Rajesh Kumar

Optimizing life, one day after the next

Glorious Conjectures

09 Nov 2006

I haven't written anything substantial in a long time. It makes me feel handicapped sometimes. No, I haven't updated not because I haven't had the time. Matter of fact, I've had lots of time. It's just that I've been spending a fair share of my time in front of either monitors, textbooks or reams of lined paper, that at the end of the day when I do have that cherished hour of free time, I just want to take off and look at something farther than a few meters. And sadly, that does not constitute a laptop.

Today, I want to talk about my academic work over my last two and a half months here at the University of Waterloo. I'm taking six courses this semester and I don't see that number dropping anytime in the near future. I joined my program nanotechnology engineering specifically for its strong lab component, but unfortunately, I only have one lab this term which contributes to a mere 20 percent of the course's final mark. This situation will hopefully improve in the upcoming years, especially with that eighty million dollar mammoth building—the quantum-nano center—being built right at the heart of the campus.

NE 224 Biochemistry. This course has been immensely interesting since day one. The only part I can't digest is all the enzymatic mechanisms. The text for this course Voet and Voet is really one of its kind. I think its the best text I've seen so far in terms of verbal exposition. We spent a large chunk of the last month studying proteins, particularly enzyme and hemoglobin structure and function. Last week we talked on enzymatic regulation — allosteric, phospholyration, zymogen and tight-binding.

Next week is going to be all about lipid and membrane chemistry and so on. The lab component is interesting although not too significant. We did some elementary protein assaying, purification and kinetics. Next week's lab on bacterial transformation is something to be sought for there are no other second years doing this kind of stuff so early in their career.

NE 225 Nanoscale Structures. This is one course I haven't learned much from through lectures. Most of my knowledge has come from my reading of the assigned material. This course intends to describe how different mechanisms of organization between atoms (and molecules) can lead to various architectures on both the nano as well as the macro scale.

Personally speaking, I consider this mostly a "tools" course that explores hierarchical views of global structures starting from the smallest atom, to the zero-charge precursor that initiates nucleation, and finally to describing the bulk properties of the material. The course ensures a sound knowledge of principles of classical inorganic chemistry. Some of the examples of successful syntheses are taken from results of research work as recent as 2000!

NE 232 Quantum Mechanics. Nothing too complicated this term, as it's only an introductory course. We started off in September with basic postulates, the Schrödinger formalism (no Heisenberg this term), state functions, commutation relations, Heisenberg's uncertainty, operators, eigen functions and eigen values, the classic particle in a box example, Hermitian operators, and finally de Broglie waves. Just last month, we looked at the momentum representation of psi by taking the fourier transform. Last couple weeks were all about the infinite potential well problem, tunneling and applications. Right now we're being introduced to Dirac's matrix notation along with a complete rigorous description of the hydrogen atom. I have a major assignment due this Monday and I haven't started yet!

I really don't know what's in store for us in the next three weeks as this course, much like the two mentioned above, is being taught for the first time. The prof is a PhD from MIT and a post-doc from Stanford, so there's very little to remark there.

I just attended a talk today on electron microscopy using TEM and its associated applications. The talk was by a Dr. Botton from the Brockhouse materials research team at McMaster. It was an interesting talk especially the part on characterizing nanoscale interfaces between say, hafnium oxide and silicon wafers. Much of the talk was targeted towards experts, so I was lost about half way through. I guess there's always got to be a starting point somewhere.

MATH 211 Advanced Calculus I: Differential Equations. This is my favorite course this Fall, no doubt. The prof, who is also the associate Dean of graduate studies in the faculty of science, is pretty good at what he does considering all he uses is a small chalk piece and four simultaneous chalkboards. The course is a gentle introduction to elementary differential equations and techniques of pinning down solutions to first and second order constant coefficient ODEs.

The course has certainly been picking up pace over the last couple days. We got into Laplace transforms, impulse (or delta) functions, Heaviside applications to causal functions, integral equations, transfer functions and convolution integrals. I'm hoping we'll have time to get into fourier series and fourier transforms before the end of the term. Its a pity we won't be doing any PDEs, or partial differential equations, this term.

Apparently this is common knowledge, but I didn't know how to differentiate a definite integral with limits that were functions of the variable of integration itself.

Leibniz rule to the rescue:

\frac{d}{dy} \int_{a_1(y)}^{a_2(y)} h(x,y) dx = \int_{a_1(y)}^{a_2(y)} \frac{\partial h(x,y)}{\partial y} dx + h(a_2(y),y) a^{'}_2(y) - h(a_1(y),y) a^{'}_1(y). $1.2$

MSCI 311 Organizational Design and Technology. With a midterm score as high as 98.3%, this is the easiest course I'm going to ever take. The course content is deeply motivating nonetheless. The course is based on contemporary ideas in organizational theory: We did some basic work on organizational research, bureaucracy, goals and their effectiveness, and organizational design fundamentals. We then moved on with the more concrete stuff on Burns-Stalker and Lawrence-Lorsch studies and finally environmental impact on organizations using examples from biology and Darwinian theory. We're approaching the very end of the course wrapping up with Ashby's Law of Requisite Variety, the most fundamental theorem in macro organizational theory which forms the basis of cybernetics, information theory and stochastic systems. Wiki it if unsure.

MSCI 331 Operations Research 1: Introduction to Optimization. This is my second elective in addition to MSCI 311, and my second favorite course of the term after calculus. I have to credit most of my liking toward this course to the prof's superior teaching skills. He's just fantastic.

The strongest part of this course is the project work we have to complete and present in front of the class. My topic is an idea based on GE's approximation of the portfolio optimization problem using a linear tangent — Taylor's first-order you could argue. Portfolio risk functions are typically quadratic, but to take advantage of the simplex algorithm, we need a problem that is linear both in its objective as well as its constraints. Our goal is to calculate the efficient frontier to estimate the most optimal trade-off between risk and return-on-investment of an arbitrary combination of assets and bonds.

University's fun.