I am having a hard time deciding what to do for my master's degree in mathematics.
Something about my background:
I have a general B.Sc. degree in mathematics from a (top 10 for arts and sciences, not sure what this means though, if at all) college in India. This is a 3 year bachelor's degree. The course structure allows you to specialize only in your third and final year, before which you take courses in three different subjects. I took physics and statistics, in addition to mathematics, until my second year.
Coursework: I really haven't taken much mathematics coursework, which I suppose is reasonable given that mathematics was only a little more than 50% of the course load of a three year degree. This involved a pretty standard four semester calculus and differential equations sequence, linear algebra (Sheldon Axler), real analysis (about the level of baby Rudin) with measure theory, introductory complex analysis, topology, differential geometry, PDEs, dynamical systems, number theory and two semesters of abstract algebra. In addition, my stats courses covered some mathematical statistics and statistical inference.
I have no research experience, something I would really like to gain during my master's degree. It seems rewarding for one, and secondly, it help me decide whether I really want to continue onward to do a PhD.
This is not much beyond "basic" undergraduate coursework, and one of my reasons for wanting to do a master's degree is to clarify my interests and a direction for my future career, whether in academia or not. Also, a 2 year master's + 3 year bachelor's degree here is probably equivalent in terms of amount of coursework, research exp etc to a 4 year bachelor's degree in the US.
I was (and still am) leaning towards statistics or applied mathematics for graduate study, so I'd applied to some of those both in India and abroad.
Here are the options I am considering:
1. Cambridge Tripos Part III for Mathematical Statistics: Admitted
Well, I didn't expect to actually get into this program because I feel like my background leaves me quite under prepared. Cambridge is, of course, extremely prestigious and I want to at least seriously consider it. My gut feeling, though, is that I don't think the program structure is one in which I will succeed. For one, I feel quite under prepared, but I could work on this the four months I have until term starts in October. Secondly, it is 5-6 modules of very rigorous coursework, followed by a a single high stakes examination season at the end of nine months on which your entire course outcome depends. No thesis component as such, but there is an essay. Overall, I would prefer a two year master's degree that would allow me time to take more coursework, take prereqs if needed, and have some research built into the course structure. I've also heard that there isn't much faculty contact which makes getting LORs difficult. Given that this is quite important for PhD admissions in the US, and I would be relying on my future grad institute for these, this is an important factor. But I don't know if I should push myself a little and go for this, anyway.
2. National University of Singapore, MSc Mathematics (Coursework), Track 2: Admitted
NUS features pretty highly in world rankings, but I don't have much of an idea what to expect. This is a two year degree, with a master's project you can do over one or two semesters. Offers a lot of flexibility in choice of coursework. It is intended to be more a terminal degree than something that is to lead to a PhD (they also have a master's by research for that purpose), but I am hoping I might use it as a pathway to apply to PhD in the US if I want to go that route. Thoughts?
Positives include a small cohort size and so a lot of faculty contact.
3.National University of Singapore, MSc Statistics (Coursework), Track 2: Pending
I might consider this over the mathematics alternative if I am accepted to it, but I am quite happy with either. The cohort size in this program is quite large, however, but this is okay.
4. Indian Institute of Technology (IIT), MSc Mathematics: Admission lists are not officially yet, but entry is exclusively determined by entrance exam (IIT JAM) ranks. I am pretty much certain to get my second choice (IIT Delhi), but my first (IIT Bombay) is iffy, going by closing ranks in previous years.
IITs have quite a brand value in India, but this is more for their undergraduate engineering. Still, this seems to be a solid 2 year degree where you take some "core" courses- Real Analysis, Complex Analysis, ODEs, PDEs, Topology, Functional Analysis, Probability Theory, Algebra, Discrete Mathematics over the first two semesters, choose from a range of electives for the third and fourth, and complete a master's thesis.
5. Tata Institute of Fundamental Research, Centre for Applicable Mathematics (TIFR CAM), Bangalore: Admitted with fellowship
Pretty competitive program, the coursework seems extremely rigorous to me, focuses very heavily on PDEs. Small cohort. MSc candidature may be extended to PhD candidature. Perhaps for this reason, the 2 year MSc structure does not involve a research component. However, there may be opportunities over the summer etc I can seek out. Alumni seem to have gone on to do PhDs at CUNY, Maryland College Park, EPFL, Tulane, Tufts etc.
At present, I am looking at it as a stepping stone to lead to doing a PhD (tentatively in the US, in the best program I can- ideally top 50) two years down the line and I would like to choose one where I would get the necessary exposure and experience to do this, provided I do well and use my time properly.
I'm also particularly interested in knowing whether you think I should do one of the degrees in India or not. The difference in cost is substantial , especially since I would be paying overseas fees in Singapore and the UK. Given that the programs I can go to in India are considered one of the top here for mathematics (but I have no idea how they compare or are recognized internationally), would doing one of the other degrees justify the difference in expense?
I'd welcome perspectives both from people who are from India and those outside of it.