The mathematics of Social Systems Dynamics Research.

April 6, 2010 2:07 PM

Assuming that I am going to be pursuing a PhD in mathematical sociology, applied mathematics, or organizational analysis with no background in higher math with only the resources to take a few classes at the local college how do I go about it? More info and 3 specific questions inside.

I finished my MS in Conflict Analysis and Resolution and realized that my low level- high school algebra 1 and some geometry - math background hinders my future goals. I realize now that my interests fall in the development and change of social conflict norms. I have found great ways of analyzing social conflict -affect control theory, network analysis, system dynamics research, etc - but do not have the math skills needed to fully comprehend the math behind them.

Assuming that I am going to be pursuing a PhD in mathematical analytical sociology, applied mathematics, or organizational analysis with no background in higher math with only the resources to take a few classes at the local college...

1) What should I make sure I know on my own/ through a tutor?
2) What classes should I take at the local college to prove I have the skills needed to succeed at the work in a PhD program?
3) What areas/fields am I ignorant of because of my lack of mathematical background that I should look into?

posted by elationfoundation to education (7 answers total)

You may be biting off more than you can chew. It is extremely rare to first enter a mathematical field at a later age with little or no previous mathematics exposure (mathematicians tend to do their best work at a young age). It's best to test the water to see how well you are suited to getting a PhD in a mathematical discipline. I suggest you take a courses in calculus, differential equations and complex variables, in that order, at a community college. You should learn very soon if your goals are attainable. I don't recommend doing this on your own. You'll need a lot of help in the beginning which is readily found in a classroom with other students and an instructor to go to. Good luck!
posted by Hilbert at 2:52 PM on April 6, 2010

From the point of view of mathematical sociology: Programming skills are enormously useful. Software to model some of your ideas just won't exist and you'll have to program it yourself. For network analysis, some basic knowledge of graph theory and matrix algebra are very useful, but you don't need to know these things before entering graduate school.

Since you'd have to do the general program requirements, not just those related to mathematical sociology, you'll also have to do stats, for which calculus knowledge is useful if you want to get anywhere beyond just running an OLS regression and reporting coefficients. Again, this is not mandatory, but will help you if you want to be a hardcore quant jock.

The skills they'll want to see that you have are the same as any grad program -- understanding of how to formulate an interesting research question and knowledge of how to design a research program to answer it. Writing skills. Decent quant and verbal GREs. If you want to learn some substance, try Coleman's book on mathematical sociology and read a little Simmel (even mathematical sociologists need theory!).
posted by If only I had a penguin... at 3:02 PM on April 6, 2010

I disagree with Hilbert*. Mathematicians do completely different work than what the OP wants to do. Mathematicians work to understand how math works/to develop new theorems etc. (i.e. it's so abstract that as a non-mathematician I'm not even sure how to describe it). What the OP is talking about is using existing math to understand how things work. So if instead of thinking about things as being additively and linearly caused (as the simplest statistical models do), wondering if they might better be explained using other kinds of math and testing out those ideas.

But mostly I came back to add: Programming skills combined with quant skills (or just quant skills, but those alone are more common) will put you in strong demand as a research assistant if you're in the sort of department where the faculty do this sort of thing.

*By which I mean I don't think one has to start this young, not necessarily that you specifically should do this, since obviously I don't know anything about you specifically.
posted by If only I had a penguin... at 3:11 PM on April 6, 2010

Hilbert, thank you for the concrete course progression suggestions. Sadly, I have no choice but to pursue this. My need to go further with my work demands this next step.

If only i had a penguin... Thank you so much. I am currently working on Java and then will pursue other programming languages. I know limited stats and with guiding text can do up to multiple regression with SPSS. I am actually quite theory heavy and as such need to focus here. Finally, my GRE scores reflect my lack of quality learning in my youth so I am working on proving my abilities in research to overshadow my timed test taking abilities. Thank you so much for the help. I will look into stats and programming courses to start.
posted by elationfoundation at 4:33 PM on April 6, 2010

1) Make sure you understand all the prerequisite material for an entry level calculus course.

2) Take a calculus course at your local college.

3) Calculus is the main analytical tool of all the major sciences, both social and natural. It forms the basis of probability theory and statistics. If you're interested in networks (social or otherwise), you'll also want to understand dynamical systems, in which case linear algebra is also very helpful.
posted by abc123xyzinfinity at 4:43 PM on April 6, 2010

Since other people have emphasized calculus so much, I want to emphasize linear algebra. Network theoretic techniques are almost entirely based on linear algebra, and it is the natural way to handle multiple variables. Calculus is useful for optimization and dynamics of continuous quantities, but as soon as you get to more than one variable at once, you'll be needing both calculus and linear algebra. Probability and statistics will require some basic knowledge of both, as well.

The excellent news for you is that linear algebra doesn't require any more background than you have. It is conceptually tricky at times, but you pretty much just add, subtract, and multiply. Almost everything also has a nice, geometric interpretation. The other good news is that when you do anything real, you'll probably be doing most of it in a computer, for which there are a variety of good tools.

Best of luck!
posted by Schismatic at 6:47 PM on April 6, 2010

First, to not answer your question: don't box yourself into a discipline. Review the literature and find PEOPLE to study under that you think you could work with on this topic. It might be soc, it might not.

Second, to answer your question. Make sure that you get an A in the stats classes that are required by undergrads in the major of the department that you are applying. Find out what the closest class is at your local community college.
posted by k8t at 8:42 PM on April 6, 2010