View Full Version : What is the Marginal Benefit?

YoungEconomist

07-31-2007, 03:07 PM

My goal is to get into a PhD program ranked somewhere between 20 - 50, and I am currently working on a math minor to try and make that a reality. There are a number of classes that I will be taking for sure, but my question is whether it's very important to add multivariable calc to this list? In other words, what will be the marginal benefit of taking multivariable calc? By the way, for simplicity lets assume I will get a 3.5 in each math class I take.

Here are the math classes I will take for sure:

Calculus (Math 124, 125, 126)

Differential Equations (307)

Matrix Algebra (308)

Introduction to Mathematical Reasoning (310) (this class introduces writing math arguments and proofs, and is the prereq for Real Analysis)

Probability (math 394)

Statistics (stat 394)I may take:

Multivariable Calc (324)I also attached a link to the math class descriptions in case it helps answer my questions. MATHEMATICS (http://www.washington.edu/students/crscat/math.html#math098)

notacolour

07-31-2007, 03:33 PM

You MUST take multivariate calc. Is 126 really not multivariate? It seems hard to believe that three semesters in, you'd still be talking about only one variable.

If it really is still univariate, drop diff eq's (MUCH less important) and add multivariate.

YoungEconomist

07-31-2007, 03:35 PM

You MUST take multivariate calc. Is 126 really not multivariate? It seems hard to believe that three semesters in, you'd still be talking about only one variable.

If it really is still univariate, drop diff eq's (MUCH less important) and add multivariate.

Below is what it says about Calc 3. I don't know if this is enough or if I need to take 324?

MATH 126: Calculus with Analytic Geometry III (5 credits)

Third quarter in calculus sequence. Sequences, series, Taylor expansions, and an introduction to multivariable differential calculus.

notacolour

07-31-2007, 03:37 PM

Okay, I bothered to read your linked page, and that does help! I stand by my earlier comment, since appearently 126 only touches on multivariate topics. Certain topics in 324 will be very important, especially the chain rule and Lagrange multipliers. Familiarity with multiple integrals will also be useful. Green and Stokes theorems, not so much, but so it goes.

Drop 307 from your plan and take 324 instead. Do well in all of those courses, and your math background will be solid. If you have room for another, you can take 307, but doffeq's aren't all that useful for most economic applications (and I know someone can respond with examples, but I'm talking in generalities here). The Real Analysis course you mentioned would probably be more useful than that, and a better signal to boot. But it's not necessary if you take 310, particularly for programs ranked 20-50.

snappythecrab

07-31-2007, 04:06 PM

...err, I don't know about dropping ODE's. I think that's a fairly important class, one which I'd certainly recommend over, say, probability.

kkitkat

07-31-2007, 04:26 PM

I agree with notacolour, Multivariate Calculus is a MUST. I also think that probability is a more important course to have then Differential Equations. I attended first year PhD micro and macro core classes during my MA and even though I've never taken DE I felt fine with the material. I don't think I could've said the same if I hadn't taken probability.

YE, MATH 394 and STAT 394 are the same class, so you don't have to (can't) take both. And, to reiterate what others have said, 324 is necessary. Many schools require a multivariable calc class for admission.

kkitkat

07-31-2007, 04:30 PM

YE, MATH 394 and STAT 394 are the same class, so you don't have to (can't) take both.

Oh... In this case OP can take both probability/stats and DE. And, of course, multivariate.

notacolour

07-31-2007, 04:31 PM

ODEs isn't important at all. While differential equations are used in certain areas, mostly macro, they can always be picked up when you need them. The topics in probability theory, linear algebra and multivariate calc are much more essential and indispensable.

The value of real analysis lies in the fact that such courses aren't taught like these others. Whereas ODEs is invariably a "cookbook" kind of class, intro to proofs and real analysis will require you to do at least some proofs and reasoning on your own. Doing well in such classes demonstrates an ability to pick up new topics that are thrown to you, rather than an simply the ability to memorize and apply tools from a textbook and lectures like you've been doing for years.

Oh, and as jcn (http://www.urch.com/forums/../members/jcn.html) pointed out, MATH 394 and STAT 394 are the same class. The topics in MATH/STAT 395 look useful, though:

Sample spaces; basic axioms of probability; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions.You'll be seeing all of this at some point, but this class might be a nice introduction to the topics beforehand. Again, I would argue that this is much more useful than ODEs.

snappythecrab

07-31-2007, 05:24 PM

I'm not sure how on earth you can claim that ODE's "isn't important at all." That's completely ridiculous. You run into them both in micro and macro, perhaps not frequently, but often enough I think to warrant some exposure, and often enough for programs to list it as a course needed or suggested for admissions (ex: Berkeley, Minnesota, BU, Maryland, UCSD, Brown, etc.). PDE's too. Heck, ODE's showed up on a micro theory midterm/final here this last year. Moreover, and though this is just personal, I don't think there was a single mathematics class that really reinforced my understanding of economics quite like ODE's. Before then, the concept of equilibrium was kinda fuzzy for me. I think an understanding of dynamics is pretty important to studying macro - half of your econ theory courses in your first year.

The level of probability theory required to complete a PhD is really quite rudimentary, and more importantly will be taught to you. The only exceptions are if you're a micro or econometric theorist in which case you'll wind up taking measure-based probability anyway. Beyond that, the very basics will do, which one will be exposed to if they take a course in undergraduate statistics. It is an important enough subject that it warrants some level of understanding. However, between both undergrad and grad level statistics and econometrics courses, you're going to get a good level of exposure.

buckykatt

07-31-2007, 06:05 PM

As the others have suggested, multivariate calc is very important. More important, certainly, than probability and dif eq. Personally, I'd put probability ahead of dif eq, but that might depend on your interests.

To add to the debate on course selection, if the goal is indeed a math minor, then the requirements (http://www.math.washington.edu/Undergrad/Handbook/minor.php) are apparently 124-6, matrix algebra, difeq, and 4 electives, 300 or higher.

With that constraint in mind, I think 310, 324, 327 (analysis), and perhaps 394, would be a good preparation.

KingOfConvenience

07-31-2007, 08:29 PM

i am just as outraged as snappycrab by notacolor's suggestion that knowledge ODEs is not that important. growth theory IS differential equations. real dynamical modeling requires knowledge of differential equations. there's nothing better to give you a good, qualitative understanding of calculus and rates of change. it's an extremely interesting, and powerful, approach to understand and to model economic systems. a number of first-year students at my school lamented their lack of knowledge of ODEs, particularly when a good background in just this mattered greatly on a macro comp exam question.

i would suggest you squeeze in the ODE without dropping any of the other classes. if not, audit the class. it's extremely useful if you are ambitious and wish to go to, and succeed at, a top 40 school.

YoungEconomist

07-31-2007, 11:24 PM

YE, MATH 394 and STAT 394 are the same class, so you don't have to (can't) take both. And, to reiterate what others have said, 324 is necessary. Many schools require a multivariable calc class for admission.

:hmm:Are you guys sure about this, because I was really under the impression that they are different classes?

notacolour

07-31-2007, 11:49 PM

Oooh, I've elicited outrage! Impressive. On this I defer to buckykatt (http://www.urch.com/forums/../members/buckykatt.html), who put it very well when he/she said that the relative ranking of ODEs and probability theory would depend on your interests. I would tend to stress econometrics and the probability theory that underlies them, while others would desire more to go into areas of theory that use ODEs more heavily. And sure, these things act in strange ways, and it may be that differential equations help you to understand concepts you never quite got before. Or the same could be true of probability theory. Whatever.

As for whether the 394s are different classes, the link you provided says that MATH 394 is "offered jointly with STAT 394," which I presume means they are the same class. Additionally, the current syllabus (http://www.stat.washington.edu/debashis/stat395syllabus.htm) for STAT 395 refers to the class as MATH/STAT 395 (and indeed, the webpage title hasn't been updated from the previous sessions, and is MATH/STAT 394). So yes, I'm pretty sure they're the same class. I love how confusing these course numbers can become...

And if the above doesn't settle the matter, the time (http://www.washington.edu/students/timeschd/AUT2007/math.html) schedule (http://www.washington.edu/students/timeschd/AUT2007/stat.html) lists the classes as occuring simultaneously in the same rooms with the same professors.

KingOfConvenience

08-01-2007, 12:59 AM

yes, outrage!! :)

snappythecrab

08-01-2007, 04:10 AM

On this I defer to buckykatt (http://www.urch.com/members/buckykatt.html), who put it very well when he/she said that the relative ranking of ODEs and probability theory would depend on your interests.

Well that's a little bit different than saying that ODE's "isn't important at all." ;)

notacolour

08-01-2007, 01:16 PM

Well that's a little bit different than saying that ODE's "isn't important at all." http://www.urch.com/forums/../images/smilies/wink.gifI should have qualified it...not important at all to me. ;) http://www.urch.com/forums/../images/smilies/wink.gif