I am back again to tell you the stories about my strange mathematical education. I was finally able to escape and arrive the Indian Institute of Technology, Kharagpur, (IITKGP for short) which was about 120 kms south of Kolkata. It was way back in 1991. Kharagpur was essentially a railway town and other than that the only thing that it can boast of was the IIT.
The IITs were mainly built for technical education but they also provide degrees in the sciences which were much effective then the one’s given by the universities. I found my way into the hostel which would be my residence for the next two years. I was quite baffled by the huge campus of IIT Kharagpur. The first thing that I faced there was ragging which was done by our seniors but of a milder version than the stories I have heard. I was told that 2 year Masters students of science are indeed considered as second class members of the IIT student community. It was the B.Techs who were the kings. But this did not bother me at all. I just wanted to learn mathematics get access to the great library. As per my other needs I was very happy that Kharagpur was also an important center for my other great love —the railways. So anyway I would have a nice time and indeed I had a nice time.
I thought that the mathematics that I would learn would be exciting. I also thought that I would be taught by fine researchers who would show us the excitement of the subject. But this just remained a dream and did not happen that way. I had wanted to learn more mechanics, more probability, more analysis and more linear algebra. I also thought that I will learn topology and differential geometry.
Alas, things did not happen in that way. The subjects that were listed for the first semester were strange for some one who had a rigorous undergraduate training in mathematics. We had to learn PASCAL programming, Numerical Analysis, Measure Theory, Complex Analysis and Fluid dynamics.
We came out of the Fluid dynamics course without learning the Navier-Stokes equation. We were taught from an uninteresting book by Chorlton. The mess was more severe in the measure theory course. It was taught in a way as if it was history and modern mathematics did not depend upon it. It was taught by someone who had worked in elasticity and possibly learned measure theory from the book by Tishmarch on function theory. That was the prescribed text when much modern texts were already in the market. The instructor in the measure theory course was also the Head of the Department of Mathematics spent most of his time during the day in the HOD’s office and did so even during his alloted class hours. He used to come to the class and ask us to read from some portion from Tischmarch. One day he came in asked us to prove that the Cantor set is of measure zero. Then he said ” this problem does not worth a cowbell, what to say of a Nobel”. He smiled and left the class.
Classical Mechanics the subject that was so close to my heart in my undergraduate days was taught in IIT Kharagpur in the most boring way. It was done in such a way that I lost almost all interest in the subject. We were taught from Goldstien’s book on classical mechanics without even bothering to tell us why we need to study mechanics in that particular way. At the end things must follow the F = ma principle. We were just blindly doing things and to my surprise I got a good grade. I then understood that we were not being taught by researchers and instead being taught by people who had actually lost all contact with serious mathematics. The only glimmer of hope was a course on the Calculus of Variations taught by Professor A. S. Gupta a leading researcher in Fluid dynamics. Then I realized how we have been taken for a ride. Analytical mechanics taught without telling us even the term , calculus of variations.
The most surprising the course that I faced during my masters course was the General Theory of Relativity. Albert Einstein has been on my mind since I picked up Nigel Calder’s book Einstein’s universe. Though I did not understand much of what was written there but I felt a thrill about making an attempt to understand relativity. I was very keen to know how E=mc^2 was derived. Luckily in the library of St. Xaviers College, Kolkata ( Calcutta at that time) I had found a book on Special relativity by A. P. French. Through that book I first learned how mechanics is actually done. I learned first time about the Galileo’s principle of relativity and the notion of a frame of reference and was surprised that these were not at all taught in our mechanics course for mathematics students. I had enjoyed the book by French and developed a life-long love for mechanics and a wonder for the theory of relativity and Albert Einstein. When I told our teacher that no one in our class really knows anything about Special Relativity he smiled and told that he assumes that we know it. What an irony. Somehow I managed to go through the course on the General Theory of Relativity and of course without understanding and I secured a decent grade and I really have no idea how. Such was my dismal training and I finally could build up some decent idea only when I was doing my doctoral and post-doctoral work.
Functional Analysis was taught in a much better fashion and we learned upto the Closed Graph Theorem and did not move beyond. The course was linear algebra was not very interesting either. In fact I also had to go through a course on Systems Programming which was taught from the book by Donovan. I was completely taken aback since we were leaning a assembly language and I wanted to learn mathematics.
I shudder at the very thought that today I am a Professor of Mathematics and I have such a dismal background. But I realize that it is my love for mathematics that has possibly carried me through.
Again as I have told before that through this blog I wanted to share my excitement of the parts of mathematics which I love. I doing so I also want to refine and relearn the subjects that I love. Euclidean Geometry, Classical Mechanics and Convexity. Albert Einstein will also be a part of our discussion.