On Comprehensive Examinations

Last week, some members of Mathematics had a meeting with our PhD students to talk about their course work, their inputs about the graduate programme etc.  A sombre mood prevailed at the meeting because these students are now preparing for their comprehensive examinations (also called qualifiers in many other places) in the last week of July.  Clearing the comprehensives is necessary for them to continue in the programme.  Over here, this means that they will write exams in three foundational topics, like analysis, algebra, topology or discrete mathematics, for which they have been prepared through course work over the last year.  They are allowed two attempts in each subject within a limited time duration, but for almost all of them, the July exam will be the first attempt.

The students were worried about the extensive syllabus for the exams (they were not as worried when this syllabus had been broken down into different courses) and expressed concern over the passing mark etc.  To allay their apprehensions, one of my colleagues told them that the exam was a way of testing their grasp of fundamental topics.  While it is very important that they focus exclusively on preparing for these exams for the remaining part of the summer, they should not feel stressed and take small breaks if they are feeling very exhausted with the preparation.  All the faculty members present shared memories of their own comprehensive exams very candidly- when and how they took it and how they chose their PhD topics after the exams.

These exams, when thought of by themselves, do seem monstrous.  But, it helps a lot if one sees them as a phase of the PhD program, after which the students can start independent study and pick up topics that they really enjoy.  Although we hope that the meeting made these students feel better, the pressure will of course persist until these exams are cleared and left behind.

This meeting brought back some memories about my comprehensive exams, way back in 2004!  The programme at my grad school was structured differently from the Mathematics programme at IISER Pune.  Students were assigned a supervisor upon joining and were expected to pursue course work and their research projects simultaneously.  The comprehensive examination was usually conducted in the second year of the program, but could also be postponed till the third year.  For this exam, the student had to submit a research proposal, give a talk on it and then face an interview in which they were quizzed about the proposal.  The interview was not restricted to what was written on the proposal - it could have questions about any fundamental topics which the committee felt the student should know before embarking upon the proposed project.

Students would usually take their comprehensive exams during the summer to avoid clashes with their course work.  However, I really wanted to go to India during the summer.  So, my advisor (Prof. RM) suggested that I take the exam during term time.  I wrote up the proposal during Christmas vacation and after running it by Prof. RM, submitted it some time in January.  The exam was scheduled exactly after a month.  Meanwhile, in that semester, I was taking three courses and also teaching a first year course to a large class (this was my first teaching experience).

The real fun started after the submission of the proposal.  Other than my advisor, there were three members in the committee, out of which one was the meeting coordinator and two (Member 1 and Member 2) were subject experts.  I submitted the proposals to them in person and asked them to give me some feedback before the exam.  Member 1 read the proposal within two days of submission and gave me some feedback about what parts needed clarification, details etc.

Member 2 was a formidable senior number theorist, of whom most grad students were very scared. The courses offered by him (almost all of which I had taken) were very challenging.  I have spent a lot of sleepless nights working through his assignments.  When I went to his office to give him the write-up, he sternly glanced at it for a few minutes and mentioned a book that he expected me to master before the exam.  I almost fell off the chair [1].  He said that he did not believe in students taking exams unless they were thoroughly prepared and went on to describe some students whom he had examined before and who had failed the comps.  

Struck by lightning and dazed, I went straight to Prof. RM's office, told him about the conversation with Member 2 and requested that the exam be postponed.  I was ready to sacrifice the India trip.  The conversation that took place afterwards is a great example of how to supervise a student!

He explained to me the basic objective of the exam: to test whether the student understands fundamental concepts and techniques that would be needed for his/her research project.  He then went to the board, mentioned a problem in elementary number theory [2] and we started discussing how one solves it.  He then mentioned that the purpose of the comprehensive exam is to make sure, for example, that I can apply fundamental summation techniques to such questions before I embark on a research project.  He then took out the book mentioned by Member 2 from his bookshelf and we went through the table of contents.  I realized that I already knew many topics from this book.  He pointed out the other sections that were relevant to my proposal and convinced me that by working for two hours a day on this book, I will master these topics and be ready to face the comps within a month.

When I again expressed my inability to do this, he started talking about the good things that would happen if I could clear the comprehensive exam within a month.  "You can visit your family, relax [3] and come back with a fresh mind to work on your research problem.  You can finish by early 2006 and also invite your father for the convocation ceremony in the summer." I got convinced that adhering to the above timelines would be great and decided not to postpone my exam.

I came out of the office feeling relieved and much more confident.  I woke up two hours earlier every morning and worked through several sections of the book.   

My exam lasted for one and a half hours.  Members started by asking me basic definitions, examples, non-examples related to modular forms.  After the warm up, I was asked to prove some lemmas mentioned in the proposal and was asked if it was possible to generalize them to other cases [4]. Member 2 came prepared with a long list of questions, as expected.  As we ran out of time, we could not cover all his questions.  So, he graciously gave me a xerox copy of his questionnaire. The exam was not half as dreadful as I had anticipated and I was declared passed.

It was lunch time when the interview ended.  After lunch, I attended a class taught by Member 1 and taught my first year course.  Later in the evening, I had dinner at my favourite Indian restaurant and saw a Hindi movie with a Japanese friend.

In the next teaching semester, Member 2 also offered a course on the topics that he had asked me to learn before the exam.  I took this course.  Later, he gave me valuable inputs and feedback for my thesis and also wrote reference letters for my job applications.

To all students taking comprehensives this summer, all the very best.  Study well, take it easy and think of all the good things that will follow after you are done with them!


[1] For those who know what I am writing about, he asked me to master Serge Lang's  "Introduction to Modular Forms" and a proof of the Eichler-Selberg trace formula (it wasn't enough to just know the proof for the level 1 case).  He was particularly insistent upon Atkin-Lehner theory.

[2] Average order of the divisor function (counting the number of divisors of $n$). 

[3] As an added incentive, he recommended some very nice non-math books to read in the summer.

[4] Again, for those who know what I am talking about, I was asked to write out the terms of the Eichler-Selberg trace formula and evaluate them for specific cases.  A lot of the questions were about class numbers of binary quadratic forms and about Dirichlet characters.

The cadet's life

A few days ago, Prof. Sanghi wrote a very interesting post on his blog about his SSB interview (for entry into NDA) as a youngster.  I sent the link to my father, a retired army officer.  He was in splits after reading it, especially the twist at the end [0]. The blog post is now being circulated among his NDA batch mates.

Of course, his own circumstances were completely different from Prof. Sanghi.  His entire school life revolved around preparing for getting into NDA.  At the age of 8, he heard some friends talking about brave soldiers and Sainik Schools.  The idea of becoming a soldier immediately fascinated him and he requested his father to get him an admission form for such a school, which his father obtained most willingly as it involved a government-subsidised education.  He joined Sainik School Tilaiya the following year.  Sainik Schools have been solely created for preparing students to join the services.  The following statement in the vision document of Sainik School Tilaiya says it all:

The primary aim of Sainik School is to prepare boys academically, physically and  mentally for entry into the Defence Services and those who do not make the grade, for responsible positions in various other walks of life.

Therefore, for him and almost all his schoolmates, the entire spectrum of competitive exams started and ended at the admission test for NDA.  It was a do-or-die kind of situation.  The school thoroughly trained them for all stages of the interview.  His memories of the SSB interview are not very vivid, but he remembers the feeling of relief and celebration when he saw his name in the selection list.

He also vaguely remembers the bus which came to pick up young recruits at Pune railway station to take them to NDA and how the recruits sat quietly without making any effort to communicate with each other.  All the memories that he now shares with us are after he joined NDA.  And yes, Prof. Sanghi is right!  Riding a bicycle from Khadakwasla to Bangalore is a breeze in comparison with the grueling schedule of an NDA cadet.

Picture this: the cadets woke up at 5 am and were served tea and two biscuits (which they called "dog" biscuits).  After that, they had three 40-minute classes, out of which two were related to physical training, drill or horse riding and one was a theory class [1]. After that, they had about a quarter of an hour to cycle back a distance of about two kilometres, take a shower, change into their impeccable uniforms, have breakfast at the mess and report to the academic building for six more theory classes.  At the mess, they could eat as much as they liked (the only restriction was on the amount of butter), but following a very rigid table etiquette and within 10-15 minutes.

The six classes included academic subjects like Physics, Chemistry, Mathematics, Social Sciences, along with service subjects like battlecraft, map reading, field engineering etc.

At 1 pm, they reported for lunch and had an official rest period from 2 to 3 pm.  At 3 pm, they were served another round of tea with "dog" biscuits.  They played sports from 3.30 to 5 pm, after which they had to shower, change and gather at what they called the ante-room, where they were read out orders and announcements relevant to the next day.

6 to 8 pm was prep period, during which they had to stay in their rooms and study.
Each cadet had to keep all the doors and windows of his room open as the duty officer dropped by to inspect whether the cadet was really studying or not!  Dinner was served from 8 to 9 pm, after which they prepared to go to sleep.  10 pm was the "lights out" time.

The following are some of the mistakes which would earn you punishments:


1) Reporting late for any session/class.
2) Wearing a uniform with any kind of defect (for example, unpolished shoes!)
3) Caught not studying during prep period
4) Dozing off during class
5) Not slinging your satchel across your back while cycling (ie, not holding your satchel in this manner while cycling)
6) Indulging in any activity after "lights out" (It's a different matter that this was also the time when the new students were gathered in the corridor and ragged.  This was 40 years ago.  This practice must have stopped now.) 
7) Speaking back to a senior or calling him "nuts" to his face :-)
8) Not being particular about your crew cut hairstyle

Forms of punishment (which were levied during the rest periods or on Sunday mornings) could include:

a) A walk up to Sinhgadh Fort and back (a distance of about 20 kms) in your battle dress carrying a heavy load [called Pitthoo]
b) Picking up your cycle and running around a training ground
c) Rolling your way through a training ground [2]

Cadets spend 3 years at NDA (a total of six terms). They have to indicate at the application stage itself whether they want to join army, air force or navy, but it is only in the sixth term that they do course work based on their choices.  In theory, they can apply to change their preference in the third semester, but it is very rare to have this change approved. [3]

After 3 years of training, the cadets receive their graduation on one of the most important days of their lives, the day of the POP (Passing Out Parade) and become gentlemen cadets.  My father tells us with a lot of pride how his whole family attended his POP and gets angry when my brother points out the other meaning of "passing out". (Imagine a contingent of cadets "passing out" in front of Indira Gandhi.)

After that, the cadet, now a gentleman cadet (GC), spends a year at the Indian Air Force/Military/Navy Academy before he gets commissioned as an officer [4].  A lot of their instructors are non-commissioned officers (NCOs) or Junior Commissioned Officers.   They are very strict with the GCs.  But, as soon as the graduation ceremony/POP is over, the GCs, as commissioned officers,  become technically senior to them.  The instructors now salute them and address them as Sir.

When I told my father that I was moving to Pune, he was thrilled.  He associates Pune with the beginning of many positive things in his life.  Earlier this year, when he accompanied me here, he took me for a visit to NDA.  While we were there, I got to see all the places where he had trained/studied/been punished as a cadet.  He even managed to show me the room where he had lived as a cadet 40 years ago.
The senior cadets currently staying in his Squadron (called Golf Squadron) welcomed us warmly.  They were very happy to meet an ex-Golfie, even though he was 40 years senior.  We were visiting on the day after the induction of a fresh batch and the freshers had been gathered in the corridor after getting their crew-cut to receive further instruction.  They looked very nervous and shyly shook hands with my father.

I tried to imagine my father in their position in the winter of 1973.  Could he possibly have foreseen that one day, he would bring his grown up daughter to the very same spot?  I am sure he had a far more pressing issue to think about at that time: namely, if he will survive the stringent training!


[0] Incidentally, my father weighed a little over 41 kgs at the time of his interview (after being fed a diet with lots of bananas) and barely made it through.

[1] A quick look at this page gives a good overview of their academic programme. The last sentence summarizes it the best:the aim is to achieve excellence in academic pursuits without compromising on outdoor activities. 

[2] Interestingly, while there are many strenuous forms of punishment, it is against NDA code to levy any punishment to cadets which involves going hungry.  Cadets are never, ever asked to give up any meal or eat very little as punishment.

[3] My father gave army as his first preference while filling up his application form.  Later, he saw the movie "The Blue Max" and tried to change over to Air Force in his third semester, but did not succeed.
[4] One cannot refer to a cadet as "s/he".  NDA and IMA still remain male bastions (and I suspect, will remain so for a long time).  Other than in Medical Corps, women still do not receive permanent commission in the services.  Those who join on Short Service Commission are trained at the Officers Training Academy at Chennai (and now also at Gaya).

Breaking news about PC Mahalanobis?

Check out the latest revelation by Deccan Herald! You may also follow this link for as long as it exists!

(On a lighter note) What not to do on a job visit

Writing about the goodness of February brought back some memories of different job interviews I have faced.  In almost all of them, I have made blunders that I am not very proud of.  As some readers of this blog have just finished interviewing or have interviews coming up soon, I thought I will share some of my job-interview-mishaps.

My first interview was within the first year of finishing my PhD.  I wanted to gain a few years of postdoctoral experience, but applied for this tenure-track position in Canada on the advice of my mentors.  Much to my surprise, I got shortlisted and was invited for the interview.  Clueless about what happens during job interviews, I asked a colleague who helpfully told me, "Don't get nervous.  The committee will not harm you." Throughout the pleasant train journey to this university, I kept repeating this to myself.

Here's how the interview began:

Committee Member 1: Is this your first job interview?
K: Yes
Committee Member 2: Are you nervous?
K: No, I am fine, thank you.
Just then CM 3, the senior-most mathematician, started coughing.
CM 2: Oh, it looks like CM 3 is getting nervous.
K: Don't get nervous. I won't harm you.

Everyone in the room, except CM 3,  started laughing and the interview proceeded very smoothly thereafter.  I did not get this job, but I am sure it was not because of this goof-up.

Now, Goof up 1 at IISER Kolkata:

IISER Kolkata had shown a lot of interest in my application and I was looking forward to my visit there.  Just before I left for Kolkata, my brother jokingly mentioned that I should play up my Bengali connection as that might help (no offence intended - it was said merely in jest. [1]).  Now, I have no Bengali connection, except that my last name is also a common last name in Bengal.

During my visit, here's how a conversation went with a senior colleague at IISERK:

SC: Hello, Koneenika
K: Hello.  err, it's Kaneenika
SC: Aren't you Bengali?
K: No.
SC: From your name, I thought you are Bengali.
K: (suddenly realizes that she has passed up a great opportunity to play up the Bengali connection and tries to make amends) I am not Bengali, but I have spent a formative period of my childhood in Bengal.
SC: That's interesting.
(On further grilling, it is revealed that this formative period of K's childhood was at Darjeeling for a few months when she was 1 year old.)
SC: (laughs and says) You have understood the Bengali psyche very well.

Goof up 2 at IISERK (and I still feel very embarrassed whenever I think of it):

On the morning of my departure, at breakfast with a senior colleague and a colleague from Mathematics:

SC:  So, are you flying back to Edmonton now?
K: No, I am also visiting City A before flying back.
SC: I see. Who is your host there?
K: Institute ABC.
SC (in a nostalgic tone, tells us about his job search long ago and return to India): In our days, we were lucky if we had one job offer. Your generation gets to choose between multiple job offers.
K (feels that it was perhaps not appropriate to bring up another prospective institute in the conversation and desperately wants to say something to change the topic and save the day.  So, with the noblest of intentions, says):  Yes, our generation is lucky.  You guys worked very hard and we are reaping the benefits.
SC: (Not amused at being addressed as one of "you guys", but maintains a practiced calm and stays quiet).
Other colleague: (Almost falling off the chair)
K: (blushes as she realizes her poor choice of words) I had a very nice time here. Thank you for your hospitality.

The conversation proceeds smoothly after that. [2,3]



And now the goof-up at IISER Pune:

CM:  What activity did you enjoy the most at IISERK?
K: (interprets the word "activity" to mean conferences, winter schools etc) I enjoyed organizing two winter schools at IISERK. (Then explains how much fun it was to interact with so many students from all parts of India and the experience of organizing something from scratch).
CM: (looks a little surprised and then explains) I am sure you must also have enjoyed your teaching and research activities there.
K: (then realizes her mistake, is embarrassed and starts talking about her research and teaching)

After coming out of the meeting room, she spoke to a future colleague about how she misinterpreted the word "activity" and gave an inappropriate answer.

Colleague: Oh no, I think they were asking about your hobbies.
K: (suddenly feels much better)


Readers are welcome to share interview-mishaps (either theirs or those of others) in the comments section.

Just out of curiosity, what would you have interpreted "activity" to mean?






[1]  He later wrote here about his experience in Bengal.

[2] In my first few days at IISER K, I shocked a lot of people with my informal language.  For instance,  I was told that it was impolite to refer to women/lady faculty members as female faculty (or men/gentlemen  faculty members as male faculty for that matter).

[3] I used the word "guys" in a generic sense to mean both men and women.

New office

My stay at IISER Pune has been going very well. Last week in particular was very exciting.  Members of the Mathematics group moved to the permanent campus.
IISER P is building an integrated academic building, which will house all the sciences in different but connected wings.  The construction of this building is well underway.  However, for the time being, we have been moved to another building in the permanent campus, which has the guest house and conference facilities.  The management has very generously converted some rooms into single-occupant offices and provided them to us until the academic building is ready.

I am happy about this move for various reasons.  To start with, for the first time in my life, I have my own office.  It is very spacious - the kind of office in which groups of students can drop by and sit comfortably while I show them something on the board.  We can have animated discussions without disturbing any office mate!  The cafeteria is on the ground floor of the same building - so, no more commutes to have lunch.  I teach my course in a classroom on the same floor.  So, all in all, the management has made a very comfortable arrangement for us, even though it is temporary.

I also like being in the permanent campus of my institute for some emotional reasons.  Somehow, it gives me the uninhibited feeling of being in my own space.  I enjoy being able to walk around the gardens adjoining the building.  I can also enjoy the excitement of observing the progress in the construction of the academic building right next door.  Recently, our registrar and the co-ordinator of Mathematics took some of us for a short trip to this upcoming building.  We went to the floor designated for our group.  My colleagues and I were so happy that we even started self-allocating our offices-to-be (although I am sure we will have forgotten this by the time the building is ready to be occupied).

Happy one month!

I have now completed a month at IISERP.  Apart from some delays in arrival of my household luggage from IISERK and acquiring internet connection at home, the transition has been very smooth.  Well equipped office space was alloted to me on Day 1, administrative joining-in formalities were done promptly, I found a suitable apartment [1] and got a new car on Day 2 and started driving practice immediately thereafter [2].  While I waited for my luggage etc to arrive from N1, I enjoyed the warm hospitality at my favourite guest house.

My colleague, Prof. Sunil Mukhi, who joined a couple of months ago, summarizes his impressions of IISERP very well in this post and I couldn't agree more.

Here are some things that I like most about my new workplace:

1) The Mathematics group, of which I am a member, is fairly well staffed.  Other than a comfortable teaching load, this ensures that committee work and other responsibilities get evenly distributed among all members.  So, while a couple of colleagues can focus on, say, building the course curriculum, some others can take care of student counseling etc.  One group takes care of seminars etc and another takes care of library matters pertaining to Mathematics.  We even have a Happiness Committee which organizes regular get-togethers to facilitate interaction between faculty and students.  I will write later about the responsibilities given to me.

2) We have a separate course structure for PhD students.  Mathematics graduate students need more course preparation than other STEM fields and we have the requisite courses to offer to our students.  My student seems to be benefiting from this a lot.  While he has started work on his PhD project, he is taking some core foundational courses that he had missed out before.

3) My colleagues, including the senior ones, across all STEM fields, are in general, very friendly and approachable.  This is totally not meant as a complaint, but it took me a lot of time to make friends in my former workplace.  For months, I went to the office, did my work and came back home without talking to anyone.  It was more common there for people from the same grad school to hang out together.
By contrast, over here, it is impossible to be left alone in a corner while having lunch at the faculty lounge.  Even if people come in groups, they reach out and talk to others on the table.  I like that very much.







[1] "Suitable" is an understatement!  This apartment is a dream.  The kitchen itself is bigger than the biggest room of my previous dwelling!

The worst kept secret ever?

This blog is no longer anonymous.  Well, frankly speaking, it never was, really! The Indian science community is very small and the things that I like to write about (or can write about) also make it very easy for people to search me if they want to!
In fact, I just realized that anyone who figures out that I am at an IISER (super-obvious) and do Mathematics (easy to see because I don't talk about setting up labs etc) can put the search words "IISER Mathematics blog" on google and be directed to my webpage!

So, N1 = IISER Kolkata

New1 = IISER Pune

My STEM field: Mathematics

I never really cared about people discovering my identity, but an anonymous blog stylistically made it easier to write about certain people and incidents without revealing their names.  Hence, the reluctance to go public!

But, I am aware that many people at IISER Pune read this blog (I don't think this was the case at IISER K). [1]

So, it is a little awkward to pretend to be anonymous!

Going public also gives me more freedom to write about Mathematics-based issues and about life in Pune, which I am enjoying very much [2].

IISER Pune, my new academic garden, is a lovely place.  I am very happy to be here and will be writing more about it shortly.  Stay tuned!



[1] A few days ago, Professor VS Rao, the registrar at IISERP, mentioned that he appreciated a certain post I wrote about the guest house at IISERP.  When I asked him how he figured out that I was writing the blog, he thought I was joking! :-)

[2] One of the things, for example, which is very Pune-specific, is that the National Defence Academy is located here.  It is my father's alma mater.  I visited it for the first time a couple of weeks ago and it was an extremely profound experience, about which I would like to write one of these days.