My reading list

Have you played a RPG where you can't open a normal looking chest at the start of the game if you want the ultimate weapon at the end of it? I think that the best approach to majoring in physics is the same thing. Now, my first semester in college looks like crap.

The road to theory of Lie groups

I'm cleared to take graduate courses shamelessly as an undergraduate by the head of department, which is nice, but probably makes me the only freshman physics major doing graduate math courses for some time... I feel kind of bad for my roommate. The courses in my first semester look like this (not in their exact names):

1. Group theory
2. Continuum modeling
3. Lebesgue integral properties and measure
4. Partial differential equations
5. Applications of complex variables
6. Complex analysis
7. Differential equations (boundary value problems) 
8. Continuum modeling (graduate level)
9. Honors differential equations
10. Geometry of manifolds
11. Abstract algebra (w/ Galois theory, rings, Abelian groups etc.)
12. Partial differential equations (applications of Hilbert spaces)
13. Partial differential equations (more methods)

It looks ridiculously long, but it makes sense if you know the prequisites - a much shorter list:

1. Single-variable calculus
2. Multivariable and vector calculus
3. Real analysis
4. Tensor calculus
5. Linear algebra
6. Differential equations

Most of these fall prey to my current reading list:

1. Spivak, Calculus
2. Courant & Fritz, Introduction to Calculus and Analysis I
3. Courant & Fritz, Introduction to Calculus and Analysis II
4. Apostol, Calculus Vol 1: One-variable Calculus with an Introduction to Linear Algebra
5. Apostol, Calculus Vol 2: Multi-Variable Calculus and Linear Algebra with Applications
6. Spiegel, Schaum's Outline of Advanced Calculus
7. Spivak, Calculus on Manifolds
8. Mattuck, Introduction to Analysis
9. Kolmogorov & Fomin, Introductory Real Analysis
10. Kolmogorov & Fomin, Elements of the Theory of Functions and Functional Analysis
11. Hoffman & Kunze, Linear Algebra
12. Lipschutz, Schaum's Outline of Linear Algebra
13. Tenenbaum & Pollard, Ordinary Differential Equations
14. Gallian, Contemporary Abstract Algebra

Bizarre ongoings

Now, among the bizarre things I've seen lately...

I saw this guy on empty roads past midnight, towing a pretty Cannondale with XT disc brake groupset etc., with vintage bike that has two flats, a chain that's sagging nearly onto the ground. I bet no one can figure out the full story.

Barcelona 1 - Inter Milan 0. Inter celebrates(?) as they advance to the finals.

What is this?

Give yourself a pat on the back if you know what's behind each picture...

Some quotes

"My complete answer to the late 19th century question "what is electrodynamics trying to tell us" would simply be this: Fields in empty space have physical reality; the medium that supports them does not.

Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics: Correlations have physical reality; that which the correlate does not."

American Journal of Physics, 66: 753-67

^LOL, I agree with the first part but not necessarily the second.

If you curl up to me, we'll have no divergence.

At the end of the tunnel, I saw a bright light of beam angle 0.62 radians, correlated CT 4500K, CBCP 14870cd.

Summary: Speeding up Windows 7 (extended for laptops)

Now that I have MATLAB on my laptop, it's time to separate the PCs from the Macs. W7 offers a much improved ReadyBoost option over Vista, but exploiting it to its fullest potential is the difficult part. Here I talk about formatting your flash memory with which file systems, allocation unit sizes; how to get this done without having flash drives sticking out from the side of your laptop permanently; and how generally everything starts faster.

Loss at 50km/h (watts) against rim depth (mm) of 57 wheelsets

This post was written to answer a question that I was asked. For the benefit of people without curve fitting software, I did some basic analysis of aerodynamic data* for rims and have a sort of opinion here. (Also,  I made this for fun since I finally have MATLAB 2010 which supports W7 on my laptop! Yes!!!)

Click to enlarge

My statistics sucks... but maybe someone can make better work of this: the norm of residuals is 15.053 (higher polynomials are badly conditioned), and the standard deviation in y is 3.999... which should imply that the fit is 74%, which is a pretty strong correlation.

The other thing I want to suggest is that we can figure out the range of rim depths that a wheelset for overall usage should fall under. From the equation, we understand that there exists a region $37.5 \leq x \leq 53.1$ where a relatively large change in rim depth incurs only small aerodynamic benefit/loss of $\pm1.0W$ at 50km/h. Now, waiving all the assumptions that we have to clear, this sounds very reasonable indeed:

Hill climbing wheelsets: <37.5mm

General-use wheelsets: 37.5 to 53.1mm

TT wheelsets: >53.1mm

Now, my point was that the Zipp 303 has kind of disposed 404 as the better overall wheelset.

*Compiled from Roues Artisanales. I removed 2 outliers from the data: Ambrosio X-Carbo '05 (46, 31.5) and Zipp 808 (82, 16.7).

Some things about mathematics

The Putnam Competition is insane. Citing a factual statement, the median score on the competition is 1 out of a possible 120.

Let's put this into perspective. You have some 4000 of the world's brightest undergraduate mathematicians, who were sifted through the upper deciles of college-entering students from high school, then filtered through some self-selection within the universities. They sit down for 6 hours to concentrate their best on effectively a 120 mark test.

And at least half of them score 1/120 and below, i.e. the majority of the world's brightest mathematicians score either 0/120 or 1/120 out of this test. To make it more dramatic, on the upper end, there are people who score 120/120 once in a while.

Imagine the feeling that you'd get if you spent 6 hours and scored zero... that must be one of the rare experiences that the Latin proverb, "Amici, diem perdidi," finds an application for. Of course, saving the dramatization, not all of the best mathematicians-to-be take part in the competition, and how good one is at mathematics competitions doesn't reflect one's academic aptitude/productivity. Competitions differ from research.

Some questions on the competition have deceptively simple solutions. For example, find

$\int_{2}^{4}\dfrac{\sqrt{\ln\left(9-x\right)}}{\sqrt{\ln\left(9-x\right)}+\sqrt{\ln\left(x+3\right)}}\, dx$ --------- (1987-B1)

(if you worked this out in full within 6 hours on test day, you would have scored 10, probably placing you ahead of at least 2000 people!)

I came, I saw, I-- huh?

"It is produced by no more than 2 carbon manufacturers in the world."

??? Like what... BP Amoco? Sumitomo? Mitsubishi? Nippon Graphite Fiber Corporation? Kureha Corporation?

Update: On further inspection, it wasn't only a puncture that I had... the rim took some dps too. Quite a headache if it can't be kept true after repair because I can't find a matching rim anymore. I was saying, that given the taxi rates over here, the break-even point for a $5000 wheelset is 7500km provided that repair/maintenance cost is included in the $5000. Of course, that's if you were riding as fast as Cancellara a taxi.

Mood: Alkan, Le chemin de fer in D-minor, Op. 27

The comprehensive guide to clear coat techniques for carbon fiber

How much weight does it add on? 3 coats over my crankset added 0.3g of weight. There was a net loss of weight from sanding down the original coat instead. The weight loss was slightly more for removing the Campy decals. I gained slightly below 2g for sealing a pair of stickers onto a fork. A proper clear coat job will NOT affect your build's weight significantly.

Carbon fiber is like your facial complexion - you don't worry about pimples when you eat chocolate right? Similarly, there's nothing to worry about a gash across your $9999 frame. I can fix that in 3 minutes. This guide covers the more essential steps, which should give the average rider the confidence to use his/her carbon fiber parts for a daily ride.

I assume that you know how to clean up your bike parts, degrease whatever... If you've waxed the parts, you can remove the wax with detailing clay. I also assume that you have some imagination... meaning you know how  to avoid giving your house a clear coat in the process, and how to leave your parts in a suitable position for the clear coat to dry. Here's what else you need for that proper clear coat job.

Be evil

Should I migrate to Google Mail?

P.S.: Had my first puncture in nearly 24,000km. It was my mistake rather than my equipment failing me actually, I tried to skip two curbs that were about 1 foot apart (effectively a pit hole), and I knew it the moment I cleared the curbs and heard that whistling sound. ):

Mood: Brahms, Variations on a Theme of Paganini, Op. 35/1