Math Education and Political Science

To quote Gary King1

Did you choose the social sciences because you thought they had relatively little mathematical content? Surprise! You're now in the bizarre situation, in which many of us once found ourselves, of learning advanced methods while simultaneously trying to back-fill some some of the most basic mathematical prerequisites

Understanding the statistical methods that are typically used in political science requires an understanding of multivariable calculus, linear algebra, and probability theory (at a minimum). This raises the question of how much learning is actually going on when statistics is taught from a purely algebraic perspective (i.e. no calculus and minimal linear algebra). This, of course, has consequences for the application of statistical methods to substantive questions, with obvious consequences. I also suspect (though I've not collected any data to back this up) that political scientists with an undergraduate degree in math or computer science do significantly better (career-wise) than political scientists without a technical background (this would apply to other technical undergraduate majors as well, just perhaps to a lesser degree). All other things equal a student with a good technical background will go to a better graduate program and have higher (quantity and quality) research output, presuming we are talking about research that relies on statistical methods.

This is not news of course, and books such as Gill's as well as various math re(pre)-fresher courses that many political science departments offer are a recognition of the problem, but I am not so sure they are an adequate solution. If, like many people (myself included), you come into a graduate program in political science with very little math background, and like most practicing political scientists you end up using statistical models to analyze data, then you have some tough choices to make (or ignore). The typical choice (based on my limited experience) is to muddle through. I am not sure how successful this is on average (from a career perspective), but obviously it works well enough that it still happens regularly. Another solution, as Gary King suggests, would be to try to back-fill your math knowledge. It might seem like the easiest way to do this is by watching some Khan Academy videos, or reading a book like Gill's. You might even go so far as to audit some undergraduate math classes alongside your graduate courses. This is of course is in addition to all your other responsibilities, which are undoubtedly more than enough to eat up all of your available time. This is, in my opinion (and I think true of almost all people), quite inadequate. To quote Paul Halmos, "The only way to learn mathematics is to do mathematics."

So to really learn the requisite math you are going to have to sit down, regularly, read a textbook or similar resource, and do practice problems (i.e. not going to happen). This is a recipe for "learning" that does not hold up (I spent my 1st and 2nd year in graduate school "learning" math this way), since it is so difficult to find the time and energy to work on something that is difficult, foreign, and may seem useless (especially at the beginning). The answer is to actually take math courses (undergraduate math) for credit. This provides more structured incentives to do practice (since you don't want to get a bad grade and lose your funding), and a means of getting help when you need it. As you might expect, this is quite painful, especially at first since we are talking about someone without much in the way of technical background, but barring Bruce Lee-esque levels of self-discipline this is the only way to rapidly acquire the necessary fundamentals.

  1. From the back cover of Jeff Gill's book Essential Mathematics for Political and Social Research