Taking a Class After 3 Years of Full-Time Research

This spring semester, I'm taking a class; as the title explains, this is the first class I've taken in 3 years, during which time I've engaged in full-time research as a graduate student and have been a TA for 3 semesters. This class is in a very different field from my current area of research, as I'm exploring other fields for opportunities after graduation. After 2 weeks of class, I've been considering how taking a class now feels different than it did in high school, college, and the first two years of graduate school.

In high school and college, my main focus was on classes, and I wanted to make sure that I challenged myself as much as I felt I could and got good grades in those classes. This mentality stayed with me through the first two years of graduate school, which is why I felt like I could do pretty well in graduate classes but had a harder time initially finding my footing in research while I remained mentally so focused on classes above all else. I felt quite relieved when I finished my course requirements 3 years ago so that I could renew my focus on research. Since then, I do feel like I've been able to establish a pretty good track record with my research, and given that I'm approaching the end of the PhD program and want to explore other fields, I am comfortable taking this class with fresh eyes and without worrying about grades; in particular, I can really feel like I'm taking this class purely to satisfy my own curiosity and am willing to accept that I'll get out of it exactly what I put into it. Moreover, for the classes I took until 3 years ago, I was fairly engaged with the instructor during lectures, frequently asking questions whether for clarification or edification; now, especially because the others in my class are all undergraduate students, I feel more comfortable letting them take the reins with their own education, and will only ask questions about points that I feel need urgent clarification.

Having been a TA for 3 semesters, I now have a much greater appreciation for the amount of work even instructors whose lectures are of average quality have to do with respect to preparation and delivery of a lecture, fielding questions from students during and outside of class, and grading assignments. Concomitant with that, I especially appreciate the instructors from my past who were particularly good at clearly communicating concepts in the class to as many people in the class as possible in an engaging way, and realize that I was truly lucky to have had so many great class instructors in high school, college, and graduate school. At the same time, my patience for instructors who do a poor job is even less than it was before, because I feel like such instructors are in some sense neglecting the responsibilities to their students fundamental to their job; while I recognize that not everyone develops skills for or interest in teaching immediately, I would hope that such instructors at least put some effort into developing such skills knowing they are responsible for educating young citizens.

It'll be interesting to see how my thoughts on taking a class shift as the semester progresses, and how useful it ends up being with respect to my exploration of other fields. At the very least, I do hope to learn more about how to teach well (and how not to teach poorly) by applying what I've learned from being a TA to my observations of instruction in this class.

Trying out Julia

This is a fairly quick post, though I previously considered making it longer and more trollish. A handful of my friends have told me about Julia, the amazing programming language made for numerical computations and other scientific computing uses. For the 14.15 — Networks final project this past semester, one of my group partners used Julia to simulate large ensembles of 10000-node random networks, and it worked far quicker than MATLAB. I vowed to get a bit more familiar with Julia (the programming language, not a woman [yet]) this summer. It was actually pretty quick to get used to, considering its syntactical similarities to MATLAB, to which I am more accustomed. I was even able to use it to port over the MATLAB code used for data analysis in 8.13/8.14 — Experimental Physics I/II to Julia. The only issue that I have consistently run into has been plotting. For some reason, the plotting packages that interface with Julia do not work in the ways that I want: Winston is too basic, Gadfly doesn't work at all (which is unfortunate because it has all the features I need and more), and Gaston being a frontend for Gnuplot while having to deal with the quirks of Julia's plot execution order means that I might as well use Gnuplot itself. Indeed, that is what I've done: I've been able to write Gnuplot scripts to plot processed data that Julia outputs into a file. Although Gnuplot's syntax is a little arcane, it is so powerful that I'm OK with using it from a script of commands and changing only a few things here and there as needed. Other than that, Julia works like a charm; its speed is fantastic, and I really like how much structure it brings compared to MATLAB (including things like types and indexing). Plus, it combines the great features of both procedural and functional programming. Given that course 18 has largely switched over to Julia, I wonder when course 8 will do the same....

Reflection: My Undergraduate Experiences at MIT

Commencement is a few days away, so I don't have too much more time on campus. I've finished all four years of my undergraduate education. It has been a really wild and amazing ride, and now that things are marginally quieter, I think I could use a little reflection on those 4 years (or, at least, the highlights, learning experiences, and more recent parts that I remember). I am no poet, so a lot of this may sound repetitive, awkward, or stilted; believe me when I say this is really how I feel. Follow the jump to read more.

Done with 8th Semester!

I'm done with my eighth and final semester of my MIT undergraduate semester! (Actually, I was done on Sunday, May 18 around 3pm upon completion of my last problem set, but I didn't get around to writing this until today.) It was extremely satisfying to see a bit about nanoparticle scattering of infrared light in a new UROP project and write about that in my thesis, along with getting excellent results for my ongoing photonic crystal UROP project and writing about that too. My thesis gave my the most trouble in the two weeks leading up to its submission on May 9, though I started writing during spring break itself. In terms of classes, I had the most trouble in 8.334 — Statistical Mechanics II (Statistical Field Theory), as the problem sets and exams alike were quite challenging, and the final project was an 18-hour marathon on Friday, May 16. Also annoying was 14.15 — Networks; it wasn't taught or organized very well, and the final project gave me and my group partners a fair amount of stress too. More manageable was 8.962 — General Relativity, which only had problem sets, and most of those were quite reasonable and straightforward. Anyway, I don't have any final exams this semester (by design), so I'm really done, and all I need to worry about now is commencement! (I will have a longer post reflecting on my time at MIT in the coming days, so stay tuned for that.) After commencement, I plan to spend most of my summer time relaxing and picking up small projects at home; I may also travel for a bit too.

Eighth Semester at College

I'm at the home stretch! This is my eighth and last semester as an undergraduate at MIT. Classes start tomorrow. I'll be taking 8.334 — Statistical Mechanics II (which is really statistical field theory), 8.962 — General Relativity, 14.15 — Networks, and 8.THU — Undergraduate Physics Thesis. The cool thing is that 8.334 — Statistical Mechanics II and 14.15 — Networks will have a bit of overlap in some places, as both discuss graph theory, collective phenomena, and phase transitions to varying degrees. More importantly, 8.THU — Undergraduate Physics Thesis is basically going to be my UROP, formalized into credits contingent on me producing a thesis at the end of it. That's also how I can start a new UROP project on nanoparticle absorption and scattering of infrared radiation. Even though I'm only taking 3 classes besides my UROP and [as far as I can tell] none of them have final exams, the semester will still keep me quite busy, but this will be the last semester where I can take more random classes that I want to take, as graduate school will likely only let me take classes related to my research interests. Here's hoping that my last semester of my undergraduate career turns out to be the best one yet, and good luck to everyone else for the new semester!

Done with 7th Semester!

It finally happened! The end of the semester rushed in and washed over just as quickly. My classes — 8.07 — Electromagnetism II, 8.09 — Classical Mechanics III, 8.333 — Statistical Mechanics I, and 14.12 — Economic Applications of Game Theory — were all together a bit more challenging than I anticipated. On top of that, I worked a lot on my UROP, and of course I had to submit graduate school applications by last weekend. Thankfully, my classes and graduate school applications are done. Now I can go home, relax, enjoy the company of family and friends...and probably work on my UROP. Of course, I'll be continuing my UROP over IAP, but I hope to be transitioning into a new project then, so I hope to get a fair amount of my current project done during the break. Happy holidays everyone!

Classes, UROP, and Applications Galore

I know I haven't posted here in a while. That's because this is around the time that a lot of graduate school applications are due, so I've been busy getting those done. At the same time, my UROP has been getting busier as I'm trying to wind down my current project, and classes are of course ever-present in the background. Anyway, my applications and classes will be done in about 3 weeks, so at that time I should have more time to write here. Meanwhile, happy Thanksgiving!

Seventh Semester at College

How did I become a senior? It doesn't feel like orientation and freshman year happened that long ago.
Tomorrow is the first day of class for the 2013 fall semester. I'll be taking 8.07 — Electromagnetism II, 8.09 — Classical Mechanics III, 8.333 — Statistical Mechanics I (a graduate class), and 14.12 — Economic Applications of Game Theory. I'm looking forward to all of these classes along with continuing my UROP (which may transition sooner or later into a new project as I wrap up my current one). The bigger things I have to deal with though are graduate school applications and the Physics GRE. The latter will be over in a few weeks. The former will be going on until around the beginning of December, but I hope to be done a while before that. Hopefully this semester goes well. Good luck to everyone else for the start of their school year/job/whatever else!

Cap and Trade and Soda

A few days ago, my family and I went on vacation. On the way back, my family and I were discussing various things including some matters of politics. One thing that came up was some of New York City mayor Michael Bloomberg's recent actions. I expressed the view that the ban on soft drinks larger than 16 ounces seemed rather heavy-handed. (After reading a little more about the exceptions for fruit drinks along with sales at grocery stores, I'm a little more happy to see that, but I still feel the ban was heavy-handed.) I then heard the argument that even if it is heavy-handed, it does help combat the obesity crisis by reducing access to drinking 16 ounces of soda at a time, because even if it is still technically possible for someone to fill up an 8-ounce cup twice, human psychology is such that said person would only fill up once, because for many people the convenience of filling up once trumps the desire to have as much as possible. I then wondered what other alternatives could be considered. The simplest alternative would seem to be a tax akin to taxes on cigarettes; if the large sodas are taxed heavily at such venues, people would naturally be discouraged from drinking as much. I have taken the class 14.03 — Microeconomic Theory and Public Policy, though, so I have seen that in many cases a Pigovian tax scheme like that may not achieve the most efficient outcome because it is difficult to adjust tax rates to control quantities precisely. Then I also remembered learning about cap and trade schemes to control quantities. Would that work? Let's take a look after the jump.

Done with 6th Semester!

I'm done with junior year! The spring semester was a bit more manageable than the fall semester, but was still challenging nevertheless. I intentionally chose to take only 3 classes: 8.06 — Quantum Physics III, 8.14 — Experimental Physics II, and 14.03 — Microeconomic Theory and Public Policy. I did this so that I could spend more time on each of those classes (especially 8.14 — Experimental Physics II) as well as on my UROP. Speaking of my UROP, things were progressing rather slowly in the beginning of the semester and only slowed further from there, until just after spring break, at which point progress went extremely quickly. I'm really looking forward to being able to make more such progress in the summer; plus, I may even be able to start on a new project about the Casimir effect, about which I wrote a paper for 8.06 — Quantum Physics III. Before that, I'm spending two weeks at home. For these next few days, I'm just going to relax and spend time and travel with family. After that, I'll probably be able to start work again on my UROP; a few weeks into the summer, I intend to start looking seriously into graduate programs in physics. Anyway, at last, it is summer!

Frictions, Subsidies, and Taxes

One of the things I learned in my high school AP Microeconomics class was that a tax causes the supply curve to shift to the left, making the equilibrium quantity decrease and price increase. Consumer and producer surplus both decrease, but while government revenue can account for some of the loss in total welfare, some part of total welfare gets fully lost, and this is what is known as deadweight loss. I didn't have a very good intuition for how this worked at the time (though I was able to get through it on homework, quizzes, tests, and the AP exam). At the same time, though, I thought that a tax should be fully reversible by having the government subsidize producers, and that as this would be the opposite of a tax, supply would shift to the right, the equilibrium quantity would rise and price would fall, and there would be a welfare gain.

Then, when I took 14.01 — Introduction to Microeconomics, we again discussed the situation with a tax. Then we talked about subsidies, but I was confused because the mechanism seemed to be in providing a subsidy to consumers rather than to producers. My intuition at that point was that taxes were creating deadweight loss because producers who wanted to produce and consumers who wanted to consume near the original equilibrium could not do so after the tax, so some transactions were essentially being prohibited. However, I still didn't quite understand why a subsidy would create deadweight loss, because it seemed to me like consumers who wanted to consume more and producers who wanted to produce more than the original equilibrium quantity could now do so, meaning it seemed to me like more transactions were being made possible. That said, I did understand why the government would never subsidize producers: unless the market is perfectly competitive, producers would rather collude and pocket their subsidies while keeping prices high when they can. On the other hand, consumers prefer consuming, so subsidizing consumers is a more surefire way of increasing the equilibrium quantity, even though the price would go up rather than down.

(In 14.04 — Intermediate Microeconomic Theory, we barely touched on deadweight loss in the way that it is covered in more traditional microeconomics classes.) Now, in 14.03 — Microeconomic Theory and Public Policy, I think I better understand the intuition behind deadweight losses stemming from taxes and subsidies, and why a subsidy is not the opposite of a tax. In a tax, the government might try to target some new equilibrium quantity below the original one, so the tax revenue collected, which increases total welfare, is the difference between the willingness of consumers to pay and the willingness of producers to accept at that quantity multiplied by that quantity. Consumer and producer surplus both decrease, and the tax revenue contribution to the increase in total welfare is not enough to offset these two, so there is an overall deadweight loss. A completely isomorphic way of picturing this is by considering the tax falling on consumers so that the demand shifts to the left; in both cases, the equilibrium quantity drops, the government collects its revenue, surpluses drop, so deadweight losses appear.
Meanwhile, for a subsidy, the government might target a higher quantity than the original equilibrium. The spending on that subsidy is the difference between the willingness of producers to accept and the willingness of consumers to pay at that quantity multiplied by that quantity. Consumer and producer surpluses both increase, but together they do not increase enough to offset government spending which is an overall drain on total welfare, so there exists a deadweight loss.

It's interesting that taxes and subsidies are not opposites. The intuition is that for a tax, the revenue is not enough to compensate for the welfare losses of consumers and producers because the new equilibrium quantity is lower. By contrast, for a subsidy, the spending is too high compared to the welfare gains of consumers and producers because the new equilibrium quantity is higher. It looks like it is not possible to spend money given by tax revenue to undo the effects of a tax; instead, the government can only overshoot and overspend. It reminds me very much of how friction works: moving in one direction on a surface with friction causes energy loss, while turning around to move in the other direction on that same surface most certainly does not cause energy gain. Essentially, in this model, the market is frictionless, and the government introduces friction.

Of course, this essentially contradicts Keynesian models of government taxation and spending and their respective effects. That's why care must be taken when putting microeconomic models in a macroeconomic perspective. This also doesn't consider externalities, less than perfectly competitive market structures, et cetera. Anyway, I hope my musings on this may help give other people some intuition on simple issues of deadweight loss in microeconomic theory.

More on 2012 Fall

Last semester, I was taking 8.05, 8.13, 8.231, and 14.04, along with continuing my UROP. I was busy and stressed basically all the time. Now I think I know why: it turns out that the classes I was taking were much closer to graduate classes in material, yet they came with all the trappings of an undergraduate class, like exams (that were not intentionally easy). Let me explain a little more.

8.05 — Quantum Physics II is where the linear algebra formalism and bra-ket notation of quantum mechanics are introduced and thoroughly investigated. Topics of the class include analysis of wavefunctions in 1-dimensional potentials, vectors in Hilbert spaces, matrix representations of operators, 2-state systems, applications to spin, NMR, continuous Hilbert spaces (e.g. position), the harmonic oscillator, coherent & squeezed states as well as the representation of photon states and the electromagnetic field operators forming a harmonic oscillator, angular momentum, addition of angular momenta, and Clebsch-Gordan coefficients. OK, so considering that most of these things are expected knowledge for the GRE in physics, this is probably more like a standard undergraduate quantum mechanics curriculum rather than a graduate-level curriculum. That said, apparently this perfectly substitutes for the graduate-level quantum theory class, because I know of a lot of people who go right from 8.05 to the graduate relativistic quantum field theory class.

8.13 — Experimental Physics I is generally a standard undergraduate physics laboratory class (although it is considered standard in the sense that its innovations have spread far and wide). The care and detail in performing experiments, analyzing data, making presentations, and writing papers seem like fairly obvious previews of graduate life as an experimental physicist.

8.231 — Physics of Solids I might be the first class on this list that actually could be considered a graduate-level class for undergraduates, also because the TAs for that class have said that it is basically a perfect substitute for the graduate class 8.511 — Theory of Solids I, allowing people who did well in 8.231 to take the graduate class 8.512 & mdash; Theory of Solids II immediately after that. 8.231 emphasized that it is not a survey course but intends to go deep into the physics of solids. I would say that it in fact did both: it was both fairly broad and incredibly deep. Even though the only prerequisite is 8.044 — Statistical Physics I with the corequisite being 8.05, 8.231 really requires intimate familiarity with the material of 8.06 — Quantum Physics III, which is what I am taking this semester. 8.06 introduces in fairly simple terms things like the free electron gas (which is also a review from 8.044), the tight-binding model, electrons in an electromagnetic field, the de Haas-van Alphen effect, and the integer quantum Hall effect, and it will probably talk about perturbation theory and the nearly-free electron gas. 8.231 requires a good level of comfort with these topics, as it goes into much more depth with all of these, as well as the basic descriptions of crystals and lattices, reciprocal space and diffraction, intermolecular forces, phonons, band theory, semiconductor theory and doping, a little bit of the fractional quantum Hall effect (which is much more complicated than its integer counterpart), a little bit of topological insulator theory, and a little demonstration on superfluidity and superconductivity.

14.04 &; Intermediate Microeconomic Theory is the other class I can confidently say is much closer to a graduate class than an undergraduate class, because I talked to the professor yesterday and he said exactly this. He said that typical undergraduate intermediate microeconomic theory classes are more like 14.03 &; Microeconomic Theory and Public Policy (which I am taking now), where the constrained optimization problems are fairly mechanical, and there may be discussion on the side of applications to real-world problems. By contrast, 14.04 last semester focused on the fundamentals of abstract choice theory with a lot more elegant mathematical formalism, the application of those first principles to derive all of consumer and producer choice theories, partial and general equilibrium, risky choice theory, subjective risky choice theory and its connections to Arrow-Debreu securities and general equilibrium, oligopoly and game theory, asymmetric information, and other welfare problems. The professor was saying that by contrast to a typical such class elsewhere, 14.04 here is much closer to a graduate microeconomic theory/decision theory class, and the professor wanted to achieve that level of abstract conceptualization while not going too far for an undergraduate audience.

At this point, I'm hoping that the experiences from last semester pay off this semester. It looks like that has been working so far!

More on My Photonic Crystal UROP

In my post at the end of the summer, I talked a bit about what I actually did in that UROP. Upon rereading it, I have come to realize that it is a little jumbled and technical. I'd like to basically rephrase it in less technical terms, along with providing more context on what I did in the 2011 fall semester. Follow the jump to see more.

Sixth Semester at College

Today is the first day of my sixth semester at college. I'll be taking 8.06 — Quantum Physics III, 8.14 — Experimental Physics II (also known colloquially as "J-Lab"), and 14.03 — Microeconomic Theory & Public Policy. I feel like taking three classes apart from J-Lab was too much last semester, so taking two this semester should make my schedule feel a lot more sane and manageable. Plus, now I have a handle on what J-Lab expects, so striving to meet that should be easier now. Finally, I did this because my UROP sort of fell to the wayside last semester, and I don't want that to happen this semester, so now I should be able to spend more time on both classes and that. Hopefully this semester will be a good one; good luck to all my fellow classmates out there!

Featured Comments: Week of 2012 December 16

There was one post that got a comment this past week, so I am reposting that one.

Done with 5th Semester!

Reader Mechatotoro said, "Good work, my friend! It's great to hear you also made it through this intense year. Enjoy your free time--you earned it!"

Thanks to him for that comment during the past week. This coming week, I will be spending time with family out of town, so I don't anticipate posting much until after new year's day. Anyway, if you like what I write, please continue subscribing and commenting! Also, happy past-doomsday, happy holidays, and happy new year!

Done with 5th Semester!

Wow. This semester was longer and far more difficult than any previous one here. Most of that is courtesy 8.13, though 8.231 and 14.04 were certainly contributing factors. Final exams were also fairly challenging as well this time. My only regret is that my UROP somewhat fell by the wayside as a consequence. I really enjoyed learning what I did in my classes, and the experiences I gained were immensely rewarding in the end, but I am so glad that I am done with it now. Right now, I'm just focusing on going home in a few hours and spending quality winter break time with family and friends. I will be back over IAP to continue my UROP. After that, in the spring semester, I intend to take fewer classes, because I realize that I may have bitten off a little more than I could chew this semester. Anyway, happy holidays everyone!

Fifth Semester at College

Well, it has indeed happened. I am now a junior! Wait, what? When did this happen all of a sudden?
Classes start tomorrow, and this semester I'm taking 8.05 (Quantum Physics II), 8.13 (Experimental Physics I, also known as "J-Lab"), 8.231 (Physics of Solids), and 14.04 (Intermediate Microeconomic Theory); in addition, I am continuing my UROP from the summer. I'm most scared about J-Lab, because I've seen other friends take it in the past and I've seen how they have had essentially no time to do anything else (often even to the detriment of other classwork). Well, I'll see how it goes; while 4 classes and a UROP will be quite a time-crunch, I think I'll make it through OK. That said, this blog will probably see many fewer posts over the course of the semester. I guess I'll wait and see how that goes too.

Done with 4th Semester!

Oh my goodness. I am done with half of my undergraduate career at MIT. This is crazy!
This past semester was even more crazy than the one before that. The great thing was that my classes this semester were way more interesting on the whole and will be far more useful especially towards the UROP that I will be doing over the summer.
For now, though, I'm not thinking much about my UROP. I'm thinking about what I'll do to relax and unwind at home. And by the way, one of the things I had originally intended to do was write a few more reviews, but because I stupidly forgot my USB flash drives in my dormitory room, that will not be happening until I get back to campus. Oh well. I'll find other stuff to do too!

Fourth Semester at College

Yesterday my fourth semester here started. This semester, I am taking 8.04 (Quantum Physics I), 8.044 (Statistical Physics I), 14.02 (Principles of Macroeconomics), and 18.06 (Linear Algebra). In addition, I am continuing my UROP (though my work will likely change soon) and doing some other work too.
It's going to be a busy semester, but given that I am now used to this kind of workload from last year, I think I will be able to manage it better. Plus, now that my classes start each day no earlier than 11am, I can get more sleep! Yay! That aside, it's going to be an exciting semester, though I can already feel the heat with problem sets and such.

Done with 3rd Semester!

I'm finally done with my 3rd semester! Yay! Although this semester I was just taking the classes for my major/that I wanted to take, thanks to the combination of 4 classes (all of which have problem sets and exams), a UROP, and grading, this semester was way more grueling than any previous semester. Thankfully, I think I've done fine, so I feel like I would be better prepared to do the same (4 classes, a UROP, and grading) next semester.
But before I need to worry about next semester or even IAP, I get to go home for winter break! Woohoo!