Posted by: scott | March 3, 2011

Shifting toward equilibrium

It’s been about 6 months since I moved to Texas, and during this time, I’ve naturally thought about how my new surroundings have influenced me. For one thing, I’ve been noticeably sleeping a lot more ever since I came here, and in fact tonight has been the first night in which I’ve stayed up until 4:30am working (which is what spurred me to jot down my thoughts). This used to be almost a daily habit when I was in college, where I would spend almost every waking minute either in class or in the library. Nowadays, I stop and chat with other students about random math topics, I go to the gym, and I even just hang out with other people for fun every now and then. In short, I’ve gotten lazier (although to be fair, it hasn’t necessarily been the case that my productivity has diminished — math is weird like that).

So as I was walking back home, I couldn’t help but stop and try to conceptualize just how much I had changed. Moreover, this also led to the realization of just how different of an environment I am in now. For instance, walking back to my apartment in New York at 4 to 5 in the morning, I would often see cabs driving on the street, and people getting ready to open up their stores on the street. In Texas, it seems like even the drifters disappear after 1 or 2 AM, and don’t appear again until almost noon (unlike the bums on W. 4th and Broadway).

So on one hand, I have clearly been molded into a more relaxed and less work-intense state of mind, and at the same time, I still see myself sticking out in an unfamiliar habitat. Not that this isn’t what you’d expect to happen. It just makes you wonder what the equilibrium is ultimately going to be, and if it’ll be somewhere better or worse than where you are now and where you’ve been before. In the spirit of basic economic theory, I (naively) hope that equilibrium lies in the direction of progress.

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Posted by: scott | July 28, 2010

back in the day

I cleaned out my room a couple of weeks ago and came across a note inside a folder that I used when I was in middle school.

From my 8th grade science teacher:
“Scott: It has been a pleasure to have you in my class this year. You will be receiving my 4th MP award for highest GPA of the year in my class. Continue to work hard but remember to have fun! Good look in JPS.”

While I don’t recall particularly liking this teacher or learning a lot in her class, that part in her message about needing to remember to have fun seems like something that has carried with me over the years.

It has been almost over 8 years now since that note was written, and while I’ve been far away from receiving the highest marks in any class that I’ve taken these days, I feel like people still tell me to try and have more fun in my life. It’s pretty unfortunate that only the bad part of that teacher’s message has withstood the test of time.

Hopefully things will flip around in the future. Let’s check back after the next 8 years.

Posted by: scott | July 18, 2010

sojourn to seattle

Having just returned from a three week summer program in mathematics in Seattle, I came back with a couple of thoughts in my mind:

First of all, I want to thank my jedi master for encouraging me to apply to this program, and for helping me with my application. Without him, I surely wouldn’t have been able to take advantage of this tremendous opportunity.

It was my first encounter with a program of this flavor — where an assortment of undergraduate and graduate students from all around the world are brought together and are introduced to a specific subfield and select topics in mathematics — and I definitely can say that I learned a lot, not only pertaining to mathematics, but relating to different people and new environments as well.

I met a lot of interesting people — some were 3rd year graduate students, others were international students from Europe, and there were also few recent undergraduates who, like me, will soon dip their feet into graduate school. I was greatly exposed to the different cultures and perspectives of these people coming from around the world, and I can honestly say now that students of mathematics are as diverse and eclectic a group of individuals as any other field imaginable. We are all nerds, for sure, but nerds can certainly come in very different flavors.

With regard to the mathematical lessons, I have to say that aside from the direct academic material and knowledge I acquired, I came out of this experience re-instilled with two concrete thoughts: 1) a sense of awe at the level of knowledge that professors and even graduate students hold in this field and 2) a feeling of enthusiasm for studying mathematics and trying to attain that level of mastery.

The chance to do so is rapidly approaching.

Posted by: scott | May 29, 2010

mornings in new york

My favorite time of day in New York is the early morning. If you ever walk along the streets at around 6am, you can feel a sense of peace and solitude that you don’t usually get. There’s no heavy traffic, no sounds of screeching brakes and honking taxis, and no trying to squeeze into a subway with dozens of other people pushing and shoving one another around.

And yet, in the city that never sleeps, nothing is ever completely desolate. You still see the occasional person on the street, perhaps power washing the sidewalk in front of his store, possibly transporting an early truckload of goods into a store, or maybe just heading towards the subway to get an early start on work. There are people in suits heading to Wall Street, and there are people in t-shirts, jeans, and an apron setting up the day’s supply of fresh fish in Chinatown.

No matter who or what, though, you get this nice sense that even though each person around you might have a different story and be about doing a different task, everyone is working hard, trying to make a living for themselves, and trying to achieve for themselves what some people might call the “American dream”.

After all, why else would anyone be awake at 6 in the morning?

Posted by: scott | May 29, 2010

decisions and flight

For those of you who know me personally, you probably know that I have spent the a significant portion of my senior year in college deciding on whether I wanted to pursue a future in investment banking or as a [math] PhD student after graduation. I thought it might be interesting to point out that one of my close friends was very incredulous about the fact that I would be faced with such a decision because the two fields are inherently different.

The common perception of investment banking is that it is a very boring job that requires extremely long monotonous hours but pays pretty well. The common perception of being a PhD student is that you are at working at the forefront of a particular field, trying to solve and explore unknown questions, and yet you get paid just enough to not be a starving homeless person (although one of the two might have to give way).

So why would someone ever be at crossroads with two so seemingly disjoint paths?

I think it’s because I could see myself being satisfied down either road with everything that I would potentially grasp and get a hold of.

If I were to work in investment banking, I would have a relatively stable job, make a decent salary, and be able to marry and support a family by the time I’m in my early thirties. I would also potentially have enough money to accomplish some of the philanthropic and social goals that I have my eyes set on before I get too old. On the other hand, if I were to become a PhD student, I would be able to learn a lot of the math and science that I am regrettably still deficient in, work on some very interesting problems with some of the most brilliant academics in the world, and hopefully gain a much better understanding of how many things work in both theory and life. I would also have the opportunity to either work in a research lab/university or to go back into finance in a more lucrative investing-type role. In the latter capacity, I would also potentially be able to make enough money to support a family and hopefully carry out my philanthropic ideals. One option is probably safer and the other is arguably more interesting.

But I struggle to say that either is better than the other. Channeling the inner economist in me (I apologize in advance for the nerdiness that is about to ensue), isn’t life is all about trade-offs? I guess that both scenarios just lie on the same indifference curve that I have, albeit near different ends. I (perhaps ignorantly) feel like the important thing is pick one of these paths and fly into it at full speed and with no regrets. After all, to quote Lady Macbeth, “what’s done, is done” and “what’s done cannot be undone” right?

Posted by: scott | April 16, 2010

dean henry

Maybe it’s the fact that the school year is coming to an end, or that the fact that I’m just coincidentally stumbling upon these sort of events, but a week or two ago, I had the opportunity to listen to another distinguished individual at NYU, the recently appointed new dean of Stern, Dean Peter Blair Henry.

Dean Henry was appointed the dean of Stern this past fall, and previously, served as an economics professor at Stanford University. A couple of interesting points about him include the fact that he was an immigrant from Jamaica (in January of 1972 if I remember correctly), that he was a wide receiver at the University of North Carolina, and that he was a Rhodes Scholar, earning a B.A. in mathematics at Oxford before getting his PhD in economics at MIT.

During his speech, Dean Henry expressed that his immediate goals for Stern were to increase alumni support and to expand the school’s global presence. One point that stuck out in his talk was that he mentioned how NYU Stern is the only school that he would have wanted to be the dean of. It’s always difficult to tell at talks like these how much of one’s speech is true and how much is sensationalism, but the reasons that he gave for saying that was that Stern was one of the few business schools with a strong undergraduate presence (many business schools do not have undergraduate programs) and that he was really enamored by the NYU experience. Having come to NYC from Jamaica when he was still fairly young, he felt like he himself could relate to the typical NYU student and the typical New Yorker. I found the relation between that comment and some of the statements that President Sexton made about NYU’s distinct personality to be pretty interesting.

On a somewhat different note, a question popped into my head during Dean Henry’s talk. Dean Henry was an economist by profession (a macroeconomist to be exact). Our previous Dean, Professor Thomas Cooley, was also an economist. Naturally, one starts to wonder if economics represents the most fitting academic area for running a business school. And even further, one asks which is the most fitting department to run a university. I can definitely see the rationale behind why economists would be good administrators, and another field that comes to mind when considering this question is definitely law. People who are trained to think analytically in a social context and to digest complicated pieces of information and come up with an overarching thought would logically be fit to handle the many intricate parts that must be managed in running a school or university. At the same time, the example of Professor Larry Summers and his infamous comment about the inferiority of women show that critical thinking must also be matched with tact when you’re the face of a public institution. Given that Larry Summers is still an economist and somewhat trained in a “social science,” one can only wonder how a mathematician would fare in running a university.

There was one last thing that happened at this event that really piqued my curiosity. It should be noted that Dean Henry was speaking at a Stern Inter-Club Council meeting (though open to the entire student body), and because of this, one of my friends, knowing that I wasn’t an officer of any Stern club, looked at me incredulously and asked me what I was doing at the event — almost as if the only reason he was there was because he was required to be. This made me start to wonder if all the other students in the room were there simply because they had to be. Was it really so out of place to want to listen to the dean of your school give a talk? Those people who know me know that I am not someone who is particularly bubbling with school spirit nor am I someone who is particularly fond of chosen institution. Yet, for some reason reason, I still felt a need to listen and learn about what will become of Stern when I graduate, and I thought that it was not only a nice but a necessary opportunity to hear the dean speak about the future of my school. That’s how you know whether or not things will improve.

Posted by: scott | April 3, 2010

continuity and boundedness of linear functionals

So a couple of days ago, a Jedi Master gave me a pretty straightforward problem to look at:

[({|f(x)| : ||x||=1} is bdd) \Leftrightarrow (f: X \to R is continuous)]

And after thinking about it for a while, I came up with the following rationale:

[({|f(x)| : ||x||=1} is bdd) \Rightarrow (f: X \to R is continuous)]

Suppose {|f(x)| : ||x||=1} is bdd. In other words, \exists M s.t. {|f(x)| : ||x||=1} \leq M < \infty .

Given \epsilon > 0, y \in X, choose z s.t. y-z=x. Then ||y-z||=1 and we know that an M exists.

Also, we know that for N \in R, \frac{||y-z||}{N} = 1/N, which gives us |f((y-z)/N)| = |(1/N)f(y-z)| = |(1/N)(f(y)-f(z))| \leq M/N \to 0 as N \to \infty .

Thus, choosing N s.t. M/N < \epsilon , we have that ||(y-z)/N|| = 1/N \Rightarrow ||f(y-z)/N|| \leq M/N. Notice that any N_1 > N also suffices for our inequality, since N_1 > N \Rightarrow M/N_1 < M/N. Thus ||y-z|| \leq 1/N \Rightarrow ||f(y)-f(z)|| \leq M/N < \epsilon .

[(f: X \to R is continuous) \Rightarrow ({|f(x)| : ||x||=1} is bdd)]

Suppose f: X \to R is continuous. Then we know that given \epsilon > 0, y \in X, \exists \delta > 0 s.t. ||y-z|| < \delta \Rightarrow |f(y)-f(z)| = |f(y-z)| < \epsilon .

For this fixed \delta , choose \delta_1 s.t. \delta_1 < \delta .

Then |f((y-z)/\delta_1 )| = |(1/\delta_1)f(y-z)| < \epsilon /\delta_1 and ||(y-z)/\delta_1 || = (1/\delta_1 )||y-z|| < \delta /\delta_1 , any vector x = (y-z)/\delta_1 s.t. ||x|| = ||(y-z)/\delta_1 || = 1 still gives us our bound |f((y-z)/\delta_1 )| < \epsilon / \delta_1 .

Said Jedi Master then responded by telling me that one can rewrite the first part as follows:

Let M be s.t. \forall x with ||x||=1, |f(x)| \leq M. Given \epsilon > 0, y \in X, choose \delta = \epsilon /M.

If ||z-y|| \leq \delta then |f(z)-f(y)| = |f(z-y)| = ||z-y|| |f((z-y)/||z-y||)| \leq \delta M = \epsilon , where we know that |F((z-y)/||z-y||)| \leq M because |F((z-y)/||z-y||)| = |F((z-y)/||z-y||)|, and ||((z-y)/||z-y||)|| = 1.

By the method applied, this actually also proves that f is uniformly continuous.

Using the exact same idea, the second part of the proof can be simplified to:

Suppose \forall \epsilon > 0, y \in X, \exists \delta > 0 s.t. ||y-z|| < \delta \Rightarrow |f(y)-f(z)| = |f(y-z)| < \epsilon .

Then |f(y-z)| = ||y-z|| \frac{|f(y-z)|}{||y-z||} = ||y-z|| |f((y-z)/||y-z||)| < \epsilon
\Rightarrow |f((y-z)/||y-z||)| < \epsilon /||y-z|| \leq \epsilon /\delta.

I guess that’s why he’s a Jedi Master, and I’m just Scott.

Posted by: scott | April 2, 2010

playing a different octave

I had the rare opportunity to have dinner with NYU President John Sexton today (along with about 25 other students), and I have to admit that it was a surprisingly enjoyable time. From the stories that he told, I gather that he must be about 68 years old now, and it seems like he’s really had an adventurous and fulfilling life. From the time he was in a Catholic high school in Brooklyn in the 1950’s, to dropping out of Fordham College to coach a girl’s high school debate team to 5 national championships funded on his own dime, to earning a PhD in religion and becoming the chair of the department, to meeting his wife at Harvard Law School, to becoming the Dean of the law school at NYU, to finally becoming the president of the university in 2001, it seemed like he has done the sort of crazy things that you imagine hearing from Huck Finn and not a university president (sorry about the run-on).

And yet, hearing all of his eclectic adventures only further convinced me of his ability to run the school and have the best interests of the university in his mind, which is interesting because it’s in despite of the fact that I disagreed with many of his actual ideas and decisions on how to run and organize NYU. I think that my affirmation really stemmed from two things: 1) the amount he seemed to care about the students, faculty, and constituents of the university and 2) his willingness and ability to try and execute new things. The fact that the first thing he did upon becoming president was look for an image and identity of the school, which ended up in the discovery of Albert Gallatin’s 1831 letter of intent on creating a university “in and of the city” really says something about his character. I feel like having the right values in your heart and possessing the confidence and conviction to abide by them is really the majority of the battle, and I’m glad that the president of my soon to be alma mater has both of those — not so much for me, but for the future generations to come.

The title of this post comes from one of the main lessons that he tried to convey to us during the dinner. Playing a different octave represents looking for and trying something new in life. While not really a novel idea and certainly one that you hear a lot of the time, I felt like it really summed up both the decisions that he made in his life and also his vision of NYU. Also, at least in my point of view, I feel like that mentality has really carried him well in his life and for the school. So kudos to him for the nice metaphor.

On a different note, I also had the unexpected pleasure of talking to a fellow student that I hadn’t really spoken to throughout college but definitely saw around from time to time. I think it’s one of those things where you are put into an new and uncomfortable situation and you immediately latch on the thing you are most familiar with. In any case, it was really nice talking to this person, finding out what she had been doing the past few years and also what her future plans are. It’s kind of wild how college is ending so soon and yet I’m still meeting people now that I wish knew better and had been in touch with before. I guess it’s just validation of the idea that you should really cast a wide net, reach out, and talk to as many people as you can.

Posted by: scott | April 2, 2010

experimentation

I started this blog not really with any particular goal in mind, but just because I thought it might be something interesting to do. I’ve been reading a lot of blogs in the past couple of months (some written by friends, some written by economists, and many regarding mathematics), and I guess it just struck me as something that perhaps I should try to do as well — purely as an experiment and without any timeline in mind.

I think two minor results that I hope might be able to accomplish will be that 1) I learn more about myself in writing stuff down and thus naturally elaborating on my thoughts and 2) I can record and keep track of the multitude of thoughts that seem to be overflowing my minds these days.  I often feel like an idea or thought pops into my head that I hope I will remember, only to be forgotten later on because so many other things happen in the interim.

The title of this blog, entitled “scott still doesn’t know,” is a play-on of the song in EuropTrip “Scottie doesn’t know”, of which I have been the target of many a joke (although I admit that I am too prideful to use the name scottie). It’s also meant to represent many of the things in life that I’m still clueless about and hopefully will be able to learn and share with you as time goes along. So here’s to the new adventure…

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