A winter well spent: AFS 1, IISER Pune

My endless procrastination about writing this post finally gave way when a best friend updated her own blog after centuries of dormancy (and also the fact that I woke up early on a Sunday morning!).

This blog-post is important because very few people in Kgp are aware of opportunities like AFS or institutes like IISERs (not that my blog is a popular news segment here but I'd like to do what I can).

I spent my December (2011) at the Indian Institute of Science Education and Research, Pune attending the Annual Foundation School - Part 1 (5th to 31st December) in Mathematics, organised in three phases every year by the National Board of Higher Education in Mathematics (NBHM). This school is meant for Mathematics Phd students in India in their first and second years of research. I wasn't selected for good reason but I insisted I wanted to attend it anyway and would arrange my own accommodation and food. My tenacity and Prof Katre's (organiser) goodness led me to IISER, and in a stroke of good luck, some registered students didn't show up getting me and a batchmate (Anirban Das) their place on the list. And thus I spent one of my best winters there with the biggest knowledge-gain/time ratio. I will summarise it under the following heads:


1. The Institute (IISER, Pune): 

IISER Pune reception

These institutes are a great initiative by the Government of India to increase focus on research and education in the pure sciences in a engineering-dominated India. I would like to see these institutes pwn IITs some day. No, really! It is high time parents stop pushing their kids to clear JEE and become "engineers". We (Indians) have done far too much low-level labor work in all industries. We need students to appreciate the pure sciences and do some state of the art research. 

IISER Pune is under construction but the main building is up and functional. The overall campus plan is quite extravagant and impressive. The rooms allotted to us were very big and comfortable and the food was simply amazing. They served us soup and dessert for lunch and dinner every single day!

The canteen

Pune itself is a city teeming with students and young company recruits, nice cafes and pubs in every nook and cranny, and a beautiful hilly landscape enveloping it. 
I loved the city.

2. AFS, the school and the teachers:

Lecture room

The school is a very good way to introduce a lot of advanced math in a very short span of time, with the intent of providing ample motivation to study the topics in detail later than on detailed exposition. We were provided a lot of supporting texts - books, lectures notes etc. There were three broad fields - Topology, Algebra and Analysis, with 6 hours of lectures and 4 hours of tutorial for each per week for four weeks. We were taught by 12 professors in total. All the professors were respected mathematicians from all over the country and more importantly good teachers. 

The syllabus that was covered is as follows:

Sr no.

Topic

Faculty, home institute

Book recommended

1. Differential Topology 

i	review of differential calculus, inverse and implicit function theorems, linearity of derivative, smooth maps	Prof. H. Bhate, Univ of Pune	Elements of Differential Topology by Anant R. Shastri
ii	Topological manifolds, Gluing Lemma, Classification of 1-d manifolds	Prof. Rama Mishra, IISER Pune	Differential Topology by Gillman and Pollack
iii	Sard and browns theorem, degree module 2 of a smooth homotopy, oriented manifolds and Brouwer degree	Prof. Krishna Kaipa, IIT Bombay	Topology from a Differential Viewpoint by John W. Milnor
iv	Morse functions, Morse Lemma,Connected sum, attaching handles, Handle decompostion theorem.	Prof. S Shastry	An introduction to Morse theory by Matsumoto

2. Algebra

i	Modules over Commutative rings/PIDs, Structure theorem	Prof. Rabeya Basu, IISER Pune	Algebra 1 by Jacobson
ii	Group Action, Sylow and Cauchy theorems, Solvable groups, Jorden Holder theorem, Nilpotent groups	Prof. Sudhir Ghorpade, IIT Bombay	Algebra by M. Artin, Alegbra by Lang
iii	Representation theory- group representations, semi simple and simple rings and modules	Prof. Gurmeet Bakshi, Punjab University	Lecture notes provided
iv	Free gorups, Matrix groups, Rigid motions	Prof. S. Katre	Lecture notes provided

3. Analysis

i	Introduction to the concept of outer measure, completion of a measure, construction of the Lebesgue measure, non-measurable sets	Prof. Sameer Chavan, IIT Kanpur	Real Analysis  by Stein and Sakarchi
ii	Measurable functions, Cantor function, almost uniform convergence, Egoroff and Lusin’s theorems, convergence in measure	Prof. V.M Sholapurkar, S.P College, Pune	Real Analysis by Stein and Sakarchi
iii	Integration, monotone and dominated convergence theorems, comparison with the Riemann integral, signed measures, Reimann-Lebesgue lemma	Prof. Diganta Borah	Lecture notes provided
iv	L^p spaces, l^2 space, Riesz Fisher Theorem, Fourier series, Fejer theorem, Fubini’s theorem, Fourier transform	Prof. Debraj Chakraborty, TiFR Bangalore	Real Analysis by Wheeden and Zygmund

As you can see, so much crammed in a month got just too much at times. I used to bunk lectures whenever I got overwhelmed (I was one of only two undergraduates with very little pre-requisite knowledge). But I tried to soak in as much as I could, knowing that this was an opportunity not to be wasted - to learn from pedagogically blessed teachers. I want to mention some professors in particular who had a huge impact on me:

Prof. Ghorpade: His charming style of teaching made everyone hang on to his every word. In a span of three days he managed to get to know the students personally - something which every student values dearly. He was friendly and very funny making very intense topics seem quite bearable.

Prof. Debraj Chakraborty: An ex-IIT Kharagpur alumnus and an incredibly ingenuous person, he and I bonded over our mutual resentment of the quality of education in Kgp and nostalgia of the campus life. A very enthused teacher whose energy is quite infectious, he made me relinquish my hatred for certain topics by treating them beautifully, opening my eyes to a whole new area - applied mathematics.

Prof. Krishna Kaipa: The most good looking Mathematics teacher I have ever come across (I am not kidding! We had a running joke that his research area should have been Mathematical Modelling :P), whose excellent clarity in communicating complex mathematical ideas immediately superseded his looks. I had been completely bewildered by the differential topology topics covered till then and had given up but was still able to understand, in essence, the portions he taught at the school.

Prof. Sholapurkar: A very experienced professor, he would encourage us to think and not be afraid of making mistakes. He left us with a very inspiring quote by Henry Lebesgue, "The only instruction which a professor can give, in my opinion, is to think in front of his students." and he truly lived up to it.

2. Friends, trips and fun:

My school friend Shreya studies in Pune so I had a very great time hanging out with her and her PG mates. The AFS group itself was very small, resulting in good bonding among the students.

Mahabaleshwar trip

Sundays were the only holiday and we all managed to go on two major outings - Mahabaleshwar and Sinhgad Fort. The former was quite a big disaster since we barely got to spend any time on the ground - we were stranded in the bus for the major part of the day. Still, it had its fun moments. Sinhgad fort trek was surprisingly awesome fun. We followed impossible trails and were burnt out every 10 minutes, only to pant and stop for a nimbu pani. We kept asking those returning how much farther we had to go and they would smile and say, "15 minutes only" and we would take a deep breath and continue (it took us exactly 2.5 hours from the first 15 min answer). The view from the top was breathtaking and totally worth the sweat. I bet I lost some 5 kgs that day! (I would atleast like to believe so.)

Sinhgad Trek

3. Concluding thoughts:

I learnt more than I ever can in such a short span of time - and not just academically, I learnt how little I know and how much there is to know - an exciting thought that one will never really know just enough. I was also appalled by the state of higher mathematical education and research in India. I had a very romantic take on the love of Maths leading one to dedicate ones life to its study and research. I was little short of heart broken to discover that for the majority of the students doing a math Phd in India, it is simply a career, a way to secure a job, an easy way out. 

On being forced to think about the bigger picture, it made sense - we live in a very populated, underdeveloped country where focus is entirely on being able to secure food, clothing and shelter. The popular and more monetarily desirable options - engineering and medicine - are fiercely competed for with a very small fraction of percentage being lucky to land it, leaving the rest with an inferiority complex and plan B - academia.
It is sad at so many levels.

Even the Government is so misguided in its attempt to improve the situation that it started a wrongly motivated scholarships like INSPIRE (click on the link for the eligibility criterion). Bribing the so-called "bright" students to take up sciences, really? Is that what it has come to? Beguiling naive young minds with big money as bait to a life of simplicity and austerity - can anything be more ironical!

I met some very good people (teachers and students) this winter and it is them to whom I dedicate this post but as Paul Lockhart points out in "A Mathematician's Lament", not much has changed since this experience of Bertrand Russel -

“I was made to learn by heart: ‘The square of the sum of two
numbers is equal to the sum of their squares increased by twice
their product.’ I had not the vaguest idea what this meant and
when I could not remember the words, my tutor threw the book at
my head, which did not stimulate my intellect in any way.”