Basic skills

Modeling is useful when multiple actors are interdependent over time such that macro, or collective, outcomes of micro interactions are hard to grasp by the unaided reason. Math is best for its clarity and explicitness: if someone claims to have a result you only have to verify the proof and its assumptions. When analytic solutions or elegant proofs are not possible, simulation models can be made, which however are much harder to verify, in particular if there are many lines of code. Yet often there is no other option.

A fundamental paper:

• P.W. Anderson (1972) More is different. Science 144: 393-396.

One of the best motivations for modeling:

• Joshua M. Epstein (2008) Why model?  Journal of Artificial Societies and Social Simulation 4:12.

On agent based modeling (ABM):

• Eric Bonabeau (2002) Agent-based modeling: Methods and techniques for simulating human systems PNAS 99: 7280-7287
• C. M. Macal and M. J. North (2010) Tutorial on agent-based modelling and simulation Journal of Simulation 4: 151–162.

You don't have to be a mathematician or a computer scientist to use math or simulation models. To develop basic skills, an excellent short book is:

• John Fox (2009) A mathematical primer for social statistics.

The title is too modest; it is a primer for any kind of mathematics in all kinds of empirical sciences.

You might continue the former primer with this still very good old textbook:

• John G. Kemeny and J. Laurie Snell (1962) Mathematical models in the social sciences, currently "print on delivery" by MIT press.

Pandas package smoothens the transition. Watch out for old Python 2 code, which is abundant on the Web and in text books, but will no longer be maintained. Translate automatically all your Python 2 files to Python 3, with the 2to3 command in Linux (which you should have anyway). If you want a single language for all your social science work, however, R is best (and the deSolve packages makes it possible to solve differential equations, too).

• The following book is an excellent general introduction to modeling, but its style of Python programs (with global variables) leaves something to be desired; Sayama, Hiroki (2015) Introduction to the modeling and analysis of complex systems. New York. SUNY.
• The best textbook on the theory behind complex systems in general, and of social systems in particular: Stefan Thurner, Rudolf Hanel and Peter Klimek (2018) Introduction to the Theory of Complex Systems. Oxford U.P.

Evolutionary game theory

People's decisions and fates are interdependent, which is formalized in game theory. To sidestep the ludicrous assumption of perfect rationality, you can resort to evolutionary game theory. With apologies to John Maynard Smith for not recommending his classic textbook, I suggest:

• Karl Sigmund (2011) Games of life.
• At a slower pace and with more examples: Herbert Gintis (2000) Game theory evolving. Models of social phenomena

Early 21st century statistical physicists have become the most prolific producers of models of social phenomena (and mathematicians, computer scientists, biologists, and engineers along with them). An introduction without math:

• Philip Ball (2004) The physical modelling of human social systems. Complexus 1: 190-206.

An overview:

• Claudio Castellano, Santo Fortunato and Vittorio Loreto (2009) Statistical physics of social dynamics.  Reviews of Modern Physics 81: 591-646.

Computation

Large computation jobs beyond the abilities of a PC can be done on the computers of the University of Amsterdam (SARA)..

Example

An aesthetically mouth-watering case study of a mathematical approach to cultural phenomena is:

• Ron Eglash (1999)  African fractals