A Candle in the Dark

A look on science, politics, religion and events

Archive for March 2009

My experiment with GATE

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If you’re an undergraduate engineering/science student in India, and you plan to do your Master’s degree in some of India’s premier institutes of higher education (like the IITs or IISc), then you’ll have to write the Graduate Aptitude Test in Engineering (GATE).

The test is similar to the subject GRE. It consists of 60 multiple choice questions over a duration of 3 hours. The first 20 questions are worth 1 point, while the last 40 are worth 2 points for a total of 100 points with negative marks for incorrect answers. The engineeering test contains two sections. There’s a general engineering mathematics section as well as the specialized engineering subject.

In the summer of 2008, I had a wonderful experience participating in an undergraduate research project at the Indian Institute of Science in Bangalore. As a result, while I had applied towards a number of graduate schools in the US, I was also looking at the possibility of doing a ME degree at IISc. This meant that I had to register for and write the GATE in 2009.

The “online” registration process is actually a bit of a misnomer. I had to download the documents from the webpage, and fill in the relevant details and submit the printed documents at the GATE office. For details of the admission procedure and the structure of the test, visit the GATE website.

A couple of months after I had registered for the test, but before the actual examination date, I received an offer of admission towards a PhD at a well-recognized graduate program in the US which I plan to accept. So, I decided to write the GATE anyway for fun without any preparation. After all, what better way to test the conceptual knowledge that one is expected to acquire in four years of undergraduate education?

On the morning of February 8th 2009, I was off to write the test at the Santhom Hr. Sec. School, comforted with the knowledge that it didn’t matter one bit even if I completely messed it up. The location was pretty decent, and there was drinking water available, although the desks had less legroom than a typical Indian Airlines flight.

The engineering mathematics part of the test was pretty straight forward. Many of the questions were on multi-variable calculus and complex numbers. Since I don’t remember signing a non-disclosure form, I’ll reproduce some of the questions below.

  • The direction of largest increase of the function xy^3-x^2 at the point (1,1) is ?
  • The value of the limit as {x \rightarrow \pi/2} of (\cos{x})/(x-\pi/2)^2
  • Using the residue theorem, the value of the integral \oint (8-7z)/(z-4) dz around a circle with center at z=0, and radius=8 is?
  • Use the Gauss divergence theorem to evaluate \int \int (2x \hat{i}-2y\hat{j}+5z\hat{k})\cdot \hat{n}dS over a sphere of radius=3 centered at the origin

I was confident that I’d got most, if not all, of the math questions right, and was pretty pleased with my progress. That is, until I hit the chemical engineering section.

  • How does the power number vary with the Reynolds Number in a mixing tank operating in the laminar regime?
  • The active component of catalysts used in the steam reforming of methane to produce synthesis gas?
  • What is the Thiele modulus?
  • How does the frictional pressure drop across a packed bed vary with the superficial velocity in fully turbulent conditions?
  • How does the mass transfer coefficient vary with the diffusion coefficient in the penetration theory of mass transfer?

Embarrassingly, I had also forgotten which way the Biot number was defined (ie, convective/conductive or the other way?). I guess that since most of my exams in undergrad were open notes/open book, there wasn’t a need to actually commit definitions and formulae to memory, and my lack of preparation was very evident in this section.

However, further into the test, there were numerous standard “homework” problems which you could immediately identify if you’d done the relevant courses on heat transfer, transport phenomena, reaction engineering and process control, such as calculating the outlet temperatures of streams in heat exchangers, number of stages in distillation columns, mean residence time calculations, stability of control systems, etc.

Overall, I though that the test was set pretty well.

However, I get the feeling that the GATE doesn’t test the innate analytical skills of the student, as much as it tests a particular method of undergraduate education (the problem solving/number crunching method, which many students may not be exposed to). In my highly subjective opinion, I don’t think that the GATE should be required for admission to a graduate program. If there is a need for a “leveler test” to attempt to compare applicants between the multitude of universities in India, I think a test which focuses on basic analytical and verbal skills (like the GRE) is preferable.


Written by parseval

March 16, 2009 at 4:51 am

Posted in education, engineering, personal

Tagged with ,

Abstruse Goose Puzzle

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You might have come across Abstruse Goose before. It’s simply a wonderful webcomic, along the lines of xkcd, but much more technical. Each comic strip usually contains an allusion to some physical or mathematical concept and ends with a humorous punchline.

Today’s comic had a simple puzzle. And, as I was curious about where it was leading, and had time to kill, I took a shot at it.

Clue 1

And how does one go solving this? It is fairly easy. In fact, all you need is to know is the first n digits of e and after that, it’s simply string manipulation and prime number checking.

I’ve embedded the C++ code which I used to solve the puzzle at the end of the post, below the fold.

It’s easier to find the first 100,000 digits of e using a quick search in google than to generate it. Once you have the string, you just need to check if every set of 10 consecutive digits is prime. Turns out, that the first 10 digit prime number found in consecutive digits of e is 7427466391.

That’s Clue #1 done. Proceeding to the url, we get Clue #2:

Clue 2

Again, very easy, and all that’s needed now is the first n digits of pi instead of e. The first 10 digit prime number found in consecutive digits of pi turns out to be 5926535897 (occurs very early!), leading to the final Clue #3.

Clue 3

I’ll leave you to do this one, and appreciate the punchline.

Code below the fold
Read the rest of this entry »

Written by parseval

March 6, 2009 at 11:40 pm

Posted in mathematics, programming

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Declaration of war?

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While I was walking back to the lab after lunch today, one of my friends informed of the terror attacks against the Sri Lankan cricket team. It’s terrible that six police officers were killed in this incident, although it might have been much worse.

However, words cannot sufficiently express the deep loathing at the pit of the stomach that I feel when reading the comments of the Pakistani Minister of State for Shipping, Sardar Nabil Ahmed Gabol.

“The evidence which we have got shows that these terrorists entered from across the border from India,” Sardar Nabil Ahmed Gabol, Minister of State for Shipping, told private Geo television. “This was a conspiracy to defame Pakistan internationally.”

“This incident took place in reaction to 26/11,” he said referring to the Mumbai attacks in November in which at least 170 people were killed. “It is a declaration of open war on Pakistan by India,”

Politicians like him are opportunistic parasites, who eagerly jump with glee at any human tragedy to attempt to gain political mileage. Even if you ignore his claim to have evidence of the geographic origin of the terrorists within hours of the attack (without even hinting at the actual evidence), and the obligatory conspiracy theory angle, to call this a “declaration of open war on Pakistan by India” is irresponsible garbage.

Written by parseval

March 3, 2009 at 7:22 am

Posted in terrorism

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