of those subtle things that I would normally never notice, that I noticed recently.

If we’re seated, how I sit is largely determined by how other people are sitting. In conversations, my gestures are different depending on whom I’m making gestures to.

My general demeanor is different, as I have found, around different people.


When I started thinking about this mirror behavior, I was alarmed because I had thought of myself as a nonconformist, and, well, doing what other people do isn’t exactly nonconformism. I thought to myself, oh my gosh, am I a robot?

So I began to look for exceptions. I thought of one immediately. In conversation, if the other people are quiet, I tend to be talkative, and when they are talkative, I tend to be quiet. But in those cases, I am consciously making a decision. If they are talking a lot, I feel the need to listen, and if they don’t, then I feel like saying something.

As I reflected further, I saw that exceptions in general were cases in which I was conscious of what I was doing. On the other hand, the cases where I had mirror behavior were the automatic ones.


Does this mean I’m still a nonconformist? Or a lesser one than I thought? Perhaps. But what interested me was whether there was a scientific basis for this. I came across “mirror behavior” in psychology, but that references a different phenomenon. Roughly, that is involved with how individuals behave when put in front of a mirror.

The closest psychology topic that I could find which still contained the word “mirror” was “mirror neuron,” which I had actually encountered before on a Scientific American article (specifically, the cover story of the Nov 2006 issue). I don’t have the magazine with me, but I remember that it linked a lack of mirror neurons to the condition of autism. If you mirror a lot, then do you have more mirror neurons? And does that make you more anti-autistic? I don’t know. Too much mirroring might have its problems too.

One last question: If I mirror other people, and this article is nominally about me, then who is it really about?

Cornell: First Weeks of Semester 2 [Photos]

It has been a good first two weeks back on the snowy hill. I selected some photos to share here.

1. After just stepping outside the east door of Mews Hall.

2. A frozen Beebe Lake and waterfall, shot from the footbridge.

3. A generic-looking lecture hall. The room is Goldwin Smith 132, where my Econ 3020 class is located.

4. An “I ♥ IB” sticker on a post in the southeast corner of the Arts Quad. Funny because I thought it meant International Baccalaureate at first.

5. A closeup of the sticker reveals its true identity.

6. A nice-looking (and postmodern) clock in Alice Cook 106, where my Phil 1112 class is located.

7. The very first thing math professor John Hubbard writes on the blackboard after introductions is “Multiple Integrals.” Math 2240 will be fun!

8. Last picture, demonstrating how fun math can be!

Alright, I still think linguistics is more fun.