5 graduate courses -smart? (math)

[Hercuflea]

I'm considering taking 4 or 5 graduate courses in my first semester. If I choose this route, I won't have any official teaching or research duties due to a fellowship. All of the courses would be math courses and one would be an engineering course.
The math courses are real analysis, differentiable manifolds, topics in applied math (mostly multilinear spaces, manifolds, applications to physics), Logic (i.e. axiomatic set theory), and then there is an engineering course.

I've seen many of the topics in the real analysis and the set theory course already as an undergrad.

Does this sound like overkill? If I had all my time to devote to this, would it be doable?

 

[RUber]

Many of the classes will overlap on theory, so you should be able to learn it all. I would look into the individual professors and their expected workloads. Any one class can kill your time if there are lots of proofs or other time-intensive assignments.

 

[homeomorphic]

Four is pretty standard if you don't have teaching duties. Five might be risky, and I'm not sure there's any great need to take such a risk, especially since you can always do more self-teaching if you don't have enough to keep you busy (plus, it's good to have a social life, etc.). I would just start with four and then see if that's an appropriate load, and from there, you could decide if five would be okay the next semester. Some people seem to do better if they have tons of stuff thrown at them all at once, but for me, graduate school is already a big overload. I would have done much better if I had a lighter load than even the standard one (3 classes + teaching/grading) because I like to be able to really think hard about a subject, beyond just doing problems that are assigned to me. The level of understanding and retention I can achieve that way is much greater than what I can get drinking from the usual graduate school fire hose where I'm struggling to barely finish all my assignments and there's not much time to really chew on things and implant them in my long term memory or put them into a wider context. Slow and steady wins my race. Other people may be different, though.

 

[Hercuflea]

Four is pretty standard if you don't have teaching duties. Five might be risky, and I'm not sure there's any great need to take such a risk, especially since you can always do more self-teaching if you don't have enough to keep you busy (plus, it's good to have a social life, etc.). I would just start with four and then see if that's an appropriate load, and from there, you could decide if five would be okay the next semester. Some people seem to do better if they have tons of stuff thrown at them all at once, but for me, graduate school is already a big overload. I would have done much better if I had a lighter load than even the standard one (3 classes + teaching/grading) because I like to be able to really think hard about a subject, beyond just doing problems that are assigned to me. The level of understanding and retention I can achieve that way is much greater than what I can get drinking from the usual graduate school fire hose where I'm struggling to barely finish all my assignments and there's not much time to really chew on things and implant them in my long term memory or put them into a wider context. Slow and steady wins my race. Other people may be different, though.

Thanks. Didn't you say you did yours in topology? Do you think there will be enough overlap between the real analysis and the differentiable manifolds class to bring the workload down some? About how much time would you say you spent studying per credit hour?

Another option I have is just to take the fellowship and go ahead and RA or TA anyways for extra money. If I did that I'd probably just take 3 or 4 classes. I really like the idea of getting my credit hours out of the way as soon as I can so I can focus on research.

 

[mathwonk]

you better ask your professors. when i taught grad courses in math, that load would have been unthinkably difficult. we just put way more content into each course and demanded too much work for anyone to take 5, or really even 4 and do well. so it all depends on the course syllabus and the requirements. if the requirements are minimal you can "take" the courses and survive, but will probably not learn all that material. to learn a subject in math requires time thinking about it.

Thinking back now, I recall our grad school made it a requirement to register for at least 12 hours credit, and we were used to giving 5 hours credit per course, which at one point they forced us to reduce to 3. As a result students who had been taking 2 or 3 hard courses, did have to register for 4 courses which was impossibly difficult So we had to make changes, like setting up courses with fewer requirements, and just changing the difficulty level of our regular courses. So every department tries to make the requirements workable, and it is possible that in your department 5 courses can be made to work, but it does not seem ideal to me. I would not be able to master the material and do the work in 5 courses. I like to think deeply about just one or two at a time.

 

[homeomorphic]

Thanks. Didn't you say you did yours in topology? Do you think there will be enough overlap between the real analysis and the differentiable manifolds class to bring the workload down some? About how much time would you say you spent studying per credit hour?

Yes, I did topology. There might be a little overlap between real analysis and topology, but I don't think it would have much effect on the workload. Is it measure theory or just undergraduate real analysis? I know some people in my program started with the honors undergraduate version.

If your program is like mine was, I wouldn't worry about getting credit hours out of the way that much. The way mine was, the main thing was just to get the quals out of the way and credits took care of themselves. Also, the 500 level courses were usually pretty hard, but the 600 level ones were more like seminar courses that didn't require as much effort.

 

[Hercuflea]

It would be "measure theory, integration, Lp spaces, and hilbert and banach spaces." I've basically seen a lot of the measure theory and lebesgue integration before, up to Lebesgue dominated convergence. So it sounds like I'm well prepared for the course.

It's starting to sound as if it might just be better to take an RA on top of my fellowship and just focus on 3 courses...and rake in the cash .

 

[mathwonk]

just for fun, i'll describe the entering year grad program, minimum requirements for everyone, when i entered in 1965:

three courses plus a seminar.

algebra: pre class reading assignment: decomposition theory of ideals in noetherian rings, chapter 4 of zariski samuel.
then the first semester focused on categories and functors, (eilenberg - watts theorem, yoneda lemma, projectives and injectives, Ext, Tor), homological ring theory, depth, tor dimension of rings, auslander buchsbaum theory, regular local rings and unique factorization, . second semester was on algebraic geometry, peskine's version of zariski's main theorem,... We also had notes we were responsible for reading on direct limits, and on classification of semi simple rings.

analysis: first month real analysis, lebesgue integration and measure theory (1st day: beppo levi's lemma); second month: complex analysis, holomorphic and meromorphic functions, cauchy theorem, residues; then riemann surfaces (the book by springer), hodge theory, and up through riemann mapping theorem for riemann surfaces (uniformization), i.e. classification of slichtartig (e.g. simply connected) riemann surfaces;

topology (the easy one): point set topology (kelley book); complete classical proof of jordan curve theorem, schoenflies theorem; covering spaces, fundamental group, singular homology.

the seminar was on field theory and galois theory.with this kind of load you do not take 5 courses and survive.