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View Full Version : My uninformed opinion on which math to take



Zeno
11-12-2010, 04:01 AM
A lot of people have the bare essentials (something in calculus, something in linear algebra, something in probability or statistics) covered and want to know which math classes to take from there. I have no inside info or even well formed opinions for what will get you in to schools. I'm also at a school that's maybe on the more mathematical side than many, so do take this with a grain of salt.

My (biased) opinion on preparing yourself for the first year:

Take the purest, most abstract math you can handle without setting yourself up to bomb. There's all sorts of useful specific knowledge -- analysis, probability, topology, and optimization first come to mind -- but I think the main value is the practice talking about math. I came into my program with more math background than other people, and I do feel it's made things a lot less stressful for me. However, every class has new material; having seen the specific topics before, while nice, can only help you so much. Get practice learning about abstract concepts, starting with technical definitions, and trying to get a sense of "what's going on" in a new-to-you subject. This is exactly what happens in first-year economics courses.

I'm not saying don't take real analysis. In fact it's my favourite non-econ subject. I'm just saying that if you're taking any abstract mathematics, you'll get most of the benefit. Also, the more the better. Mathematical thinking is a habit like any other, best built under prolonged exposure. The value isn't primarily derived from the content you learn, but rather from the habit of a mathematical style of thought.

scienceofsleep200
11-12-2010, 05:02 AM
Great post.

norules4suresh
11-12-2010, 08:45 AM
Indeed a great post. But Abstract Math generally would mean topics such as groups, rings, commutative algebra, lie groups, etc. Are you saying these would help in making the 1st year easier or in getting admissions?

I am a math major and I have the chance to take all those above listed topics but since they are not related to economics I thought of dropping them.

Thanks in advance!

zurich_econ
11-12-2010, 09:02 AM
Except for linear Algebra, everything related to algebra, e.g. modern algebra, commutative algbra, algebraic topology, cryptography, cohomology theory,... is almost entirely useless for economics, and definitely totally useless for the first year.

On the other hand, everything related to analysis, in particular real analysis, measure theory and functional analysis, but also dynamical systems, stochastic analysis and of course all variants of optimization is tremendously helpful, not only for the first year, but (I'm not yet as far, but I'm very sure) in particular also for your own research. With respect to this second strand of mathematics, but by no means with respect to the first, do I concur with the OPs opinion.

But anyway, not every economist needs to be a second Debreu or Aumann, and for those who don't aspire to be in the most mathematical fields of economics, I think the additional economics course might be of greater value than the additional maths course, provided the economics course has some standard of quality.

Zeno
11-12-2010, 01:04 PM
But Abstract Math generally would mean topics such as groups, rings, commutative algebra, lie groups, etc. Are you saying these would help in making the 1st year easier or in getting admissions?


e.g. modern algebra, commutative algbra, algebraic topology, cryptography, cohomology theory,... is almost entirely useless for economics, and definitely totally useless for the first year.

My whole point is that, while the material won't be of direct use, the mathematical practice is still very valuable. Sure, economics courses are great, and everyone faces constraints. I'm just saying that a course in, say, Lie groups will benefit you by working your mathematical muscles.

As an analogy: Even though the skill sets are very different for hockey and basketball, I would still expect the typical NHL player -- as a trained athlete -- to be a far better basketball player than I am.

Just as I said before, no idea about what will help you in admissions.

jeeves0923
11-12-2010, 01:19 PM
But anyway, not every economist needs to be a second Debreu or Aumann, and for those who don't aspire to be in the most mathematical fields of economics, I think the additional economics course might be of greater value than the additional maths course, provided the economics course has some standard of quality.

I wanted to quote this because I believe it whole-heartedly.

If you aren't a high brow theorist or an econometric theorist, once you get through the first year, you won't be so worried about the high level maths you took in undergrad. The point after the first year is to think like an economist- not a mathematician. It won't impress anyone at a labor seminar if you talk about some abstract math concept from functional analysis. Perhaps you'll find a use for dynamic programming in applied work, but really the kinds of math you'll need for your applied work you should be able to pick up without all having had full classes on the abstract math.

I feel like it's an easy thing to do when you don't have anything interesting to say in a project, to fall back on a lot of complex math. To me, that's not an interesting way to look at the world, and I don't appreciate seminars that have a lot of math to go with an obvious or irrelevant or flagrantly wrong idea. I'd much prefer to see a relevant and interesting idea where the person needs a little help to make the model sound proof. Most of my professors seem to have the same preference. I guess those preferences are correlated.

I'm not trying to say that abstract math won't help you get in or succeed in the first year- it probably will. I'm also not saying that abstract math isn't interesting in it's own right. I took a lot of math myself.

All this is to say, surviving the first year and getting admitted to graduate school are very different endeavors than the rest of graduate school and probably the rest of your life. asquare has said this many times, but I definitely believe it.

Zeno
11-12-2010, 01:30 PM
^

Well said.

Liwanyo
11-12-2010, 02:16 PM
All this is to say, surviving the first year and getting admitted to graduate school are very different endeavors than the rest of graduate school and probably the rest of your life. asquare has said this many times, but I definitely believe it.

Not to derail, but it seems like this is a mistake by the profession/adcoms? Mismatching skill sets for admissions vs. actual study in the field doesn't seem like a particularly good idea. I know they have to distinguish between the hoards of applicants somehow, so maybe it's correct... Anyways, thanks for the post, this forum has the tendency to make me feel hopeless given the great math backgrounds of many here

tm_member
11-13-2010, 01:28 PM
Have to agree with jeeves, three months into my program and the math is not that bad. Seriously.

It's more the quantity of work that's scary!

zurich_econ
11-13-2010, 05:49 PM
My whole point is that, while the material won't be of direct use, the mathematical practice is still very valuable. Sure, economics courses are great, and everyone faces constraints. I'm just saying that a course in, say, Lie groups will benefit you by working your mathematical muscles.

As an analogy: Even though the skill sets are very different for hockey and basketball, I would still expect the typical NHL player -- as a trained athlete -- to be a far better basketball player than I am.


But it would certainly be a bad recommendation for somebody to practice as much hockey a he can in order to become a better basketball player, wouldn't it? (Well, maybe it is if you're used to thinking like an abstract mathematician, but not if you're used to thinking like an economist ;) ...it may still be a good recommendation to do some running, or weightlifting (i.e. analysis and the like) for somebody to become a good basketball player (economist), however.

Popolo2
11-13-2010, 08:55 PM
You know what I wish I had done more of as undergraduate? High-level computer programming. Being a whiz with SAS or Matlab, I think, is worth its weight in gold, when it comes to collecting and analyzing data, that is. Maybe not so helpful with regard to admissions.

Zeno
11-14-2010, 12:22 AM
Yeah, I intended to be far less controversial....

I wasn't saying to do anything to the exclusion of anything else. I was just commenting that a background in random abstract math -- something commonly considered useless -- is helping me out a lot, and predicting that it would do the same for others.