Tales of a teacher

A few days ago, I realized that I have now been teaching for 20 years. I taught my first course in the Spring of 2004, as a 23 year old PhD student. Once the teaching committee at my university identified grad students who could do a reasonable job on the blackboard and were ready to face large classes, they would give us an option to either teach a full semester course, followed by a teaching-free semester, or perform teaching assistantship duties such as marking and tutoring for both semesters. I chose the former option. My very first course as an instructor was in the year when I was to take my comprehensive examination, which would determine if I could stay on for a PhD or not. 

This was a service course in linear algebra for a class of around 80 students: most students taking the course were from other departments, and had to take this as a required course. Many students were in the senior years of their programme. So, it turned out that many were older than me. Some had decided to start or resume university studies after several years: in some cases, their children were in university at the same time, and would help them with the assignments. I continued to see this phenomenon through all the years that I was in Canada. Teaching in Canada gave me a chance to experience their culture in a unique setting. I also learnt how much these people valued politeness, kindness and sensitivity. On one occasion, for example, an older student was concerned that I was looking unwell, and offered to drive me to the medical clinic, as there was heavy snowfall outside. Students would regularly show up for office hours, and apart from working on their assignments, we would occasionally discuss other parts of our lives: this is how the class came to know that I was getting ready to face the dreaded comprehensive examination. On the day of the exam, a large part of the class showed up for the "public" part of the exam: the research proposal had to be presented in a 20 minute presentation. They probably did not understand any part of the talk, but showed up to support and encourage me. I deeply value this memory. 

I taught again the next year; this time, I was teaching a course in Complex Analysis to 100+ engineering students. In complete contrast to the previous class, these were a bunch of brats: this was the only class I've ever taught where I had to request students to not whistle in class [1]. After a few lectures, a sombre mood prevailed in the class. Complex Analysis has this effect on most of humanity. We started getting on well, and the course proceeded smoothly. One other crazy experience with this batch was on St. Patrick's day (or was it the morning after?) While half of the class was absent, the other half showed up drunk. Let's just say that thanks to this class, I had the "now, I've seen it all" moment quite early in my teaching life! No other batch of students has come close to putting me through what this class did.

The year after that, I was getting ready to defend my thesis. I was again assigned the same course in Linear Algebra that I had taught before: this time, the students got to know about my defence date [2], and some showed up for the public presentation. To make the presentation more relatable to them, I kept using words from linear algebra such as finite dimensional vector space, diagonalizable linear operators, basis of eigenforms etc (in the context of my thesis work, of course) which made some members of my defence committee smile. Incidentally, my class was scheduled soon after the defence, but I had requested a friend to cover for me. While the students sauntered down the hall after the presentation, she waited outside the defence room while I went through the closed-door exam. We cut a celebratory cake with some other friends after I was declared a "Doctor", and she ran down to teach my class, while I sat numb and dazed in the lounge [3].

My teaching reviews that semester were filled with congratulatory messages. In these reviews, I got some of the earliest reference letters of my career: several students recommended that I be hired as a "full-time" professor. 

My first faculty position (or as my former students would put it, my first position as a "full-time professor") was at IISER Kolkata, which was then functioning out of a temporary campus on the ruins of an older university. For my very first course, we did not have a classroom. So, some chairs were arranged next to a board in a computer lab. While the students were excellent and super-motivated (one of the best things I like about being at an IISER), one vague memory I have is of the director or some HOD often walking into the lab with a prospective faculty candidate to show them the computational facilities. The candidate would often shoot a confused glance when they saw me lecturing to a handful of students, while people worked on their computers in the other half of the room.

For the next batch, I managed to get a classroom. It had a pillar right in front of the board. Every single day, I had to resist the temptation to swing around it like Shah Rukh Khan in Swades (in case you don't know which scene I am talking about, watch here from 2.25 onwards). Sometimes, clueless goats and cows would wander into our classroom. I was fortunately spared the experience of snakes entering the classroom (they seemed to have a preference for labs, hostels and faculty homes, including mine). On one occasion, due to a failure of coordination between IISER security and that of the university that we were functioning from, the building gate was locked with all of us inside. Again, I have a vague memory of it raining and the mobile networks not working: so, it took a while for someone to come and let us out [4]. The good thing is that with all these shared experiences, this batch and I developed a special affinity: students from this batch still call me up or email me on Teachers' Day, and also stay in touch with me. 

Soon, I moved to IISER Pune. Almost all my teaching has happened here. In the 20 years since my first course in the Spring of 2004, I've now taught all kinds of courses at many levels: from first year undergrad to PhD students, with class sizes ranging from 2 to 200, including general, introductory courses, standard courses for math majors, specialized topics courses (one of which led to writing a book) and PhD-level courses. Fortunately, I never again had to deal with students whistling in class, or showing up drunk (not that I know of, anyway). I occasionally see people scrolling on their phones or falling asleep: but that is okay, as long as they do not disrupt the class. 

The pandemic teaching was an entirely different experience: for nearly two years, I lectured to an empty class, my lectures were recorded by the staff members from our Science Media Centre (who, surprisingly, never fell asleep in the lectures) and the recordings were shared with students. 

One of my most recent experiences was in Autumn 2023, when I taught probability to a large class of 200 students. I was curious about this experiment: I was teaching probability for the first time, and to a batch of students who had finished the last few years of their school in online mode due to the pandemic. In addition, many of our students in the early years have not had mathematics in Classes 11th and 12th. The course had its challenges, but was successful overall. In fact, the teaching reviews indicate that I seem to have taught long enough to develop a sense of humour.

In complete contrast, this semester, I am teaching a course on Fourier Analysis to a small class of 7 math majors in the fourth year. Thanks to their previous preparation and high motivation levels, we finished more than 90 percent of the syllabus before the midsem. So, we now have the freedom to explore more advanced topics. I am using this opportunity to learn a new topic and teach it to them as well, namely Fourier analysis and the theory of uniform distribution on compact topological groups. Fourier analysis mostly focuses on one particular such group, namely the unit circle. From what I am learning so far, showing it all as a special example of a more general theory makes the treatment of the subject neater and more elegant. 

This course (and the larger experience of teaching over the last 20 years) has taught me how closely intertwined the experiences of self-study, learning and teaching are. May this go on.

[1] "Request" is a euphemism. My exact question was: "Am I in a university class, or a fish market?" The whistling stopped, but some students told me later that they were confused by the allusion to a fish market. This seemed to be a uniquely cultural phrase, that is more relatable to Indians than Canadians. 

[2]  From their super-chatty prof, naturally :-)

[3] In retrospect, I suppose I could have pushed myself a little more to teach the class as well.

[4] If you visit the sophisticated, permanent campus of IISER Kolkata today, you will have no inkling of how it was in the early days.