Mathematical Sociology seminar

Winter 1999

Mondays, 2:00 - 4:50, Bunche 2150

Prof. David D. McFarland

347-853-200, Soc. 197h (undergraduate)

747-486-200, Soc. 281 (graduate)

Topics this quarter will be:

• Mathematical models of population.  Emphasis will be on the Leslie formulation, in which numbers of people various ages are arrayed in a column matrix, which is projected over time by applying successive powers of a square matrix containing fertility and survivorship rates.  Changing age distribution has important social implications, affecting such things as crime rates and demands on the welfare and health care systems.
• Stability and change in exchange networks.  Experimental social psychologists have studied how position in a small network yields power, as exemplified by larger payoffs in exchange experiments.  We will review this work, especially a theoretical piece by Bonacich, and then apply the latter theory to a different but related question, about the stability or instability of such a network itself.  We will want to examine the conditions under which network participants might benefit from adding exchange links to the initial network.  
• If time permits, I would also like to spend some time on John Logan's TSL (two-sided logit) models, which improve on the one-sided and simpler two-sided models that I and others have developed for such really paired phenomena as jobs and workers, or prospective brides and grooms.  This is technically difficult material, and I am not sure we will be able to do much with it, among the various other things on the agenda for this quarter.  
• Throughout, we will need to use Mathcad or other software, to do our matrix calculations.  
• As we work, we will communicate by posting things on our web sites.  Two years ago I devoted almost an entire quarter to problems in publishing technical material on the web.  I do not intend to repeat that ( i281s97.htm ), as things have much improved since then.  However, I expect to be giving updates on such matters as Acrobat technology, HTML table editors, and XML.

Requirements:  All students should attend regularly, at least attempt the readings and exercises, participate in discussions, and post selected work to a web site.  There is not a research paper assignment per se, but smaller assignments more in keeping with the duration of one quarter.  Graduate students and others who have ongoing research projects related to the seminar topics should consult me about how they might best coordinate contributions to the seminar and to their own research.