## is this the mathematical sociology book i’ve been looking for?

If you want to learn mathematical sociology, you don’t have many good options. There are very few math soc courses. Or you can do a math intensive area and then pick up various journals. Or you can pick up books, many of which are out of date. I remember being in grad school and reading Coleman ’64. Good for its time, but terribly outdated. But I’ve found a solution. James Montgomery, a Wisconsin soc prof/econ PhD, has a very nice website with his math soc course notes. The lectures will be a text book. I say it hits the right note. It has classical math soc, like influence models and Markov chains, but newer stuff like cultural evolution models and segregation dynamics.

My only criticism is that it exclusively focuses on computational models and solving particulat models and less on theorem proving. As I’ve suggested before, math soc has enough computational models, but we need to build a core set of “classic math soc theorems” that define the field, in the same way the microeconomics is built around a set of equilibrium theorems. Aside from that, I recommend that people interested in math soc read this website. I hope to buy the book one day.

Thanks very much for the pointer!

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RuchiraApril 22, 2010 at 3:07 am

Nice resource. And, the chapters are downloadable, excellent.

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tfApril 22, 2010 at 3:31 am

Fararo ’73 is old but not as outdated as you’d think. Also Bob Hanneman at Riverside (http://www.faculty.ucr.edu/~hanneman/) keeps online chapters of a pretty good book on mathematical simulation.

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OmarApril 22, 2010 at 12:43 pm

What kind of questions would be answered using such theorems? I can understand a theorem that proves the conditions needed to achieve a Pareto efficiency. However, I cannot think of anything similar in sociology.

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GuillermoApril 22, 2010 at 3:28 pm

That’s the point, Guillermo. Sociologists should defined a state of a social system that reflects social theory. The theorem would then establish that the state happens under certain conditions. Sadly, sociology hasn’t done enough of that in my view.

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fabiorojasApril 22, 2010 at 3:31 pm

Well, Guillermo, if you are interested, maybe you should take that step: what’s the outcome described by sociology? How can it be formalized? What can be proved about it?

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fabiorojasApril 22, 2010 at 3:35 pm

I nominate the Ising Model and spin glass theory as the most important undertheorized models in sociology or economics. Mathematical sociologists could steal a march on economists by demonstrating how weak links can lead to collective behavior in ways that are not possible in neoclassical theory.

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Michael F. MartinApril 22, 2010 at 5:07 pm

MM: I once looked into Ising models. Easy to simulate, but it’s pretty hard to prove things, even for the 2-d case.

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fabiorojasApril 22, 2010 at 6:05 pm

“Sadly, sociology hasn’t done enough of that in my view.”

Perhaps sociology is too focused on the externalities and disregards simple models?

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GuillermoApril 22, 2010 at 6:09 pm

Guillermo: I wish it were that fancy. Too many sociologist think formalization has nothing to offer, or that formalization will lead to an econ style stamping out of qualitative research.

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fabiorojasApril 22, 2010 at 6:11 pm

[…] Mathematical Sociology Textbook Fabio highlights a freely available mathematical sociology textbook in-progress by James […]

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Montgomery’s Mathematical Sociology Textbook « PermutationsApril 22, 2010 at 6:41 pm

Not quite what you are looking for but I believe that quite a few game theorists are beginning to formalize sociological theories. For example here is a Gintis paper on social norms.

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Dan in EurolandApril 22, 2010 at 7:17 pm

Xkcd comic worth reading:

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GuillermoApril 22, 2010 at 7:36 pm

I like that comic — and the field of management is even further off to the left.

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tfApril 22, 2010 at 7:44 pm

Teppo is right, the sociologist in that comic should be saying, “At least I’m not in a business school”

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adamApril 22, 2010 at 7:46 pm

@adam: unless the income matters ;-)

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REWApril 22, 2010 at 11:12 pm

Fabio: Be sure to also check out Gintis’s book — http://www.umass.edu/preferen/Mathematics%20For%20Humanists/mathlit.pdf

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tfMay 1, 2010 at 3:35 am

And by humanists does he mean “dummies”?

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OmarMay 1, 2010 at 3:47 am

In terms of titles, I prefer “Physics for Poets”.

http://www.amazon.com/Physics-Poets-Robert-H-March/dp/0070402485

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GuillermoMay 1, 2010 at 3:53 am