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
(Reid)
5. Preference Rankings
(Kemeny
and Snell Ch. 2)
6. Preference Structures – Partial Orders
(Bogart)
7. Introduction to Shapley-Shubrik index
(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
(Lundgren)
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.
Reid, K. Brooks. Equitable Agendas: agendas ensuring identical sincere and sophisticated voting decisions. PAM Technical Report, California State University, 1993.