Econometrics Vs. (Functional Analysis and Measure Theory)

[concern]

Hello all. I just need your suggestions regarding my rigorous class selection this fall. Further, I'll be applying to grad schools this fall itself.

 

I've got chance to take both, Measure Theory and Functional Analysis in the fall 2010 semester itself !! Feels really great. But, Econometrics is also offered this fall semester and won't be offered untill next fall (I'll be in a phD program by then).

 

So, what do you think would be better as an applicant and give me an edge in the application process (at this point not much concerned with how valuable econometrics will be and all that. Just want to know the comparatie advantages only):

 

a) Taking either FA or MT along with Econometrics

b)Taking both FA and MT and skipping econometrics class

 

I don't think I'm inclined towards taking all three at once, because I'm doing independent study for my Honors Thesis also and I need a good amount of time for that also. Further, by the time fall grades become available at my university, I can still send them to many graduate programs without missing the deadline.

 

So, I invite your valuable suggestion, relating which will delight adcoms more: great performance in such 2 rigorous Math courses Vs. taking just one of those courses with undergrad version of Econometrics (this second loks less rogorous than taking both MT and FA)

 

Another last thing. After having taken and done well in FA and MT, will it even matter if I've taken econometrics or no? Anyway, I'll be taking Game Theory in another semester.

 

Thank you all.

[scienceofsleep200]

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.

[Peot]

I think MT and econometrics is a nice way to hedge your bets. Not having 'metrics could be perceived as a glaring hole, while having Measure Theory puts you ahead of the pack.

[Gecko]

I really won't recommend doing functional analysis without prior knowledge of measure theory since the former builds on the latter :)

[scienceofsleep200]

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.

[concern]

I've talked with my professors and they said that both FA and MT can go concurrently, but FA only can't be taught well without proper background in MT. Anyway, if things do not work out and I still get confused, then I might even opt for taking all three this fall itself!! I'll burn out myself with those three and research, but this will anyway be my chance to prove myself (as I don't want to waste another year waiting, having taken all the rigorous courses by this fall itself, and that many schools will still receive my fall grades).

 

Any other insights on this is highly valuable.

[Gecko]

I'd say not to risk it. Scoring well is an important part of things too :)

[APJ]

Ecotrix + Measure theory. (In ideal world all three, but given constarint, this is optimum in my opinion) For two reasns:

1) Trix will be interesting to know before you start with graduate level trix

2) FA comes after Measure

3) Measure theory will be useful in its own right

[concern]

I noted one thing regarding MT being a pre-requisite for FA course.

 

At MIT, the pre-requisites for FA is not MT (they call it Measure and Integration), rather the prerequisites are RA and Linear Algebras. And, I tried to find what book was used, and I see nothing. Prof. Richard Melrose teaches it and he has many lecture notes (both his and that of others) and he lists the topics to be covered as 3 sections (here is the link 18.102: Introduction to Functional Analysis) Check out the syllabus link at the end of the page.

 

I am assuming that they teach things of Measure Theory as needed in the course (as in the syllabus topics section one of the things to be taught in this course is Lebesgue integrable functions, which definitely gets started in MT).

[chisquared]

While measure theory is important to get a full understanding of functional analysis, I'm inclined to believe that it (FA) can be taught (probably fairly well, in fact) even without MT.

 

Efe Ok, for example, develops FA in his popular RA text, while acknowledging that he does not deal with MT at all. (Which I think is a little strange, considering how graduate real analysis is usually more about measure theory than anything else..)

 

In fact, this book claims that it will teach you FA while only requiring background in calculus, linear algebra, and differential equations. (There's no indication of this idea on the Amazon page; I just read this when I was looking through the preface in the bookstore this afternoon.)

 

I would imagine that it's the same as teaching probability without MT. You can do without it, but you'll appreciate the theory so much better if you don't (do without it, I mean).

 

To go back to the OP though: do you have some other means of signaling background in econometrics? Like, say, can you have one of your LOR writers say that you did some RA work for him/her that involved regression analysis, or something like that? If so, it may be a good idea to do FA and MT.

Edited June 3, 2010 by chisquared
Follow up comment for relevance and PC-ness

[concern]

Yes, I've already taken a course in Applied Regression Analysis, which is from the economics department and have knowldege of SPSS also as it was used a lot in this course. This can well be mentioned by my LOR writers also, but anyway, it'll show up in my transcript.

[treblekicker]

another perspective: you will definitely be taking econometrics during a phd, while you may never be able to learn FA and MT in as much detail during the first two years of your phd. in general i'd suggest avoiding redundancy and to take things in undergrad that you'll seldom, if never, have a chance to take again (this goes for things outside of math and economics, especially).

[chisquared]

Yes, I've already taken a course in Applied Regression Analysis, which is from the economics department and have knowldege of SPSS also as it was used a lot in this course. This can well be mentioned by my LOR writers also, but anyway, it'll show up in my transcript.

 

In that case, I think definitely go for MT and FA. But if you're not too interested in the math, or even pure theory (micro or metrics especially) I'd consider substituting FA for grad micro.

[Zeno]

Everybody keeps talking about MT as prerequisite knowledge to FA. I think a more precise way of putting it is the following: understanding the basics of MT gives the student a collection of examples to discuss in the context of FA. IME, this is really the only way in which the material of MT is a prereq to that of FA.

 

At my undergrad school, they have a class which is a common prereq to both MT and FA. This prereq introduces the Lebesgue measure on the real line and then covers some Fourier analysis. The MT goes on to discuss more abstract measure spaces, and the FA course draws on the prereq for examples -- namely L^p® and some key results in Fourier.

 

I don't know if this is typical, but my FA course (very well-taught) could easily have gone without any of the (already minimal) reference to the prereq course.

[concern]

Everybody keeps talking about MT as prerequisite knowledge to FA. I think a more precise way of putting it is the following: understanding the basics of MT gives the student a collection of examples to discuss in the context of FA. IME, this is really the only way in which the material of MT is a prereq to that of FA.

 

 

This is exactly the thing my professor told me(regarding examples), as to why the concepts of MT become important in FA course. This way it is can be considered as a pre-req, though not strictly. Else, if MT was a must pre-req for FA, then why would univerity like MIT would not specify it so clearly, they are not unaware, for sure ,about this fact.

[azzobrother]

If Measure theory is recommended before taking Functional analysis, whats a good course to take before Measure theory? is real analysis sufficient?

 

Thanks!

[Zeno]

That really depends on the specific topics covered. One school's "Real analysis" is another school's "Advanced calculus" is another school's "Real variables" is another school's "Introductory measure theory."