PDA

View Full Version : How would you rank the importance of these MATH courses

soundchaser
01-21-2014, 12:03 AM
Hi, I am a sophomore who intend to apply for PhD program after graduation

I have taken (am currently taking) Calculus I-III, Matrix Algebra, Math Proof, Prob and Stat (for econ students), and expect to take two courses on real analysis (basically covering Rudin's textbook materials), Differential Equations, and an econ course covering Dixit's book on Optimization.

I am not sure what else should I take in the following two years. Options are

1, Two further courses on Real Analysis
(covering topics like Sigma-algebras, measure theory, integration, convergence theorems, Lp spaces, Lebesgue differentiation, Banach spaces, bounded and compact operators, topology. Hahn-Banach, open mapping, Hilbert spaces, symmetric and self-adjoint operators.)
2, Calculus IV
3, Linear Programming
4, a 3rd-year course called "Intro to Probability", which is neither a pre-req nor an equivalence of the fourth-yr one.
5, a fourth-year course on Probability, and then Stochastic Process (which requires the fourth-year Prob)
6, intermediate Stat and Prob (in Stat department)
(4, 5, 6 seem to be substitutes to some extent)

I am aiming high, and I know more is always better, but obviously I have limited credits and do not want to devote all of them to Math. So there's trade-off. How would you rank the relative importance of the courses above? Thanks for any opinion.

As for now, I want to specialize in either game theory and mechanism design, or development economics and new political economy, for my Phd study. But, As a sophomore it's probably too early for me to say that. But I don't think I'm ever going to do finance. Macro is also unlikely but I'm not that sure.

coffeehouse
01-21-2014, 12:18 AM
I may be biased but I would put 4, 5 and 6 above the rest. Especially if you've only taken prob an stat for econ students.
2 further courses in real analysis seems like overkill.
Calculus IV and LP are usually rather useless.. LP may be interesting depending on how the course is taught.

moneyandcredit
01-21-2014, 12:31 AM
People will probably disagree, but:

5. Fourth-year probability and stochastics
3. Linear programming.

The first is very important in general, and linear programming will help you if you decide to pursue advanced game theory, but I'm certainly not an expert so take my suggestion with a grain of salt. Since you don't mention wanting to pursue raw theory as a specialty I've relegated the "real" real analysis sequence to the next tier of options.

1. Two further courses on Real Analysis. This is "for real" real analysis. There are some topics that you'll find useful, but I suspect the full sequence is overkill unless you decide you want to change careers and study quantum mechanics and particle physics. The second course literally sounds like the senior-year mathematical physics class that I audited with one of my friends who was a Physics major.
2. Calculus IV, but I don't really know what that is. Is it mostly stuff for physics and engineering like I suspect?
4&6 - Don't bother if you can enroll in and handle #5.

soundchaser
01-21-2014, 12:46 AM
I may be biased but I would put 4, 5 and 6 above the rest. Especially if you've only taken prob an stat for econ students.
2 further courses in real analysis seems like overkill.
Calculus IV and LP are usually rather useless.. LP may be interesting depending on how the course is taught.

Thanks! good to see you again, I am the guy who started a thread on Canadian Big 4.

How would you choose among 4, 5, 6?

I tried to send you a PM but the system says your box is full. Could we find a way to chat privately?

soundchaser
01-21-2014, 12:52 AM
People will probably disagree, but:

5. Fourth-year probability and stochastics
3. Linear programming.

The first is very important in general, and linear programming will help you if you decide to pursue advanced game theory, but I'm certainly not an expert so take my suggestion with a grain of salt. Since you don't mention wanting to pursue raw theory as a specialty I've relegated the "real" real analysis sequence to the next tier of options.

1. Two further courses on Real Analysis. This is "for real" real analysis. There are some topics that you'll find useful, but I suspect the full sequence is overkill unless you decide you want to change careers and study quantum mechanics and particle physics. The second course literally sounds like the senior-year mathematical physics class that I audited with one of my friends who was a Physics major.
2. Calculus IV, but I don't really know what that is. Is it mostly stuff for physics and engineering like I suspect?
4&6 - Don't bother if you can enroll in and handle #5.

Thanks a lot!
I actually have very little idea what LP is. Is it mostly about optimization? Is it still useful to take LP if I take a fourth-year econ course covering Dixit's Optimization in Economic Theory?

Catrina
01-21-2014, 01:00 AM
What is calculus IV? Are you on a quarter system where calc IV includes some of what would be included in calc III at semester-system schools?

Regarding the advanced analysis courses, they sound like a mixture of measure theory and functional analysis. I have heard that measure theory is useful in graduate econometrics, although I have never taken graduate econometrics so I don't know for sure.

I did take functional analysis (without having taken measure theory first, which was a mistake). I personally liked the class, although it was incredibly hard. There apparently are some applications of functional analysis in economic theory, so since you are interested in game theory you may want to consider it. However, given that you have limited credits, I would recommend taking the fourth-year probability/stochastic processes sequence and the measure-theory part of the analysis sequence (I'm guessing the first semester).

soundchaser
01-21-2014, 01:09 AM
What is calculus IV? Are you on a quarter system where calc IV includes some of what would be included in calc III at semester-system schools?

Regarding the advanced analysis courses, they sound like a mixture of measure theory and functional analysis. I have heard that measure theory is useful in graduate econometrics, although I have never taken graduate econometrics so I don't know for sure.

I did take functional analysis (without having taken measure theory first, which was a mistake). I personally liked the class, although it was incredibly hard. There apparently are some applications of functional analysis in economic theory, so since you are interested in game theory you may want to consider it. However, given that you have limited credits, I would recommend taking the fourth-year probability/stochastic processes sequence and the measure-theory part of the analysis sequence (I'm guessing the first semester).

This is our calculus IV description:
Parametrizations, inverse and implicit functions, integrals with respect to length and area; grad, div, and curl, theorems of Green, Gauss, and Stokes.

However "integrals with respect to length and area" is covered in the previous courses in the sequence.

dragonslion
01-21-2014, 01:21 AM
The answer depends on the quality of the classes you have taken so far. A first class in probability and statistics varies wildly from school to school. Unless you are at a very good school, you will certainly want a stronger preparation. Was your initial course calculus based? Linear programming will likely be useless. The two further analysis courses sound like measure theory and functional analysis. If you like analysis then you will likely want to take these classes, especially if the professor has a good reputation. Not sure how useful they will be outside of theory, but they will be great for your mathematical maturity anyway. I've heard that measure theoretic probability theory is more important than measure theory anyway. Functional analysis is sort of weird, you will want a good professor.

chrishacker
01-21-2014, 05:21 AM
I copied your course description in Google and find where you are...and find the course catalog for math department, too.
It seems that 5 is measure-theory based. I would recommend it.

coffeehouse
01-21-2014, 05:38 AM
Thanks! good to see you again, I am the guy who started a thread on Canadian Big 4.

How would you choose among 4, 5, 6?

I tried to send you a PM but the system says your box is full. Could we find a way to chat privately?

This may give away my identity but I also just googled your course syllabus and we go to the same school.
Math 420 is extremely difficult (it is cross-listed with grad). We can talk in person if you'd like.

Edit: For someone who is only a sophomore and has not yet taken any real analysis yet, maybe you are worrying too much about your future 2 years.

Definitely do not take LP and do not take Calc IV. Optimization with Dixit's book is a good idea, do well and that's a guaranteed letter from one of the top theorist from our school.

coffeehouse
01-21-2014, 05:48 AM
^ Now I wonder how many people are going to google and find out who that professor is... LOL -_-

soundchaser
01-21-2014, 07:02 AM
What is calculus IV? Are you on a quarter system where calc IV includes some of what would be included in calc III at semester-system schools?

Regarding the advanced analysis courses, they sound like a mixture of measure theory and functional analysis. I have heard that measure theory is useful in graduate econometrics, although I have never taken graduate econometrics so I don't know for sure.

I did take functional analysis (without having taken measure theory first, which was a mistake). I personally liked the class, although it was incredibly hard. There apparently are some applications of functional analysis in economic theory, so since you are interested in game theory you may want to consider it. However, given that you have limited credits, I would recommend taking the fourth-year probability/stochastic processes sequence and the measure-theory part of the analysis sequence (I'm guessing the first semester).

We are on a semester system. Our Calculus III basically covers differentials and integrals in 3-D space, langrange multiplier, etc.

soundchaser
01-21-2014, 07:05 AM
The answer depends on the quality of the classes you have taken so far. A first class in probability and statistics varies wildly from school to school. Unless you are at a very good school, you will certainly want a stronger preparation. Was your initial course calculus based? Linear programming will likely be useless. The two further analysis courses sound like measure theory and functional analysis. If you like analysis then you will likely want to take these classes, especially if the professor has a good reputation. Not sure how useful they will be outside of theory, but they will be great for your mathematical maturity anyway. I've heard that measure theoretic probability theory is more important than measure theory anyway. Functional analysis is sort of weird, you will want a good professor.

The Stat and Prob class I've taken is not calc-based. It seems I have to do more courses on Prob...

soundchaser
01-21-2014, 07:08 AM
I copied your course description in Google and find where you are...and find the course catalog for math department, too.
It seems that 5 is measure-theory based. I would recommend it.

Thanks.
Then I am probably not going to do more RAs.

Kaysa
01-21-2014, 02:15 PM
I wouldn't waste anymore time on math courses. You have so much time on your side. I would rather use it to learn econometrics, take a couple graduate courses, pick out an interesting topic, and write an awesome thesis.

dragonslion
01-21-2014, 04:49 PM
The Stat and Prob class I've taken is not probability-based. It seems I have to do more courses on Prob...

I'm assuming you meant calculus based? You certainly won't regret taking more probability and statistics, even up to the measure theory based #5. A friend that recently started at a T4 said her undergrad probability theory notes helped her get through that part of metrics. Probability theory and statistical theory are actually quite fun and tricky.

RonSwanson
01-22-2014, 03:20 AM
IMO 3 and 5 sound like your best bets. Why would you take 4 if you could take 5?

soundchaser
01-22-2014, 03:28 AM
I'm assuming you meant calculus based? You certainly won't regret taking more probability and statistics, even up to the measure theory based #5. A friend that recently started at a T4 said her undergrad probability theory notes helped her get through that part of metrics. Probability theory and statistical theory are actually quite fun and tricky.

Sorry for that typo.
Definitely going to do more statistics and probabilities.

soundchaser
01-22-2014, 03:31 AM
IMO 3 and 5 sound like your best bets. Why would you take 4 if you could take 5?
I have heard 3 and 5 are hard and cross-listed with grad courses. Just found there's a 3rd-year stochastic process course that can form a 3rd-year Prob-SP sequence with# 4. Probably this us what I wan to do

thegripe
01-22-2014, 04:35 AM
hmmm, math 420/421 is just not going to be needed for grad school, real variables (math 320/321) is plenty. Scrap Cal 4, it really isn't advanced calculus either. Advanced Cal would be something like "advanced calculus" by folland, which would be more suitable.

4,5,6 are solid choices, as well as taking graduate econ courses. The institution you are attending has quite the variety of graduate mirco courses which you should take advantage of.

Obviously the extra math courses are indicative of your ability to do quantitive work, but the emphasis on real analysis has really snowballed out of control. You might want to consider trying to enrol in a graduate econometrics class ( econ 527) as the institution which you are attending does NOT emphasis enough econometrics during your undergrad.

coffeehouse
01-22-2014, 04:59 AM
hmmm, math 420/421 is just not going to be needed for grad school, real variables (math 320/321) is plenty. Scrap Cal 4, it really isn't advanced calculus either. Advanced Cal would be something like "advanced calculus" by folland, which would be more suitable.

4,5,6 are solid choices, as well as taking graduate econ courses. The institution you are attending has quite the variety of graduate mirco courses which you should take advantage of.

Obviously the extra math courses are indicative of your ability to do quantitive work, but the emphasis on real analysis has really snowballed out of control. You might want to consider trying to enrol in a graduate econometrics class ( econ 527) as the institution which you are attending does NOT emphasis enough econometrics during your undergrad.

i agree on the 527, but Econ 425 is not an intro course even though the course name is.

thegripe
01-22-2014, 07:46 AM
i agree on the 527, but Econ 425 is not an intro course even though the course name is.

I'm sure it's not an elementary econometrics course, but said institution only does 1 semester of econometrics if i am not mistaken. Most other schools with top tier programs (stretching this definition to include top 30) have a part 1 and part 2 econometrics.

I've just been checking out the roll call for 2014 and you have quite the "stellar" profile. It's a very impressive profile for someone at essentially a state school (large population and most undergrads get largely ignored unlike liberal arts colleges in the U.S.) and at any school really. I am interested in seeing your admissions. I think you've really capitalized on everything that is possible at such an institution.I really can't think of anything that would keep you out of the top 10(i can't see your B- in 320 really holding you back either, because everything else quantitatively is so strong). LOR, maybe, but it sounds like you have that covered. Good for you and good luck.

excuse the grammar i just don't put in effort when writing on these forums.

coffeehouse
01-22-2014, 07:56 AM
I've just been checking out the roll call for 2014 and you have quite the "stellar" profile for someone at essentially a state school (large population and most undergrads get largely ignored unlike liberal arts colleges in the U.S.). I am interested in seeing your admissions. I think you've really capitalized on everything that is possible at such an institution. Good for you.

Thank you, I appreciate your kind words. I think you make a good point about the "large state school/undergrads ignored". You wouldn't happen to also be associated to my university would you? Recent graduate maybe? Alumni?

I'll be posting my results in the admissions thread if you are interested :)