My College Experience

Cornell

Yesterday, I took my final final exam. Now, short of receiving a piece of paper, I am done with college and also with the formal education system (for at least the time being).

I’m not a sentimental person, but I am a reflective person, so I feel compelled to write about my experience.

Several other posts already covered various aspects of college and also of Cornell specifically:

There are in total 35 blog posts (as of writing this) under the College category, including the ones listed above. But the most important post comes from before any of these, before even stepping onto the Cornell campus, and it is related not directly to Cornell, but to the University of Chicago, a post on Andrew Abbott’s “The Aims of Education” speech.

Abbott’s main argument is that education is not a means to an end, but the end in itself. He goes through why education is not best viewed as a way to improve financial status, a way to learn a specific skill, a way to improve general life skills, or a way to survive in a changing world. Instead, “The reason for getting an education here—or anywhere else—is that it is better to be educated than not to be. It is better in and of itself.

This philosophical point I carried throughout my college experience. It is why I find it absurd to worry about the GPA of oneself and others so much: you’re here not to beat other people, but to be educated.

There is a lot of interest in the relation between academic study and the real-world job market. One hears jokes about English or psychology majors working in jobs having nothing to gain from an English or psych degree. But my situation is actually similar. As a math major pursuing a theoretical track (originally thinking about academia), I’ve encountered concepts that, at least currently, have no practical application. That’s a blessing and a curse. In the post I wrote about why I chose math, one of the pro points was precisely the abstraction of it. So, even though I will be working in a math-related area, it is almost certain that knowing that normal spaces are regular, or that the alternating group on 5 elements is simple, is useless.

Of course, it does help to know calculus and to have a good understanding of probability. But at least over the summer, we rarely ever used concepts that were outside my high-school understanding of probability or calculus. In other words, I could have majored in English and have been just as qualified.*

*(Perhaps taking many math classes trains you with a certain type of thinking, but this is hard to specify. I haven’t thought too much on this so if anyone has other ideas, please share them.)

Another thing I haven’t really talked about in other posts is socializing. I’m an introvert (INTP), and I could easily spend all day reading thought-provoking books or watching good movies without the slightest urge to unnecessarily talk to another person. I used to ponder this, but after reading Susan Cain’s wonderful book Quiet, I’ve decided to not worry.

Academically, I’ve expanded my horizons a lot since coming to Cornell, though not from math courses. While academia in general can be thought of as an ivory tower of sorts, math (and/or philosophy) is the ivory tower of ivory towers, so it is sometimes refreshing to take a class in a different subject that is only one step removed from reality.

In addition, I managed to keep this blog alive through college, though there was a period of time in late freshman/early sophomore year where there were few posts. By junior year, I was back in a weekly posting routine. And a couple of months ago, I started doing 2 posts per week, and that has been consistent so far.

Finally, I also subscribe to a quote allegedly by Mark Twain: “I have never let my schooling interfere with my education.” Even after college, I will always find opportunities to learn.

Overall, Cornell has been a great experience, and I would definitely recommend it, even if not for the reasons you were looking for. Enjoy, and keep learning!

The Hypercritical Condition?

liberalism-hegemony

Michael Roth, president of Wesleyan University, recently wrote a piece in The New York Times titled “Young Minds in Critical Condition.”

It happens every semester. A student triumphantly points out that Jean-Jacques Rousseau is undermining himself when he claims “the man who reflects is a depraved animal,” or that Ralph Waldo Emerson’s call for self-reliance is in effect a call for reliance on Emerson himself. Trying not to sound too weary, I ask the student to imagine that the authors had already considered these issues.

Instead of trying to find mistakes in the texts, I suggest we take the point of view that our authors created these apparent “contradictions” in order to get readers like us to ponder more interesting questions. How do we think about inequality and learning, for example, or how can we stand on our own feet while being open to inspiration from the world around us? Yes, there’s a certain satisfaction in being critical of our authors, but isn’t it more interesting to put ourselves in a frame of mind to find inspiration in them?

Being a student in the sciences, I don’t experience this kind of humanities phenomenon directly. But this ultra-critical mindset pervades everyday life, at least at an elite university. Students engage in this “intellectual one-upmanship” all the time without even realizing it. Try using Thomas Jefferson in a pro-freedom argument and you get the response that TJ owned slaves, thereby invalidating whatever moral or legal progress he allegedly made; therefore, the takeaway point is that the liberal notion of freedom was built on detestable foundations.

Also from Roth:

Liberal education in America has long been characterized by the intertwining of two traditions: of critical inquiry in pursuit of truth and exuberant performance in pursuit of excellence. In the last half-century, though, emphasis on inquiry has become dominant, and it has often been reduced to the ability to expose error and undermine belief. The inquirer has taken the guise of the sophisticated (often ironic) spectator, rather than the messy participant in continuing experiments or even the reverent beholder of great cultural achievements.

Even for my own blog posts, I sometimes run into critical comments which, instead of saying something substantive, completely miss the main point and belittle some small detail that I had usually already considered and addressed elsewhere in the article. One is powerless to defend against such criticisms, as preemptively placing ample amounts of caveats is no deterrent. It just changes the criticism from “The author does not consider X…” to “The author dismisses X…” followed by a pro-X argument, where X is a counterargument that the author has already considered.

Not that critical comments are bad—they’re quite useful. Constructive criticism is a hundred times more helpful than praise. Perhaps the issue is a self-fulfilling prophecy of blogging: since people don’t expect complex arguments with caveats, they assume that everything you say is absolute, even when that is clearly false. And it is not just in academia or blogging. Go to the comments page of any remotely controversial news story (I really enjoy reading CNN comments), and you can effortlessly predict which arguments and counterarguments are used.

Hilariously, one of the comments perfectly demonstrates the point of the article.

From user “reaylward”:

“Critical” in this context means close or analytical, not disparaging or condemnatory. Thus, a critical reading of a text means a close or analytical reading of the text, not a disparaging or condemnatory reading. The “historical critical method” of interpreting the Christian Bible, for example, means a close or analytical reading of the text, not a disparaging or condemnatory reading. “Critical thinking” doesn’t mean “exposing error”, it means thinking analytically. I think they need a dictionary at Wesleyan. And I mean that in the critical sense.

And a response by “Austin Uhler”:

Your comment is an example of the type of thinking that the author is discouraging. While you are correct about the strict meaning of “critical” in this context, your uncharitable reading means you are missing the author’s point: it is becoming more common for students to take critical thinking down negative, dismissive and unproductive paths.

This is probably the best comment-response pair I have ever seen for a NYT article.

Is the hypercritical condition a legacy of postmodernism? Is it simply a byproduct of the Internet? Are we becoming more cynical? I don’t know.

Being hypercritical is certainly a better problem to have than being uncritical. I appreciated Roth’s article nonetheless, for addressing the overly critical crowd.

On Senior Year

Cornell Tower

I’m a couple of months into my final year of school. This post is a reflection on my senior year so far and the Cornell experience in general.

Differences

Senior year has been quite different from any other year. This is largely due to a more carefree attitude resulting from having post-college employment already lined up. In addition, this is the first semester in which I don’t have to take any distribution requirements, so I get to take whatever I want.

At first glance I seem less incentivized to do work. But in fact, it has made me more productive than ever before. Not having to research companies/grad schools, fill out applications, prepare for interviews, etc. frees up a lot of time. I feel much less stressed than in earlier years, and I feel happier in general. I now have the time for introspection, to put aside the act and think about what I truly care about.

Cornell

Cornell

Even though I am majoring in math, most of the greatest classes I’ve taken were not in the math department. Intro classes in astronomy by Steve Squyres and sociology by Ben Cornwell were very eye-opening. Computing in the Arts (by resident genius Graeme Bailey) was a refreshing multidisciplinary class that truly combined everything together. And in math, the honors intro sequence (2230 & 2240, by Ravi Ramakrishna and John Hubbard respectively) shattered and rebuilt what I thought math was.

But the learning extended far beyond classes. I’ve met some really amazing people here from all over the country (I wanted to say world, but that would be a lie). And of course, the Cornell experience wouldn’t be complete without seeing famous people, whether through lectures, connections, alumni status (Bill Nye), or even pure coincidence (*cough* Bill Murray).

The Future

It feels strange knowing this will be my last year of school. If you count kindergarten as a grade, that’s school for 17 years consecutively, and that could have been more if I were going to grad school. I’ve lived the vast majority of my life in the academic life, and it feels like almost a relief to be headed next year into the real world.

My Spring 2013 Semester (Part 2)

Part 1 can be found here.

I’m finally done with the semester. As I wrote in part 1, this has been my busiest semester at college. Most of the time was spent on one class: CS 3410, or Computer System Organization and Programming. I’ve probably spent twice as much on this class than all of my other classes combined.

On the other hand, I did learn a lot from this course. While I do not regret taking it, this kind of workload does call into question the decision to go for the CS degree. As I wrote before, going for the CS degree will negatively affect my ability to take more advanced math courses. Even this semester, I felt I had almost no time to study math on my own. In my math classes I was pretty much doing the bare minimum so that I would have time to work on CS. Next semester I will most likely be going pure math.

Relatively-Prime-Grid-Points

Anyways, for the summer I have an internship in New York City, with one week in London.

My Spring 2013 Semester

I am sorry for not having posted in a month. My schedule has been busymainly from some heavy projects in computer science courses.

pipelined_processor

For instance, one of our projects was to implement the above with fully functional logic circuits. If anyone is wondering, this diagram outlines the high-level design of a pipelined computer processor. We then wrote some assembly code to run on this processor, specifically to compute the stopping time of the hailstone function.

As a result of the CS workload, I haven’t had much time to do math—my math blog has not been updated since March.

Anyway, this has been my busiest semester yet at Cornell. Now that classes are over, I will get back into a weekly posting schedule.

Stress and GPA-centrism in College

studying

Every time papers, projects, and prelims come around, the campus stress level rises dramatically. Sleep is lost (or outright skipped), meals are avoided, and all activities other than studying are brushed off. This happens not once a semester but throughout, corresponding to large assignments for every class.

And every time this happens, it seems that many students are focused not on actually learning the content, but on scoring higher grades than others. Of course, this phenomenon occurs in certain majors (engineering) much more than others. And I would guess that it happens at Cornell at an above average rate compared to that of the typical university. But it raises some questions that I want to explore.

Just a couple of notes. First, this article will mainly focus on the math/science/engineering side. And second, I do not think I need to mention why Cornell should be concerned about student stress.

Should Competition Be GPA-Focused?

Competition to a certain degree is beneficial, and I think no one would argue with that. As a math major I know very well that competition leads to efficiency. But there is a line where the marginal benefit in efficiency is not worth the huge increase in stress levels, and in this respect I think Cornell has crossed the line for good.

In addition to the GPA competition, there is the additional factor that students are competing for jobs, internships, and research positions. I think the competition here is mostly fine (except regarding salaries vs societal contribution; this topic deserves its own post). Combined with academic competition, however, this induces a vast amount of anxiety and stress in the students.

Without mentioning names, I will list some of the extreme behaviors I have observed of people I know:

  • A student pulled multiple all-nighters in a row to finish a project. While this might be plausible in real life for a rare occasion such as a doctoral thesis or a billion dollar merger, the student did this regularly for his classes.
  • A student has problem sets due on four out of five of the weekdays, and spends literally all his time outside of class eating, sleeping, or doing problem sets. In one particular class, the problem sets he hands in are 10-20 pages per week.
  • A student took 50+ credits in one semester, though he claims to know of someone who took 61.
  • A student brought a sleeping bag, refrigerator, and energy drinks to one of the school computer labs, and pretty much lives there, returning to his living place once every few days to shower.

Interestingly enough, I think these particular students will do fine, as they seem to know their own abilities and limits, and more importantly, they are all aware of what they are doing. They are also all very smart people who can actually learn the material. This “top tier” of students is not really adversely affected by competition, since they are smart enough to excel regardless of whether competition exists. Moreover, these students don’t seem to be grade-focused: they learn the material, and the grade comes as a byproduct of learning.

The group I am actually concerned about is the second tier. (Note: I just realized after typing this how judgmental that statement sounds, but hey, from statistics, unless you define the first tier to include everyone, there must be a second tier.) This group I would define to be the smart people who don’t seem to understand how the first tier operates. They see the students in the first tier getting high grades and know those students are smart, so they think that if they prepare the tests well and get high grades, they will become as smart.

What they don’t realize is the difference in cause and effect. The first tier prioritizes understanding first and the grades come as a byproduct, whereas the second tier prioritizes grades first and hope to gain some understanding as a byproduct.

Again, just as a disclaimer, these are just arbitrary definitions for first and second tier I made up for this particular observation. I am not saying that this criterion is the final say, and of course, there are numerous other factors regarding how well one does in college.

But from my experience, it is precisely the students in this second tier who are stressed. They are the ones trying so desperately to beat the test instead of to learn the material. And they are the ones who make college seem so competitive, as you can always hear them talking about tests and what their friends got on the tests and how they are being graded and what the format of the test will be.

On the other hand, the student I mentioned above who lives de facto in one of Cornell’s computer labs—I have not once heard him talk about anything specifically regarding a test.  The closest was talking about the material that was to be covered, but he was talking about stuff that was beyond what the class taught for the topic, stuff that he knew was not going to be on the test.

Some of you might be thinking, “That’s great, but what kind of job is he going to get if he is not grade-focused?” Good question. After working there for a summer internship, this same friend rejected a return offer from Goldman Sachs.

How to Break from GPA-centrism

I am not worried about this person’s career at all. I am worried about the second tier, the smart people doing mundane tasks, wasting a lot of potential creative brainpower that the world needs more than ever. Renewable energy, bioengineering, artificial intelligence, space exploration and colonization, nanotechnology—there are so many people here who would be excellent for these fields, yet many of them seem too bogged down by current competition-induced stress to even think into the future.

Indeed, this GPA competition is a force to be reckoned with, as it really is self perpetuating. Those students in other groups or who are apathetic to grades will tend to become more grade focused just from sitting in lecture, as there are always people who ask for as much details of the test as possible. I feel that this defeats the purpose of a test, which is to measure how well you know the material or how well you can apply a certain skill, not how much of the test structure you can memorize or how much content can you cram the night before.

Overall though, there are some measures that can be taken to reduce this kind of stress.

  • Reduce the importance of the GPA. I do not know if I would go so far as to remove it, though. For example, at Brown University, the GPA is not calculated. Somewhere in the middle ground should be best.
  • Stop showing score distributions, or show them only for major tests like a midterm/final. In many engineering classes at Cornell, the first thing that is requested after a test is graded is to see the score distribution (often in graph form), along with the mean, median, standard deviation, etc. In fact, this has become so common that it is now the first thing the professors put on their lecture slides. Moreover, the computer science department uses an online course management system which automatically tells students the mean, median, standard deviation, etc. for every single assignment, not just tests. Being a math major who would normally love extra statistics, I thought this was cool at first. But now I despise it—it is just too much information that I don’t need in order to learn the material, and it only detracts from my learning experience. And the way the page is setup, it is not something you can just ignore.
    • A side note: One of my classes in the CS department actually does not list grades, and I definitely feel more pressured to actually learn in that class, not more pressured to beat other people at grades like in other CS classes. Props to Professor John Hopcroft.
  • Teach better math/science/engineering/CS much earlier in the education system. A friend showed me this article today, a comparison between the CS education systems of the US and Vietnam, a comparison that is horrific for the US. If students already knew the foundations, then college would be what it was supposed to be: going really deep into a topic in a learning atmosphere, not treating us like elementary school children because, well, frankly that’s the level of engineering/CS of many college entrants. For instance, I think it’s great that students are trying to take Calculus 1 freshman year and then do engineering. Hard work is certainly a virtue. But wouldn’t it be much better for both the student and the college if they mastered calculus in high school? Imagine how much better our engineers would be.

What I envision is a class where students are trying to learn, not to beat each other on a test. I hope this vision is not too far-fetched.

Math or Computer Science?

Well this is an interesting situation. Just a month ago I announced that I was adding a computer science degree, so that I am now double majoring in math and computer science. The title of the post, after all, is “Computer Science AND Math.” Given the circumstances at that time, I think it was a good decision. My work experience had been mostly in software, and a CS degree from Cornell should look pretty good. In addition, I was wanting a more practical skillset.

decisions-2

In the past week, however, things have changed. I received and accepted an internship offer from my dream workplace, based on my background in mathematics and not in CS (though my prior CS experience was a plus). Based on this new situation, I have considered dropping the CS major (next semester) and taking more advanced math:

  • The CS degree has some strict course requirements, and I am afraid that if I go for the degree, I may be forced to skip certain math classes that I really want to take. For instance, I may have to take a required CS class next semester that has a time conflict with graduate Dynamical Systems, or with Combinatorics II. And given that I am currently a second-semester junior, I don’t have that much time left at college.
  • Even this semester, I am taking Algorithms, which meets at the same time as graduate Algebraic Topology. While Algorithms is pretty interesting and the professor is excellent, I am already very familiar with many if not most of the algorithms, extremely familiar with the methods of proof, and I feel that the experience is not as rewarding as possibly taking Algebraic Topology with Allen Hatcher, who wrote the textbook on the subject. I feel that I could learn algorithms at virtually any time I want. But learning algebraic topology with Allen Hatcher is a once-in-a-lifetime opportunity that I am afraid I am missing just because I want to get a CS degree to look good.
  • Even not being a CS major, I will still be taking some CS classes out of curiosity. However, these classes will no longer feel forced, and will not restrict me from taking the higher level math courses that I want to take.
  • My risk strategy for grad school is different now because of the internship. In the past, I would have been willing to take a decent grad school in math or really good job. (I would prefer grad school over getting a job, but of course, a good job is better than a mediocre grad school.) However, now that I have my dream internship, I am willing to play the grad school game with more risk.
  • But whether for grad school, trading, or just for curiosity, I would prefer taking advanced (graduate) math classes over undergraduate CS classes. In a sense, my taking of the CS degree was a hedge bet, as I wanted to reduce the possible cost of the worst case scenario. I knew that it would directly inhibit my ability to take advanced math classes via class time conflicts, but the thought was that if I couldn’t get into a good math grad school or get a good job using math, at least I would have a CS degree from Cornell. But, in this new situation, I think the risk is significantly reduced and the hedge is no longer necessary.

Interestingly enough, the primary motivation for dropping CS wouldn’t be to slack off, but to be able to explore more advanced math. (At least, that’s what I tell myself.)

I think this might be the second time in my life where I have had to make an important decision. (The first time was deciding where to go to college, and I certainly think I made the right choice there.) Unfortunately, I really can’t be both taking as many interesting math courses as I can, and at the same time be pursuing a CS degree. As much overlap as there is, I can’t do both. In an ideal world this might be possible, but not currently at Cornell.

So instead of the idea of having math and computer science, I am now having to think in terms of math or computer science. I am currently in favor of going with math, but I am not completely sure.

Edit: Thanks for the discussion on Facebook.