Master's-Level Math-Econ or PHD-level?

[zaiguo]

I'm currently an undergrad and one of the requirements for my econ major is the "Intro to Mathematical Econ" class for master's students, which is essentially basic math methods for masters-level theory. I requested a waive for the course because it's pretty much just Calc 3 and Linear Algebra with econ applications. The professor who teaches it said I could waive it, but I'd have to substitute the PHD mathematical analysis course in its place. Given my math background, he said the masters class would probably not teach me much behind some computational methods, but the PHD-level class might be quite a challenge. Normally I'd be up for that, but it's only offered in the fall, and I'm worried that, since I'll also be taking Real Analysis 1 and Probability, I might die.

According to the professor, the course uses these textbooks:
--Corbae, Dean, Maxwell B Stinchcombe, and Juraj Zeman. (2009) An
Introduction to Mathematical Analysis for Economic Theory and
Econometrics. Princeton, NJ: Princeton University Press.
--Stachurski, John. (2009) Economic Dynamics: Theory and Computation.
Cambridge, MA: MIT Press.

I also pulled the topics from a syllabus from 2007. The books it gives seem to be different, though, so I don't know how accurate they necessarily are, but I'm guessing it's a rough estimate:

Week 1-3: Sets and Logic
Week 4: Relations
Week 5-6: Analysis
Week 6: Continuity
Week 7: Functions, Exponents, and Logarithms
Week 8-9: Multivariate Functions
Week 10-11: Introduction to Matrix Algebra
Week 11: Economic Models
Week 11-12: Comparative Statics of Linear Models
Week 12: Continuity, Differentiability, and Optimization, Comparative Statics of Non-Linear Models
Week 13: Quadratic Forms
Week 14: Multivariate Optimization

It seems somewhat innocuous, but the professor implied it would be very hard or at least time-consuming. Just as an aside, the PHD program of the school I go to is somewhat low-ranked--it didn't break 200 on econphd, but it did break Grijalva/Nowell's top 100.

If you've read this far, thanks for your help!

[walt526]

Have you taken a proof-intensive math course before, or will you be learning how to write proofs plus in the Real Analysis course?

[zaiguo]

In the spring I'm going to be taken Foundations of Mathematics, which is the gateway course for master's-level math and I guess it's a baby proofs class. I've also done Linear Algebra before, although I'm sure that's not a very high level of proof. I also MIGHT be taking Complex Analysis in the spring, although that isn't guaranteed.

[walt526]

It's been my observation that most students who struggle with undergrad Real Analysis aren't really struggling with the material covered, but rather how to construct a good, rigorous proof. That's why I asked. If you're comfortable writing proofs, then Real Analysis and the PhD Math Econ class might be doable. I guess the real question is how challenging do you expect Real Analysis to be? What text do they use for it?

I do agree 100% that MA-level Math for Economists would not be a great use of your time.

[zaiguo]

Just by checking the textbook website, the textbook appears to be Intro to Analysis by Wade.

I honestly have no idea how hard it'll be for me. I didn't have trouble in Linear Algebra, and my current professor for ODE is confident enough in my abilities that he is trying to recruit me for his Complex Analysis course. I don't know how it compares.

Yeah, the MA course I figured was a waste of time AND money. And I'd just rather not be bored, you know?

[HopefulFutureEcon]

I wouldn't take the class as its not worth the overall hassle. I'm at the same school as you and the class is very labor intensive. Considering you are taking RA and probability at the same time (both fairly rigorous), taking this additional class will only burden you while posing a significant risk to performing poorly.

Taking RA and then complex analysis in the spring (of 2011, yes?) is way more valuable and doing well in those classes is far more important (as complex is icing on the cake in regards to Math).

I've actually taken some classes with PhD people from the program in question, and they mentioned that they spent more time on the HW for this class than for the 1st semester Micro. So, that should give you a good idea of the work required/expected (ie alot, as the micro class uses Varian).

Basically, RA and probability are way more valuable. And the MA class in question is actually a pretty rigorous review of a great deal of concepts that some need refreshed on. And, it could be a nice boost to your GPA, and, depending on who teaches it, actually fun....of course, it does depend greatly on who teaches it.

PM me if you would like to discuss any of this further. I am applying to programs for next fall if you would like any advice (especially at getting the best profs possible for good letter of reference's at your school).

[zaiguo]

That's really helpful, thanks. I'll definitely rethink my choice.