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Thread: How would you rank the importance of these MATH courses

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    How would you rank the importance of these MATH courses

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    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.
    Last edited by soundchaser; 01-21-2014 at 06:55 AM.

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    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.

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    Don't overthink it moneyandcredit's Avatar
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    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.
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    Quote Originally Posted by coffeehouse View Post
    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?

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    Quote Originally Posted by moneyandcredit View Post
    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?

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    An Urch Guru Pundit Swami Sage Catrina's Avatar
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    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).
    Attending Rice University

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    Quote Originally Posted by Catrina View Post
    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).
    Thanks for replying!
    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.

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    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.

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    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.

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    Quote Originally Posted by soundchaser View Post
    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.

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