What Math preparation is necessary for a new economics Ph.D. student?

[rockboy]

Hi there, at first I would like to express my deep appreciation to all of you who are sharing your experiences on this forum. I never posted before but have read much... This is because I am a Chinese student thus know little about the situations in the US and Europe.

I am going to attend a economics Ph.D. program in the US and before the new semester there will be the math camp. What math preparation is necessary before I take the math camp and first year micro theory sequence?

In China the usual math courses in Economics Department are Calculus, Linear Algebra and Probability Theory, all of them rely on calculation rather than analysis. I did very well on them (all A+ or A) but I think I lack the formal training of mathematical analysis, although I did take Real Analysis with Department of Mathematics.

I am planning to take efforts to study Walter Rudin's Principles of Mathematical Analysis in June (I hope I can read it quickly because I have studied Real Analysis), and if there would be enough time, I will further read Rudin's Real and Complex Analysis. Also Rudin's Functional Analysis, perhaps read it along with the Ph.D. courses after September.

So are those preparations enough? Or I am too inconfident on my math background? hehehe~~~ I hope it would not be too difficult for me to be adapted into the Ph.D. program which is really completely new to me.

Thank you for your patience of reading and any answer is deeply appreciated.

PS: Who is going to attend Department of Applied Economics in University of Minnesota? HAHA~~~ looking forward to meet you!

[jeeves0923]

Rudin is fantastically clever. So clever, in fact, that you almost surely will need a professor to help you through it. I mean, it will be helpful to read it, but a lot of his proofs are very unintuitive.

I suggest that in addition to Rudin, or maybe even instead of Rudin, you read through chapters 12-23 of Simon and Blume's Mathematics for Economists.

[rockboy]

Originally Posted by jeeves0923

Rudin is fantastically clever. So clever, in fact, that you almost surely will need a professor to help you through it.

Thank you jeeves, it sounds like that I must read this book through in the following a few weeks (possible?) on campus only where I can find a academic tutor...

[jeeves0923]

You could be much smarter than me (a distinct possibility) and be completely fine by yourself, but it is always nice to have someone to help your intuition, especially if you don't have a lot of experience with analysis.

Pay particular attention to the continuity, sequences and series, basic topology, etc. Those are the most important sections and probably the most intuitive. However, I think Simon and Blume does a great job in preparing you for what you'll actually use in graduate economics.

[rockboy]

Originally Posted by jeeves0923

You could be much smarter than me (a distinct possibility) and be completely fine by yourself, but it is always nice to have someone to help your intuition, especially if you don't have a lot of experience with analysis.

Pay particular attention to the continuity, sequences and series, basic topology, etc. Those are the most important sections and probably the most intuitive. However, I think Simon and Blume does a great job in preparing you for what you'll actually use in graduate economics.

Hi jeeves please don't say this, I just hope myself is smart enough to survive the prelims.

You advices are really very helpful, at least I know what parts are of the priority to be read in Rudin's book. I only have limited time so I have no idea whether I can read the whole book before the math camp. Also I will find Simon and Blume ASAP.

Again, thank you sincerely!

[Golden Rule]

With baby Rudin, it's really dense, and you just have to be really patient, and go proof-by-proof, and make sure you understand each step before moving on. I'd really make sure I understood chapters 2-4 inside and out (which are basically what jeeves listed). It's a really concise and wonderful treatment once you get to know it. I much preferred Rudin's proofs to the analysis proofs, in say De La Fuente or Sundaram, which were two other books I looked at (though I thought those books were better for other things).

Right before/during math camp I reviewed with Rudin and Simon-Blume and thought that was just fine. I used the other books I mentioned for reference during math camp once we got into constrained optimization.

[asianeconomist]

If you're indeed going to the AE program @ Minnesota, I believe you'll be taking the Micro core along with the Econ department people.

I perfectly agree with what jeeves0923 has mentioned. In addition to S&B, it would also be helpful for you to cover the mathematical appendix of MWG. I really do not think that you need to cover 'baby' and 'papa' Rudin to such copious extent.

[rockboy]

Originally Posted by Golden Rule

With baby Rudin, it's really dense, and you just have to be really patient, and go proof-by-proof, and make sure you understand each step before moving on.

Yes, I do read it patiently with great attention to the details in proofs, and find that it would be impossible to read this book through quickly. I am struggling in the appendix of Chapter 1... and suppose I can't completely understand it until times of reviews... I am hoping to finish this book before August when the math camp will start, it seems like that this really needs crazy work.

Anyway, thanks very much for all the advices in this thread!