Math Pre-requisite for Quant. Schools

[rustytrix]

Turns out, if you want to get published in APSR or the likes (or even prosper in quant-heavy grad schools(read:most schools)) you better be doing a lot of quant work. So why not have some mathematical pre-requisites (or at least recommendations) for non-theory applicants like the econ departments?

P.S. If you are a new applicant and have time to take math courses at your undergrad inst., get these over with before u start grad school (if u plan to do quant work, of course):

-3 Semesters of Calculus (including multi variate)

-Probability

-Mathematical Statistics (using calculus)

-Real Analysis (def do this one to save yourself some misery later in life)

-Linear Algebra

-Topology

...in other words, just do a double major including math.

Edited October 24, 2010 by rustytrix

[oasis]

could you explain which math topics are more applicable to what subfields?

[polisciphd]

On average, the math mentioned above is most applicable to those doing quant American or quant IR.

[rustytrix]

could you explain which math topics are more applicable to what subfields?

i would add quant. comparative to tidefan's list (not to mention methodology, obviously). in other words, if u are not doing political theory just do the math (pun unintended).

[oasis]

My question was more along the lines of this. One area of math not mentioned above is differential equations, which are used in dynamic systems, typically in macroecon and IPE. What are the applications of real analysis and topology?

[The Realist]

Turns out, if you want to get published in APSR or the likes (or even prosper in quant-heavy grad schools(read:most schools)) you better be doing a lot of quant work. So why not have some mathematical pre-requisites (or at least recommendations) for non-theory applicants like the econ departments?

P.S. If you are a new applicant and have time to take math courses at your undergrad inst., get these over with before u start grad school (if u plan to do quant work, of course):

-3 Semesters of Calculus (including multi variate)

-Probability

-Mathematical Statistics (using calculus)

-Real Analysis (def do this one to save yourself some misery later in life)

-Linear Algebra

-Topology

...in other words, just do a double major including math.

This is just untrue. That sort of preparation is unnecessary. I expect PhD applicants to have taken calculus to the level of AP Calc, first semester college-level stuff, and a class or two in applied statistics. Most of the results that we work with in political science require little more than what you would know from those classes, and the rest you can learn in graduate school (that's what graduate school is for). If you expect to make fundamental discoveries in statistical methods or pure game theory, then perhaps you need more preparation, but I don't think so, and that only describes less than 1% of all political scientists.

The idea that you have to double major in math or take all of these classes is just a way to scare prospective students. Prospective students, listen: this advice is just utterly wrong. Even if you want to do quantitative work in quantitative-heavy fields, this advice is wrong.

That's not to say that logical and/or mathematical reasoning is irrelevant to your preparation. It is not. But you can demonstrate that many ways: a major or minor in econ, substantial coursework in analytical philosophy or computer science or engineering/physics, a good senior thesis, many different ways. It's just nonsense that students of a human science need a course in topology as undergraduates.

[polisciphd]

This is just untrue. That sort of preparation is unnecessary. I expect PhD applicants to have taken calculus to the level of AP Calc, first semester college-level stuff, and a class or two in applied statistics. Most of the results that we work with in political science require little more than what you would know from those classes, and the rest you can learn in graduate school (that's what graduate school is for). If you expect to make fundamental discoveries in statistical methods or pure game theory, then perhaps you need more preparation, but I don't think so, and that only describes less than 1% of all political scientists.

The idea that you have to double major in math or take all of these classes is just a way to scare prospective students. Prospective students, listen: this advice is just utterly wrong. Even if you want to do quantitative work in quantitative-heavy fields, this advice is wrong.

That's not to say that logical and/or mathematical reasoning is irrelevant to your preparation. It is not. But you can demonstrate that many ways: a major or minor in econ, substantial coursework in analytical philosophy or computer science or engineering/physics, a good senior thesis, many different ways. It's just nonsense that students of a human science need a course in topology as undergraduates.

The question (at least what it came to be) wasn't whether someone should take these classes before going to grad school, but whether they apply to what's being done in the field. I would only recommend that someone take calculus and maybe matrix algebra in order to be comfortable in a grad stats sequence. Surely there are applications for such things as diff. eq., or structural equation models, but most people will never use these in their career.

[rustytrix]

This is just untrue. That sort of preparation is unnecessary. I expect PhD applicants to have taken calculus to the level of AP Calc, first semester college-level stuff, and a class or two in applied statistics. Most of the results that we work with in political science require little more than what you would know from those classes, and the rest you can learn in graduate school (that's what graduate school is for). If you expect to make fundamental discoveries in statistical methods or pure game theory, then perhaps you need more preparation, but I don't think so, and that only describes less than 1% of all political scientists.

The idea that you have to double major in math or take all of these classes is just a way to scare prospective students. Prospective students, listen: this advice is just utterly wrong. Even if you want to do quantitative work in quantitative-heavy fields, this advice is wrong.

That's not to say that logical and/or mathematical reasoning is irrelevant to your preparation. It is not. But you can demonstrate that many ways: a major or minor in econ, substantial coursework in analytical philosophy or computer science or engineering/physics, a good senior thesis, many different ways. It's just nonsense that students of a human science need a course in topology as undergraduates.

I never said it was "necessary" i just said that it would help a lot. Nobody expects prospective applicants to have taken those, a claim which I did not make. And it is true you can learn it in graduate school, but they usually tend to cram a lot of things into "Math for Social Science" type of courses (that will include things from basic algebra to real analysis in one or two semesters), so my point was if an undergraduate were to take those courses, like a proper real anlysis class, they would have more time working with the material and possibly have a better foundation for later work. And not to mention the distinct advantage a new student will have if s/he has already taken these courese; they will not have to sit through a semester or two of one of those all in one math courses and instead focus on other core areas and take seminars.

So yeah, you don't "need" to be math major but somebody who tells you that it doesn't help is lying.

[Charlie2010]

There are a lot of undergrad courses I would recommend before topology. Even real analysis I would only recommend if you like the stuff and hope to become a methodologist or formal modeler. So I wouldn't recommend a full math major unless you really love the stuff in its purest abstraction. But I'll second the rest as being useful for the majority of students who will do applied multi-method empirical work. For that reason, a double major in econ might be better since it would give you some experience seeing how math can be applied to social science questions. A stats double major would also help on the purely empirical side. Other science majors or a pure math major will give you a ton of skills you will ultimately be able to apply, but will leave you with no clue about how any of it might pertain to the political science that you are presumably passionate about. Evolutionary biology is less quantitative but might be a better fit because they face many of the same challenges we do in dealing with non-experimental data.

[catchermiscount]

As more and more applicants become more and more savvy about what to expect in grad school thanks to undergraduate curricula that include more and more exposure to articles that are more and more quantitative and/or formal, more and more people seem to think that more and more math is required to begin a program in political science. I agree with Realist and think this sentiment generally overstates the facts.

To be sure, exposure to math is a good thing. In particular, if one wants to have any kind of understanding of what's going on in the basic regression context, one needs some familiarity---though certainly not mastery---of basic matrix algebra, probability theory, and differential calculus. If one intends to do any kind of formal theory, being able to construct proofs is the key skill, along with some familiarity of real analysis in n-dimensions. Computing skills are also quite useful.

But, you will get exposure to all of this in grad school. Just as most people don't come in with theories that will alter the way that we think about politics, they don't come in with a complete toolkit to analyze political processes. Just breathe, kiddies. I am a student at one of the most rigorous departments in the discipline, and I hadn't heard of regression or game theory when I applied to grad school.

I also disagree with the original sentiment, which seems to imply that, to be successful, one must use the bells and whistles for the sake of using the bells and whistles. While my own work relies on the bells and whistles heavily, a lot of excellent, systematic study of politics is still being produced that uses qualitative analysis, informal theoretical arguments, or very rudimentary quantitative techniques. Indeed, even basic formal models can be taken off the shelf and applied in a variety of ways. So, yes, the business is technical, but it's not technical for the sake of the technique. Don't get caught up in the scientism that some use to overcome their own pathologies on the state of the discipline.

Now, go get drunk, or read something you like, or watch some YouTube videos. Or do all of those.

[rustytrix]

In one sentence: If you decide not to take Real Analysis and you end up at a rigorous quantitative department, you will regret not having done so.

[polisciphd]

I am at a rigorous department and have never regretted not taking real analysis.

[catchermiscount]

In one sentence: If you decide not to take Real Analysis and you end up at a rigorous quantitative department, you will regret not having done so.

This is just untrue. Good introductory formal classes will introduce all the real analysis topics necessary---suprema, infima, convergence, Rolle's theorem, intermediate and mean value theorems, and abstract treatments of functions and their properties. Good advanced formal classes will introduce more difficult topics as needed, particularly regarding correspondences and their characteristics.

At departments that are not as formal-oriented, a basic seminar in formal theory---the standard required class at most departments---will not require such topics at all. You don't need real analysis to solve games, including games of incomplete and/or imperfect information. Just as most political scientists use canned packages in statistical software environments (Stata, R, SAS, SPSS, etc.) for their quantitative analysis, so too do many of them use formal models that are well understood and easy to solve even after minor modifications. You need the more powerful tools if you intend to make up games on the fly and need to, say, confirm the existence of an equilibrium in a game that has never been considered or offer some of its characteristics.

For those of you interested in getting the facts straight, go check a game theory text like Osborne's introductory one. Is it hard? Yes, it's hard in that it's a different way of thinking about things than most of us are used to. And there are obviously more advanced texts that one uses as one progresses. But, it remains that it's quite doable and does not require a math degree. After all, we're all just interested in talking about politics, right?

[expatbayern]

In one sentence: If you decide not to take Real Analysis and you end up at a rigorous quantitative department, you will regret not having done so.

Rustrytrix, "in one sentence," how about you tell us where you got your PhD, where you're now employed, and where some of your recent publications have been placed, since you you know so much about what applicants will regret.

I don't know if you actually mean quant or formal above (since its generally the latter that people will argue a course in real analysis is helpful for).

If the latter, want me to run downstairs and ask John Duggan whether his BA in Philosophy from Whitman included a real analysis class (or any of the others you're pushing for)?

If you really do mean quant, how about you send a note to Gary King asking how much real analysis he took with his BA in Poli Sci from SUNY-New Paltz?

I don't know, it doesn't necessarily seem to me like they regret their lack of math training. Nor do any of the countless other extremely smart formal theorists and methodologists who weren't undergrad math majors.

As for me, I'm just a PhD student specializing in both formal modeling and quant methods at what may still the be most "high-tech" political science department in the country, with my last "math class" taken in my junior year of high school.

[catchermiscount]

Rustrytrix, "in one sentence," how about you tell us where you got your PhD, where you're now employed, and where some of your recent publications have been placed, since you you know so much about what applicants will regret.

I don't know if you actually mean quant or formal above (since its generally the latter that people will argue a course in real analysis is helpful for).

If the latter, want me to run downstairs and ask John Duggan whether his BA in Philosophy from Whitman included a real analysis class (or any of the others you're pushing for)?

If you really do mean quant, how about you send a note to Gary King asking how much real analysis he took with his BA in Poli Sci from SUNY-New Paltz?

I don't know, it doesn't necessarily seem to me like they regret their lack of math training. Nor do any of the countless other extremely smart formal theorists and methodologists who weren't undergrad math majors.

As for me, I'm just a PhD student specializing in both formal modeling and quant methods at what may still the be most "high-tech" political science department in the country, with my last "math class" taken in my junior year of high school.

See, I tried to be nice and all, but my officemate expat tends to take things to their logical conclusions with more vigor than I. He hadn't taken anything since high school; to offer even more information, I took two math classes in college and failed both. And yet here we are in the land of Math and Honey (and Snow) and, if I can speak for expatbayern, doing just fine indeed.

[rustytrix]

Rustrytrix, "in one sentence," how about you tell us where you got your PhD, where you're now employed, and where some of your recent publications have been placed, since you you know so much about what applicants will regret.

I don't know if you actually mean quant or formal above (since its generally the latter that people will argue a course in real analysis is helpful for).

If the latter, want me to run downstairs and ask John Duggan whether his BA in Philosophy from Whitman included a real analysis class (or any of the others you're pushing for)?

If you really do mean quant, how about you send a note to Gary King asking how much real analysis he took with his BA in Poli Sci from SUNY-New Paltz?

I don't know, it doesn't necessarily seem to me like they regret their lack of math training. Nor do any of the countless other extremely smart formal theorists and methodologists who weren't undergrad math majors.

As for me, I'm just a PhD student specializing in both formal modeling and quant methods at what may still the be most "high-tech" political science department in the country, with my last "math class" taken in my junior year of high school.

Please allow me to re-emphasize the difference between what is "necessary" and what is "recommended". Maybe not everyone in the world is as super-smart as coachcrj or expatbayern, thus building a solid foundation on 2-3 semesters worth of caluclus, linear algebra, real analysis, and differential equations might prove to be to quite challenging for us mere mortals in one or two "formal" course sequence.

I have a question: Can you tell prospective applicants that you do not recommend taking Real Analysis (or calculus, or LA,or..) if they have the opportunity of doing so as undergrads? I hope I have made my point clear, if not then enjoy bashing the strawman.

PS: I think John Duggan forgot to tell you about his M.A. in Economics.

[catchermiscount]

Please allow me to re-emphasize the difference between what is "necessary" and what is "recommended". Maybe not everyone in the world is as super-smart as coachcrj or expatbayern, thus building a solid foundation on 2-3 semesters worth of caluclus, linear algebra, real analysis, and differential equations might prove to be to quite challenging for us mere mortals in one or two "formal" course sequence.

I have a question: Can you tell prospective applicants that you do not recommend taking Real Analysis (or calculus, or LA,or..) if they have the opportunity of doing so as undergrads? I hope I have made my point clear, if not then enjoy bashing the strawman.

PS: I think John Duggan forgot to tell you about his M.A. in Economics.

If the question is: should I take real analysis or some substantively interesting senior-level poli sci class? I would recommend the latter every day of the week and twice on Sunday. Far better to get a sense of what kinds of conversations you'd like to enter or what kind of questions you'd like to ask.

If you disagree, then I am sad for you, because it's a lot more fun to get the tools when you know what you'd like to use them on.

Edited November 16, 2010 by coachrjc

[rustytrix]

If the question is: should I take real analysis or some substantively interesting senior-level poli sci class? I would recommend the latter every day of the week and twice on Sunday. Far better to get a sense of what kinds of conversations you'd like to enter or what kind of questions you'd like to ask.

If you disagree, then I am sad for you, because it's a lot more fun to get the tools when you know what you'd like to use them on.

As long as we can convey to prospective applicants that taking math courses over "getting drunk" or "watching youtube" is a better idea, I don't care what you regurgitate every Sunday.

Edited November 17, 2010 by rustytrix

[catchermiscount]

As long as we can convey to prospective applicants that taking math courses over "getting drunk" or "watching youtube" is a better idea, I don't care what you regurgitate every Sunday.

I'm not convinced real analysis is better than having a meaningful collegiate experience, particularly in the last semester, which should be a celebration of one's intellectual curiosity through fun but challenging coursework and of the important friendships one has made in undergrad. I'm not preaching senioritis, but nothing's worse than a kid that's burned out before s/he even gets to math camp. And, in many cases, that means having a cocktail or eight with friends. If you're lucky, that spills into grad school as well---hopefully with a balanced social portfolio that included colleagues and non-work friends.

So nope, not going to grant you that one, either. It can't be all work, and, importantly, if you make it all work, the work will suffer for it. I can only speak in my own case, but I find a drink or two twice a week and a good dose of YouTube good for the soul, which in turn is good for the political scientist in me. It can be anything: poetry, music, sports, crochet, watching Martha freaking Stewart, whatever. Maybe you and I need to find a few things we both find fun and use it as a starting point for our budding friendship---and, for the record, I don't think real analysis would be a good starting point along those lines. So, how about Charles Mingus? I bet you love Charles Mingus like I do. I'm working on a paper while grooving out to Peggy's Blue Starlight even as we speak. MAKE THE BOOTSTRAPS GO FASTER, CHARLIE!

Edited November 18, 2010 by coachrjc

[catchermiscount]

Ooooh oooh ooooh and then Wednesday Night Prayer Meeting came on the Pandora right after Peggy's Blue Starlight!

Seriously, the most important thing anybody can tell prospective applicants or first year grad students: constructing and maintaining a good work playlist is the best thing you can do to maintain sanity and excellent work in the first year. That and buying and reading the Kennedy econometrics book.

Edited November 18, 2010 by coachrjc

[balderdash]

So, how about Charles Mingus? I bet you love Charles Mingus like I do. I'm working on a paper while grooving out to Peggy's Blue Starlight even as we speak. MAKE THE BOOTSTRAPS GO FASTER, CHARLIE!

Last.fm: Charles Mingus, Thelonious Monk, Davis, Coltrane, and all the others: it's how to get reading done without losing your sanity.

[rustytrix]

Desperate tangents aside, I truly and sincerely hope all the math paranoia here is not borne out of some people's own apprehensions (conscious or otherwise) about having to compete with new generations of mathematically/statistically well trained students.

For me, this thread has outlived its utility but I hope it will be of help to all current and future applicants.

[catchermiscount]

Last.fm: Charles Mingus, Thelonious Monk, Davis, Coltrane, and all the others: it's how to get reading done without losing your sanity.

Well dammit, you need to apply to Rochester, friend! We love us some violence and IR theory, and, MUCH MORE IMPORTANTLY, I need somebody to talk jazz with.

[balderdash]

Desperate tangents aside, I truly and sincerely hope all the math paranoia here is not borne out of some people's own apprehensions (conscious or otherwise) about having to compete with new generations of mathematically/statistically well trained students.

For me, this thread has outlived its utility but I hope it will be of help to all current and future applicants.

Look, we're joking because it's a bit silly. I think for me the point is that quant helps, but it's not necessary. If I wanted to specialize in heteroskedacity or something then I wouldn't be applying for Poli Sci.

Also, you're a bit off base with the whole "desperate tangents," "paranoia," and "some people's apprehensions" bit. It's not that we're "scared" of quant: I took multivariable calc in high school and loved it, and I'm sure that my experience isn't at all unique to the forum. It's just that it's not where the passion is. And I don't think that I should subjugate my academic endeavors to something as base as pandering to adcomms or potential hiring committees. If they want me for my theory and specialization, they'll take me whether I've taken 4 quant courses or 5. I'm just not going to do something I don't like to get hired to do more of what I don't like.

If that means taking a PhD and going to work in the policy world, c'est la vie. But life's too short to spend it poring over regressions.