Scavenger Hunt

Today, we were supposed to have this event in our college from 10 PM. I was really excited about it from the morning. We have a huge auditorium in our campus where all such cultural events are hosted. We had had a quiz in the afternoon. Prof. Jacobi had invited us to attend his daughter’s eight birthday party. Besides us, the third year undergrads, the second year post-grads had also been invited along with some professors and their families. Prof Archimedes had come with his daughter and Prof Young was also there with his wife. The dinner was excellent, the cake not so good. There was a magic show too. That was pathetic but then it was meant for the kids. Anyway, that’s all beside the point. I came back to my room after dinner to take some rest before the Hunt.

I have never participated in a scavenger hunt before. We have had three scavenger hunts in the last two years, but I organized all of them, so I never got the chance to play.

At 10, I went to the auditorium, quite excited. There were only three of my batch mates sitting in the auditorium. To give you some idea, our batch has a strength of twenty three. Now, here at the Sikinian Institute of Statistics, everyone is very lazy. When an event is supposed to start at 10 PM, it usually starts after 11 PM. But I never thought that this could happen.

Our batch can be broadly subdivided into four groups: the Girls, the Northerners, the Retards and the Easterners. Of course, none of the girls were there. The Northerners were playing FIFA in the TV Room. The Retards were doing what they did best. And some of the Easterners were sleeping or studying while the rest of them came back to the hostel quietly to look for other ways to waste our time.

The list which had lots of interesting items such as coupons with numbers divisible by exquisite primes, and activities such as taking pictures wearing similar t-shirts went into the dustbin.

And this, dear friends is a glimpse of the exquisite campus life at the Sikinian Institute of Statistics.

The Probabilistic Method

This summer, I began studying the Probabilistic Method under Prof. Young from the book The Probabilistic Method by Noga Alon and Joel H Spencer.

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The book is very interesting but equally advanced. I have only managed to complete three chapters in three months. Most of the exercises are beyond me but the subject is fascinating.

The first chapter was about the method itself and a few “basic” examples. Say, we want to find a structure with some desired properties. Sometimes, it’s difficult to find the actual structure. But, what we can do is define a probability space of structures which have these properties. Also, we show that these properties hold in the space with positive probability. Thus, although we can’t find the actual structure(s) with this method, we can confirm its existence.

The second chapter dealt with Linearity of Expectation. Easy enough. The main fact is that if we have some random variables X_1, X_2, ..., X_n and X:= c_1X_1 + ... + c_nX_n, then \mathrm{E}(X) = c_1\mathrm{E}(X_1) + ... + c_n\mathrm{E}(X)_n. The applications this simple result has can never fail to amaze you.

The third chapter was on Alterations. Sometimes, the random structure we deal with may not have all the desired properties. There may be a few “blemishes” as Alon and Spencer put it. Then we tweak the method a bit to remove these blemishes. This chapter is quite non-trivial and requires some higher concepts from general mathematics.

I hope I can finish this book in some time. It will take me more than a year at my current speed and the difficulty seems to be increasing exponentially.

Back to college – Prof. Jacobi in particular

So, after a vacation of two months, I think I’ll start posting again. My semester has begun and life is beginning to become frustrating again. A friend at college has captured this situation with a perfect WhatsApp status:

“Back to the salt mines!”

We have five courses in this semester: Complex Analysis, Differential Geometry, Statistics, Physics and an elective for which I have chosen Representation Theory. The other contenders were Differential Topology, Computer Science and Economics.

Prof. Jacobi has been assigned to teach us Complex Analysis. He has been teaching this course for a couple of years, and he was our favourite to take this course. He wasn’t in campus the first two weeks. He returned this week only.

On Thursday, he took our first class.Within minutes we were enthralled. We know he’s a very lenient teacher. But that didn’t stop him from frightening us. He told us to pass at one go, in his words, “Pass in the front paper itself.” (His English is not the best) Otherwise,

“If you kill my time (by making me prepare a back paper), then I will kill you! Period.”

Whoa!

He told us how Nevanlinna (and Paatero)’s book Introduction to Complex Analysis is like Edmund Hillary and Tenzing Norgay’s conquest of Mt. Everest. Rolf Nevanlinna‘s book is one of the foremost text books in Complex Analysis. We shouldn’t use it as a text book. But we should keep it under our pillows. Everyday before going to sleep, we should study one page of the book. Then we’ll be good mathematicians, he said.

At the end of the class, he recommended Louis Armstrong’s What A Wonderful World and the movie Good Morning, Vietnam. Now that’s the first time a professor has acknowledged the existence of a life outside of Mathematics.

Today, he took a night class to cover for the classes he missed at the beginning. And he was at his best.

“Don’t come to me and ask questions. I won’t able to solve them. Ask your seniors. They are all geniuses. If you ask me to solve your problems, I will ask you to solve my problems. So be prepared.”

He was trying to decide which day he would be able to take another extra class. And he asked a classic question.

“Which day is Tuesday?”

At the very end, he made another one. We usually have 10 marks for homeworks, assignments, quizzes, etc. while the rest is divided among the mid semester and the end semester exams. He wanted to know what we wanted to do for those 10 marks. He said

“Here, no one wants to do anything. I don’t want to set questions, the grader doesn’t want to check answers and you don’t want to study! But unfortunately, we have to do something.”

ROFL

Ganit Anweshan

A few days ago, a couple of friends & I were talking about opening coaching classes like Ramanujan School of Mathematics in Kolkata & Cheenta Ganit Kendra. Before a day had passed, we created sites on WordPress, Google Sites, Facebook, etc.

For our first project, we decided to post a solution of this year’s ISI entrance exam for B.Math & B.Stat. We completed that in two days. Now we are waiting for the CMI paper. Besides that, we also have plans to share our interview stories, to help this year’s applicants.

Here’s a link to our blog on WordPress: Ganit Anweshan

Acronyms in Math

You probably use a lot of acronyms when you write a proof, let it be in an exam or a lecture. And let’s face it. Some of them are very popular and easy to understand:

  • WLOG: Without Loss Of Generality
  • TFAE: The Following Are Equivalent

You have probably seen QED in some texts and even used it, perhaps. But do you know its meaning? Some people joke that it means Quite Easily Done! Actually, it means Quod Erat Demonstrandum, which in Latin, loosely means “that which was to be demonstrated”.

Then, of course, there are the millions of acronyms, such as RTP, TST, ETP, which all mean “to show that”, “enough to show that”, etc.

One acronym I read today in West’s Introduction to Graph Theory is TONCAS. It means The Obvious Necessary Conditions Are Sufficient!

Internships

On Facebook, I see my engineering friends going off here and there to do internships every now and then. They even have workshops during the semester and sitting at home doing nothing is just not an option. Some people manage to visit an IIT, an IIM and some foreign university in their four-year undergraduate course in order to do an internship.

For us, however, it’s different, very different. The students, of course, want to do internships and courses and projects. But there is an alarmingly large number of professors (and parents) who don’t want that. In our institute, Prof. Archimedes tells everyone during admission that an internship is a waste of time. He becomes angry (literally) when someone mails him saying that he/she wants to do a project under him. And he tells everyone’s parents not to let their “kids” go off to other colleges instead of returning home.

Another problem is the behaviors of professors. At every institute, there are usually four-five professors in your field(s) of interest. And it is very likely that at least one of them will not be available during that time, one of them has already got two-three students and doesn’t want any more and the remaining two or three won’t bother to give you a reply. And then of course, some institutes have centralized procedures that ensure your favorite professors are not guiding any projects or you need recommendations or you don’t satisfy the eligibility criteria, or worst of all, the last date was half a year ago.

I understand that we don’t want to study during the semesters but if we are so interested in studying during the summer break, isn’t that a good sign?

PS: Fingers crossed. Hoping to get a project this summer at one of the better colleges.

J S Milne

jamesmilne
An impression of Milne on his site.

James S Milne is a professor of Mathematics at the University of Michigan, Ann Arbor. He mainly works in arithmetic geometry. He has written a few books on the subject as well as some related fields. He hails from New Zealand.

His personal website can be found here.

His site has the most awesome notes on several topics in Algebra, including Group Theory, Ring Theory, Fields and Galois Theory, Algebraic Number Theory, Algebraic Geometry, etc. Here’s a link. I read a few pages of his ANT notes in my first year and I loved it. I am thinking of completing that in the coming summer.

For more information on him, check Wikipedia.