How much actual math in PhD programs - (once you're there, not to get in)

[user_name]

Originally Posted by gredow

this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

Actually if you're on a trimester system, then this is "theoretically" possible. You can take cal 2, 3, and analysis in term I, II, III respectively. You can take linear algebra in any term, but most likely it'll be term III. The problem is I think you'll have schedule conflicts because calculus and real analysis are usually intended for students of different years.

[andyecon]

I use almost all the math I took, all of the time right now. I took one semester of real analysis (Rudin) and one semester of Topology (Munkres). Those two courses have been very valuable. The only thing I wish I had taken in addition would be a course in optimization theory (not available at many schools) and a stronger course in Linear Algebra (or perhaps taken it seriously when I did have it).

In short, take analysis. If you can, take something just beyond analysis as well.

[Econ07]

Originally Posted by gredow

this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

Although it may be listed as a prereq for analysis, I don't see why you would need Calculus III to understand Real Analysis. It's usually thought that the whole calc sequence would give you more maturity to take RA, but if you are really constrained by time you could try Calc II+Linear Algebra, then Calc III+Analysis.
But this course load may be incompatible with work. Anyway, you should be aware that it's a difficult task.

[snappythecrab]

With all of this said, I would suggest taking RA even if it comes too late for the admissions process. I really don't believe a person can be over-prepared in mathematics. The best voices on this subject are those already in programs. Zavera, Ramlau?, Snappy, etc

I'll agree with this. No such thing as too much math prep. Taking RA, anywhere along the lines will help. Taking any sort of analysis course will help, or really, any serious proof-based mathematics course. RA is still the most desired because it has the most direct application.

I'm starting in on my fourth week here today, and I use RA, measure, and even my Matrix Analysis, material on just about a daily basis. If nothing else, picking up a solid foundation on how to write proofs - esp. knowing when you've actually proved something, - seems to be very, very important. And the material is quite important too.

A good grade in Analysis seems to be a signal of three things:

1) being able to write proofs
2) being able to read/write at a high technical & high level
3) knowing analysis

1 and 2 are imperative. 3 is very important.

as far as being able to pick up mathematics when you're in grad school...I don't know how anybody can do it, or do it well. in grad school, you're pretty much expected to learn more than you can really handle - I figure we cover 6-8 chapters a week. that's a struggle in and of itself without trying to pick up a course like RA, which makes even some of the best math majors squirm. Get it done ASAP.

[asquare]

Originally Posted by snappythecrab

as far as being able to pick up mathematics when you're in grad school...I don't know how anybody can do it, or do it well. in grad school, you're pretty much expected to learn more than you can really handle - I figure we cover 6-8 chapters a week. that's a struggle in and of itself without trying to pick up a course like RA, which makes even some of the best math majors squirm. Get it done ASAP.

This is absolutely true. I'll add that in an econ PhD program, math is supposed to be a tool -- something that helps explain and organize economic concepts. But if you aren't comfortable with the math before starting the program, then your first year classes become about the math more than the economics. It turns something that's already difficult into a very frustrating experience where you're struggling to keep up and not developing strong intuition for the foundational material of the field.

There are some people who do fine in their PhD without ever having written a proof before graduate school. But for most, it's a lot easier to really get a handle on the material -- to learn it in a solid enough way that it becomes the basis for your own future research -- if you speak the "language" in which it is being taught.