It’s a long time since I last posted on this blog. The last two months, since I returned from Paris, have largely been holiday time for me, and I’ve been doing some miscellaneous stuff to prepare myself for the next important phase of my life. On September 8, just ten days from now, I will board a plane to Chicago, to begin my five-year doctoral programme in mathematics at the University of Chicago.
The first year of the programme at the Universty of Chicago is mainly compulsory coursework. There are three quarters (each three months long) and three course sequences (Algebra, Analysis and Topology). In each quarter, there is one course from each sequence. So a total of nine courses for the first year.
Chicago differs in this respect from other graduate schools. In some graduate schools like Princeton, there is no well-defined framework of compulsory courses, rather students have to pick and choose their courses from a set of recommended courses and prepare themselves for examinations at the end of the first year. From what I can infer, the emphasis in places like Princeton is to get people started on research-like work from a fairly early stage. The pressure to publish thus begins in the first two years itself. In Chicago, on the other hand, there is no pressure to publish; the first few years are meant to strengthen the fundamentals in various areas of mathematics and research is intended for later years.
A couple of months ago, I received an email from Peter May, addressed to all the incoming graduate students, about coursework for the first year. I found that a lot of the material in the courses, particularly the Analysis sequence, was completely unheard of, and thought I should probably start reading up for it. However, I started reading up measure theory and analysis only recently, and am finding it somewhat hard for now. This is probably the consequence of not having done any courses in measure theory and not having a good analysis background. I hope that by contrast, my somewhat better background in algebra will prove an asset to me for the algebra courses, particularly the courses in representation theory and groups. Areas where I have a little, but not a very good, background, are algebraic topology, commutative algebra, and algebraic geometry. In these areas, I hope to keep reasonable pace with the coursework, though I probably will not find it too easy.
I think that the course-based structure for the first year at Chicago will definitely be a help to me so that I can get up to scratch in all important aspects of mathematics. More importantly, I will be able to overcome the fear and reluctance that I currently have with certain kinds of proof techniques and terminology (particularly that of analysis). Another advantage of such a structure is that I will automatically get an opportunity to interact with a number of Chicago faculty members in all branches of mathematics, something I may not be able to achieve of my own initiative. Further, I will also get to interact with my fellow graduate students in and outside the classroom.
In my second year at Chicago, I will be expected to write a paper in a topic of my choice, acquire a working knowledge of a language other than English (I’ll probably choose French, given that have already picked up some French) and submit a master’s thesis. During the second year, I will also be functioning as a Teaching Assistant for an undergraduate math course.
From the third year onwards, I will be expected to start doctoral work full-force, and simultaneously I will need to teach a course of Freshman Calculus. In Chicago, as in many American universities, all freshmen (incoming undergraduate students) need to study one calculus course, irrespective of their stream of specialization. The job of teaching these courses is assigned to doctoral students in the mathematics department.
Currently, it is too early for me to think of questions like what topic I will choose for my thesis, who my thesis advisor will be, how many years it will take me to complete my thesis work, and whether I want to continue to a post-doctoral position in mathematics after that. I do have some ideas and preferences on these counts, but it is only after I go to Chicago and observe the work environment there, and assess my own research abilities in that environment, that I can take the correct decisions. For now, my focus is to equip myself to get the best out of my first year, and to understand the temperament and qualities needed for research, through close observation.