Graduate course load (in mathematics)

[JoshSmith]

Hi, all. I'm currently in a graduate program in philosophy and simultaneously doing work in mathematics. Since I've not experienced advanced math until now, I have no way to judge how realistic my projected course loads will be. Any input would be useful.

A little about my situation. I'm doing extremely well in my philosophy courses and am not terribly concerned about poor performance in my current program. I'm currently starting the calc sequence and am taking a transition to advanced math course. Next semester I will do a course covering the first seven or so chapters Baby Rudin, Calculus II, and Modern Algebra. This seems a reasonable load to me.

The semester after will cover Linear Algebra, a graduate-level course in Analysis (we use Royden), undergraduate mathematical logic, and Calculus III. Linear Algebra I expect to be no more difficult than Modern. Analysis will be the toughest. Multivariable calculus, I understand, will be the most difficult of the sequence, but my plan is to prepare some the summer before. Again, nothing about this course load seems prima facie unreasonable (even including my philosophy coursework).

After crossing over into a graduate program in mathematics, I'd likely do courses, say, like graduate-level Algebra, metamathematics, and complex analysis. Would doing these three courses in the same semester be possible? Again, I would have some time to prepare the summer before.

I really just have no way to judge difficulty or load potential, except from what I'm doing now. In addition to my math courses, I'm enrolled in another 3 units of undergraduate philosophy (clearing up a prerequisite), and 6 units of graduate work. I'm doing just fine.

Any advice on this would help, even if it's out of left field. Thanks!

 

[n!kofeyn]

What I would recommend is going and talking with an advisor or someone associated with the graduate program in mathematics at your school. They will be the best judge on the difficulty and time consumption of their courses.

That said, I think it will be challenging to complete this course load. You will be taking 6 courses, 3 of them being math courses. Your next two semesters will probably be rough. The first courses in real analysis and abstract algebra are usually very tough and they include a transition in thought not really encountered before. Just be prepared to spend possibly hours on a single problem with no results. I don't know how much your course load in philosophy will weigh you down, but in my graduate program in math, with our part-time teaching load and 3 required courses, it is nearly impossible to take a 4th course, at least in the first 2 or 3 years. The only ones I have known to do this are those who have no teaching duties for the semester.

Calculus II and III usually take some time in terms of homework load, but are pretty computational, so they aren't too hard to conquer. The courses using Rudin and Royden will be tough, because in my opinion, these two books are way overrated and in no way employ any sort of pedagogical approach.

I think this course load will keep you extremely busy, but it may not be impossible. I just don't know the amount of work required for the philosophy graduate courses. I'd be interested to see the opinion of others on the matter.

 

[Sankaku]

You might want Linear Algebra before Calc III. I may be wrong, but you will also probably find it better to do LA before Modern Algebra. The order of some of your other courses seems a little surprising to me, but others here have more experience and can offer better feedback.

 

[JoshSmith]

I've been working Rudin now, and have a supplement I found online which I've also been working. The transition to advanced math course has helped immensely for figuring out how to tackle these problems. I've also been using David Velleman's "How To Prove It" and Chartrands book on mathematical proofs to get up to snuff.

I really can't emphasize enough how little difficulty the philosophy courses are for me; relatively little time and effort is required on my part to succeed in that work. And believe me, I plan to spend a good amount of time doing this work. I don't plan to have any real social life (my girlfriend is at a different institution), and I'm finding it enough social interaction talking about interesting work with colleagues and going to seminars. So I can devote a good deal of time to working through the text and the problems.

I've been advised by faculty in this department that there is no need to take LA before Calc III or Modern. The material in Rudin that involves computational work done in Calc II is material will be covered by the time we get there. From there, I don't know what ordering would be surprising. Mathematical logic is a prerequisite for the course in metamathematics. Graduate-level Algebra won't be done until after Modern Algebra II (at the graduate level).

Actually, going back through, I realized I had accidentally copied a course twice. My most difficult graduate semester would include Algebra, metamathematics, and a special study in topics in philosophical logic. That seems to be at about the level you were saying you're at, n!kofeyn.

My most difficult semester while in this program would be the one semester where I'm taking multivariable. And I really do have an entire summer to devote to preparation before that semester.

 

[kote]

At my undergrad institution Calc II is generally considered harder than Calc III. Just an FYI - not sure how it will be for you. Calc III adds extra dimensions to Calc I and II, but it seemed to be more an extension of existing concepts than entirely new material.

It's too bad your philosophy courses aren't more challenging, but at least you have time to learn the math! Good luck.

 

[JoshSmith]

Well, I'd hate to imply that the philosophy courses aren't necessarily challenging. Indeed, they are! It's just that it comes much more naturally to me than mathematics. I'm getting a lot from my philosophy courses, but I need not give nearly as much effort. That is, they're at least high reward for me.