Math 36   Mathematical Modeling in the Social Sciences 

Course Outline



1.    Voting Theory and Arrow’s Impossibility Theorem 

(Olinick Ch. 6)

2.    Tournaments in Voting Theory

(My notes)

3.    King Chicken Theorems

(My notes)

4.    Voting with an Agenda – tournaments


5.    Preference Rankings

(Kemeny and Snell Ch. 2)

6.    Preference Structures – Partial Orders


7.    Introduction to Shapley-Shubrik index

(my notes)


Dynamic Models

8.   Richardson Arms Race Model

(Olinick ch. 2)

9.     Lanchester Combat Models

(Modules, v.1, ch. 8)

10.           Population Models – logistic Equation

(Olinick ch. 3)

11.           Two Species Models – Predator/Prey

(Kemeny and Snell ch. 3; Olinick ch. 4)



12.           Intersection and Interval Graphs

(Roberts ch. 3.4)

13.           Phase Space and Boxicity

(Roberts ch. 3.5)

14.           Competition Graphs


15.           Trophic Stasus

(Roberts 3.6; Kemeny and Snell ch. 8)


Stochastic Models (Markov Chains)

16.           Stochastic Models introduction

(Olinick ch. 9)

17.           Markov Chains – Absorbing and Ergodic

(Kemeny and Snell appendix C; Roberts ch. 5)  

       Applications of Markov Chains:

18.           Learning Theory

(Olinick ch.12; Roberts 5.9.3)

19.           Conform/nonconform Study                    

(Kemeny and Snell ch. 5)

20.           Social Anthropology

(Olinick ch. 11)

21.           Influence and Social Power

(Roberts 5.10)

22.           Money Flow

(Kemeny and Snell ch. 6)


23.         How to ask sensitive questions without getting punched in the             nose.   (My notes).
























Kemeny, John G. and Snell, J. Laurie, Mathematical Models in the Social Sciences.  MIT Press, reprint 1972.  (Originally 1962).


Olinick, Michael,   An Introduction to Mathematical Models in the Social and Life Sciences.  Addison-Wesley, 1978.


Roberts, Fred S.,   Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems.  Prentice Hall, 1976.


Lucas, William, ed. Modules in Applied Mathematics, Volume 1: Differential Equation Models.  Springer-Verlag, 1978.


Bogart, K. P.  Preference Structures I: distances between transitive preference relations.  Journal of Mathematical Sociology, v. 3, 1973.


Lundgren, J. Richard.  Food webs, competition graphs, competition-common enemy graphs, and niche graphs.  In F. S. Roberts, ed., Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, IMH Volumes in Mathematics and its Application, p. 221-243.  Springer-Verlag, 1989.


Reid, K. Brooks.  Equitable Agendas: agendas ensuring identical sincere and sophisticated voting decisions.  PAM Technical Report, California State University, 1993.