scienceofsleep200

Great post.

1) My guess is that it's the same thing. 2) As far as I remember, all the attachments are at the end.

Of course it is enough! As people have said repeatedly, there is no minimum (aside from calc and linear algebra). There are many people doing great research who had a lot less math than that. All the OP (and a few others) wanted to say is that people with a strong math background seemed to have gotten more attention from the adcom at Princeton last year, than at similar universities.

I think that you should have a good shot at schools you listed. Funding should not be a problem, it always seems to work out at most of the schools you listed (I can't really comment on UCSB, did you mean UCSD?). I would listen to your advisor as he/she probably has some experience with sending students to US universities and would be able to judge the situation best. Your references look like they will come from people who should be able to compare you to PhD candidates at top schools and that's always useful for adcomms. In short, I don't think you are aiming too high, but if you definitely want to get in somewhere, I would add a few more safety schools (you can try Wisconsin Madison as they admit quite a lot of people). Good luck with it all anyway!

Usually the first semester of graduate real analysis is measure theory with an introduction to functional analysis. The second semester is all functional analysis. Measure theory is normally a pre-requisite for functional analysis, as some of the most important examples rely on it. As Galoisj said, take measure theory first.

Hi Restranga, 1) I think this refers to economic development. From memory these options are basically the courses which you can choose to take in second year. 2) The SOP and CV part comes at the end of the application. Good luck!

A rough guess is between a third and a half. A couple of the students have symbiotic relationships with their copies of Folland.

Measure theory is a must if you are doing any type of theory. Aside from its use in probability theory (and related areas), many papers from just about every (theoretical) literature employ the language of measure theory. Plus it's fun and it's not hard, so although you won't see it in a serious way in first year grad courses, taking measure theory is definitely worthwhile.

I tell them that money doesn't really exist.

I largely agree with popolo2's suggestions for specific courses. Take graduate math courses if possible. Take anything that is taught by a good (or famous) professor. Learn as much math as you can at this stage. Learning math is a young man's game (von Neumann apparently thought that math ability declined after the age of 26). My impression is that a course in functional analysis will be more beneficial than undergrad labor economics--both for admissions and your future research career.

My impression is that TAing falls into the latter category. IMO TAing is only useful if you have NOT done the course as a student. TAing a course you haven't done allows you to learn the material and says to the adcoms that you are certainly capable of getting an A in that subject. For me that was the case with Public Economics, Advanced Macro, Linear Algebra I and II, Calculus I and II. The fact that I TAed applied regression, econometrics and a few other courses I had gotten As in probably didn't do much for my admissions.

IMO Linear Algebra II.

Micro.

I was objecting to the implication that grad micro is taught at an easier level than MWG. From what I've seen, this is not the case (this may be a biased sample though). This is true of undergraduate courses as well. IMO there's a fairly good probability that a course using MWG will be more rigorous (and thus better preparation) than a course assigning JR or Varian as the primary text.

I don't mean to scare people, but I do want to share my experience since it's wildly different to the above. The first-year lecture notes that I've seen at the top schools (i.e. in the top 10) are MUCH harder than MWG. This is because the courses tend to be taught by theorists who specialize in these areas and they start including topics of current interest to researchers early. It actually seems that you would probably be going to MWG to try and understand their lecture notes (and not the other way around).

In principle, all you need is mathematical maturity to succeed. From looking at the courses on their website and the graduate studies book, the U of T MSc in Math is a very serious degree. I would be taking the first option (i.e. doing the 6 units of coursework rather than thesis only) and I'd be doing their sequences in analysis and topology for sure and then whatever else interests you (or whatever has a good lecturer). Anyway, the program looks awesome--faculty is strong and they use the right textbooks for the core courses (I'm a fan of Stein and Shakarchi's books). As I said, I think that there are no hard prerequisites for these courses (I did courses using the same textbooks without having done a calculus sequence). BUT, be prepared to work hard as it takes quite some time to read a proof and really understand it (particularly if you are not used to reading proofs). Also it will help a lot if you are very familiar with key results in calculus, linear algebra and topology in R. Those things come up everywhere and from the looks of it, they will be assumed in your courses.

I should also say, it may also be a good idea to apply to places like Stanford GSB or HBS. They have strong reputations and usually offer somewhat better funding (if funding is a consideration for you).

I'll go a step further and say that you should only apply to the top 8 schools (Berkeley, Chicago, Harvard, MIT, Northwestern, Princeton, Stanford and Yale). If you really want to attend another school then try for that, but there should be no need.

I've long wanted to write a post disagreeing with some of these "all you need is calculus" and "analysis is overemphasised" comments. This seems like a good place to put it. Firstly, if one wishes to understand theory, calculus is nowhere near sufficient. It may have been enough 70 years ago, but since the publication of von Neumann's and Morgenstern's book economic theory has emphasised separating hyperplane theorems, various fixed point results, convex analysis, measure theory, etc. Even if all the theory you want to learn is in MWG, the book will not make complete sense without an understanding of compactness, convexity, continuity, topology, extreme value theorem... An introductory real analysis course may get one through MWG, but it won't be enough to give one an understanding of modern economic theory (which I guess is what a PhD student should aim for). Advanced math courses also help if one has the nobler aim of contributing to economic theory. By solving problems in pure math you are not only exposed to important results, but are also required to think deeply and clearly. It is not a coincidence that many of the economists who have made significant contributions in theory (in the last 70 years) happen to be very good at math. Friedman, Arrow, Debreu, Aumann, Nash, Lucas, Mas-Colell, Shapley, Hurwitcz etc have seen further because they were able to stand on the shoulders of giants (math allowed them to truly understand the work of previous greats, reformulate it and extend it). Robert Lucas recommends graduate students go through "Introductory Real Analysis" by Kolmogorov and Fomin before they start their program. I for one think that Lucas has a good reason for recommending a serious introductory analysis text and not Stewart's Calculus.

P.S. It's a subject worth studying in its own right, so if you are planning on studying topology on your own, may I suggest a few good books: * Morris, Sydney - Topology without tears (one of the best introductions to undergrad topology--you may find it a useful reference if you take Math 450) * Borges - Elementary Topology and Applications (good general introduction, but you may want to skip the bits on algebraic topology--chapters 5, 6 and 8) * Munkres - Topology 2e (the classic equivalent in fame to Rudin's principles, only much more pedagogical)

My feeling is that it would be helpful in general (not to mention that it's really interesting!). The course covers introductory point-set topology and these ideas are used in MWG (you may see that sometimes making their arguments more general by thinking of topologies can make the proofs simpler). Also, keep in mind that this is only a first year course and that you would certainly need to know about topology if you were to do any more advanced courses in theory. In terms of admissions--given that topology is so important in analysis (since it discusses the most general spaces on which we can define continuous functions) I think that many schools would like to see this along with analysis (or an analysis course which covers some topology). It also a better signal more mathematical maturity-- you can get through an introductory analysis course with a good knowledge of calculus, but the added abstraction of topology makes that impossible.

IMHO topology is a must, esp since it's not covered by your analysis courses. Seems like they teach it in a very accessible way. I would also suggest MAT 710 and 711 if you want to do theory. Take anything that's rigorous and makes you think deeply about things (if you enjoy topology, then do algebraic topology instead of MAT 711).

Good point Gecko, I forgot to mention that. It depends on the way the subjects are taught, but in some cases it may be possible to take them concurrently. Anyway, MT + metrics is an excellent option as well.

There is a good list of lecture notes on GT at gametheory.net.

From personal experience, I would suggest FA and MT over undergraduate Econometrics. This is because >95% of applicants will have something like undergrad 'metrics, while However, I got the impression that some adcoms didn't care much for advanced math courses and that they would have preferred advanced (graduate) economics courses (with a solid math background of course). On the other hand, there are schools which really seemed to care a lot about graduate math--I think it may even depend on who is looking at the applications.