If you’re a regular reader or contributor to this blog, you probably agree that mathematics have an indispensable role in the social sciences. Lately, however, I’ve been thinking a lot about something: what kind of mathematical tools do sociologists of the future require?
The reason I’ve been thinking about this is a talented undergraduate who is strongly considering going to grad school in sociology. Interestingly, part of what has moved him in that direction seems to have been two classes he’s taken with me. The first was the required undergraduate statistics class and the second a substantive class that includes a lot of network analysis, structural theory, and associated material. As it turns out, it’s entirely possible to teach Mayhew & Levinger to undergraduates. Who knew? In any case, in this second class he’s gotten a strong sense that sociology involves a lot of math and this excites him. I’m all for it, since this student is very smart and we need more mathematically-gifted grad students. Yesterday during a conversation, though, he asked me what sorts of math he should be thinking about taking as he prepares for graduate school. I gave him my answers- and an regression analysis textbook to work through during winter break- but I wonder what others think.
If you could somehow start over again in the field, what areas of mathematics would you make sure you learned right from the start?
Permutations 
This is a great question, and one that I have thought about a lot over the past 1.5 years of grad school. As I look back, I wish the fundamentals of probability theory had been taught to me at a much earlier age. As much as I appreciated the beauty of calculus in high school and beyond, the practical value of understanding probabilities has proved much more useful.
On top of that throw in some early set theory and combinatorics and I would have been far ahead of the curve.
I look forward to what others propose.
Abstract algebra, formal proofs, maybe advanced linear algebra…
Ironically, i failed one class as an undergrad (i, for some reason, had a hard time finding my way to actually show up for that particular class). Of course, i’d now have to say it is likely *the* class i took as an undergrad that is most directly useful in things i do today. So it’d be my first recommendation – Linear Algebra.
When it comes to recommending an actual math class I’m with jimi. I really wish I took linear algebra, I’ve had to pick up a little on my own and in my advanced statistics courses. Probability theory / mathematical statistics is of equal or greater importance.
Programming is really good experience.
I agree with what others have suggested. My list of things to learn would include: the basics (e.g., set theory, functions, logic, etc.), mathematical probability and statistics, linear algebra, calculus, and linear models. Then throw in a subject or two related to one’s domain of interest: for me that would be things like psychometrics, multivariate statistics, social network analysis, and so on. I also agree with Michael that programming skills are important. Getting involved with a project that will require the application of these skills can be a motivating experience and help to show how these skills can be applied.
There are also a lot of resources online that allow people to catch up on mathematics and statistics.
I posted a list of links to full course videos on mathematics and statistics on my blog:
http://jeromyanglim.blogspot.com/2009/05/online-mathematics-video-courses-for.html
I agree with Jimi and Michael about linear algebra. The obvious reason is its use in network analysis, but also because it’s risky to treat statistical techniques like PCA as black boxes without having some intuition behind the mathematics underlying it.
I also think every sociologist should take at least one programming course, perhaps learn a scripting language like perl or python. Even if you’re not doing computer-intensive things like agent-based modeling, the ability to do data manipulations that are more complicated than what Stata/R/Excel can do for you is invaluable. I see lots of my fellow students spending a very long time manually parsing/rearranging or categorizing data, which can be done in a fraction of the time using regular expressions.
Mathematical statistics, and of course, as one interested in rational choice, learning to take carry derivatives and find integrals is important.
Question: Did you apprise the student that ASA’s mathematical sociology section has a difficulty time recruting and maintaining members?
[…] 6, 2009 · Leave a Comment The mathematically-gifted sociologists over at Permutations are discussing what sorts of math a prospective graduate sociology student should enroll herself […]
Every once and a while, I pick up some students who have left (voluntarily or not) physical and life sciences, engineering, or pre-med. Most aren’t math specialists, but it is wonderful to have some students who just regard it as normal to express ideas formally. For folks like these, who have solid basics, I usually recommend probability, and as much linear algebra as possible (good for statistics, and also for equation systems and networks).
More common are folks who have been avoiding, or never learned the basics. For them (indeed, I wish it was for all sociologists), basic algebra and just a little bit of matrices and the most introductory calculus can really take them a long way.
There are some good books out “Basic Mathematics for Economists” and “Basic Mathematics for Social Scientists” (really more political science than anything else). That are good tools. Someone might write a parallel one aimed at sociology/anthropology.
I thought I’d link to my previous post about mathematics education more generally. https://permut.wordpress.com/2009/11/04/which-mathematics-to-teach/