Math 36
Mathematical Models in the Social Sciences

General Information Syllabus Homework


Differential Equations
(Due Friday, January 14)
Exponential and Logistic models:
  • Read: Olinick, Chapter 3
  • Topics: the four steps involved in modeling; solving differential equations using the seperation of variables technique; assumptions, differential equation, and function for population model (both exponential and logistic); solving population growth and radioactive decay problems
  • Homework 01: available
Arms Race models:
  • Read: Olinick, Chapter 2
  • Topics: arms race assumptions and corresponding terms in differential equations; creating slope graphs to analyze long-term behavior of equations: interpreting the lines dx/dt = 0 and dy/dt = 0, the regions they bound, and their intersection; analyzing effects of changing parameters in equations
  • Homework 02: not yet available
Predator-Prey models:
  • Read: Olinick, Chapter 4
  • Topics: assumptions for predators and prey, and corresponding terms in differential equations; finding a single equation relating predator and prey populations; modifying assumptions and differential equations (prey population with logistic growth, predator population dependent on "critical ratio")
  • Homework 03: not yet available
Epidemic models:
  • Read: Olinick, Chapter 13
  • Topics: stages of disease; assumptions for population and progression of disease, corresponding differential equations, and possible modifications; time at which demand for medical services is highest; how preventing an epidemic is reflected mathematically
  • Homework 04: not yet available
Problem Session:
  • Extra problems: not yet available

Game Theory
Access our Game Theory Text book, by Kockesen.
Introduction to Game Theory
  • Read: Kockesen Introduction
  • Topics: Introduction to Game Theory. Types of games. Extensive and Strategic forms of games.
  • Homework: none.
Dominant Strategies
  • Read: Kockesen Chapter 1
  • Topics: Dominant and dominated strategies. Iterated Elimination of (Weakly or Strongly) Domininant Actions.
  • Homework 05: Given in class
Nash Equilibirum
  • Read: Kockesen Chapters 2 and 3
  • Topics: Introduction to Nash Equilibrium. Solving for Nash Equilibria. Comparing Nash Equilibria with Dominated Strategy Equilibria.
  • Homework: none.
Applications of Nash Equilibria and Mixed Strategy Equilibria
  • Read: Kockesen Chapters 3 and 4
  • Topics: Nash Equilibira of First-price and Second-price sealed bid auctions. Introduction to mixed strategies and mixed strategy equilibira. Solving for the value of games. The Minimax Theorem.
  • Homework 01: none.