Yet another real analysis thread *sigh*

[michaelmas]

Ok, this is hopefully not the please-rate-my-chances-I-havent-taken-analysis-Im-so afraid thread, but I want to know exactly why real analysis is so important in graduate econ study. Why all the fuzz?

 

Is it so that you understand the textbooks/lecture notes better?

 

Is it to help you with the problem sets?

 

Is it so that you can memorize/understand and derive a specific before-seen proof on the final exam?

 

Is it so that you can construct your own proof of an unseen theorem on the final exam?

 

Or is it something else?

 

And I hope these questions haven't been answered zillion times before on the forum.

[asquare]

Real analysis helps you understand the text and notes, and helps with problem sets. In my classes, we rarely had to prove things on exams (though we might be asked about the assumptions necessary for a proof to go through, for example). We have one professor who likes to put true/false/justify questions on exams and prelims. "Justify" doesn't necessarily mean "prove," but a proof would certainly be sufficient.

 

But while those things are important, I think there are other reasons that real analysis is emphasized as well. The first, and substantive, reason is that concepts and techniques from real analysis are useful tools in developing a deeper understanding of economic theory. If you aren't comfortable with the math, then you wind up struggling with that rather than using the math as a tool to understand the economics.

 

A second reason is that real analysis is a signal to admissions committees. I think the importance of the signal is often overstated on these forums, but because real analysis is often the closest thing on an undergraduate transcript to the type of coursework found in the first year of an econ PhD program, it makes sense that doing well in the subject conveys some information to the admissions committee.

[jeeves0923]

I have an alternate theory as a mathematician (don't mean to sound high and mighty or anything).

 

Real Analysis focuses not on one's ability to memorize, but on one's ability to think and reason creatively. People who can reason in the way required by a text such as Rudin often are the most capable of coming up with really creative thought both in theories and methods. If you pass Analysis by memorizing proofs, it will have little to no value other than a signal to adcoms that you took it. So while you might not prove the Stone-Weierstrass theorem or something similar in your research, your ability to do so might come in handy when developing your own theories.

[TruDog]

There are a countably infinite number of reasons why real analysis is so important in today's economics PhD programs, not including my mathematical pun at the beginning of the sentence. I came to Wisconsin having only self-studied Rudin and didn't think that math was that important in the beginning. But now I realize how important math truly is...and here are a few reasons why:

 

--In macro, many mathematical results are needed to show that a solution exists for a value function in a Bellman equation. What needs to be shown is that there is some sort of contraction mapping that guarantees that the value function does is bounded. Additionally, one needs to show that the metric space of interest (typically a supnorm) is complete. This also requires the use of an epsilon argument, which is something that real analysis helps with.

 

--The Separating Hyperplane Theorem is used in many parts of micro, including general equilibrium and game theory. This requires that there be some plane in R that can 'slip between' two convex sets.

 

--In general, you're asked all the time about whether some set is closed or bounded as well as about existence and uniqueness. You're also asked to prove a lot of theorems, both on problem sets and exams.

 

Real analysis is critical to surviving the first year of graduate study in economics (I can't speak as to what happens after that, as asquare can). I spent a lot of time trying to pick up the arguments behind proofs instead of reviewing all the other material covered in class. Mathematical rigor is essential, but economic intuition is perfectly optional.

 

So take real analysis if at all possible. It'll make your first year a LOT easier, in addition to being a good signal to the adcoms.

[paradox3696]

Ok, this is hopefully not the please-rate-my-chances-I-havent-taken-analysis-Im-so afraid thread, but I want to know exactly why real analysis is so important in graduate econ study. Why all the fuzz?

 

Is it so that you understand the textbooks/lecture notes better?

 

Is it to help you with the problem sets?

 

Is it so that you can memorize/understand and derive a specific before-seen proof on the final exam?

 

Is it so that you can construct your own proof of an unseen theorem on the final exam?

 

Or is it something else?

 

And I hope these questions haven't been answered zillion times before on the forum.

 

 

Yes RA will help you all of the above. As it has been mentioned by others, you will require to do little or no proof at all during your Econ phd program. If you have taken any mathematical proofing course , you shall be in no disadvantage as opposed to someone who has actually taken RA.

 

I spoke to 2 Directors of graduate studies over the phone and they are really more concerned about your preparation in Matrix and Linear Algebra, Differential Equation, and Statistics.

[mtjsvc]

I go to a top-25 school by most rankings, and I took a year of real analysis and a semester topology before starting the program. The first year courses at my school didn't draw on these topics much, if at all, but I would argue that taking such courses is helpful because it develops one's mathematical maturity. You need to be able to comfortably read abstract mathematics to stay in top of things. If you are spending a lot of time figuring out what the notation means or interpreting abstraction into heuristic terms, you will have a lot more work to do. So I guess it helps in that sense, even though the actual theorems and techniques learned in real analysis were useless to me in my first year. Of course, at my school and schools of a comparable rank, students are not expected to become theorists. At higher-ranked schools that aim to train theorists, the first-year treatment may be more rigorous, so you may need to actually know real analysis to survive.