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: 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: 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: available
|
Problem Session:
- Extra problems: not yet available
|
Game Theory
(Due Wednesday, February 2) |
Two-player zero-sum games (Part I):
- Read: Ferguson, Part II, sections 1 and 2
- Topics: mixed and pure strategies; solving 2 by 2 matrix games;
the minimax theorem
- Homework 05: available
|
Two-player zero-sum games (Part II):
- Read: Ferguson, Part II, sections 1 and 2
- Topics: solving 2 by n games; basic poker endgame analysis
- Homework 06: available
|
Matrix games:
- Read: Ferguson, Part II, section 3
- Topics: matrix multiplication; solving n by n matrix games
- Homework 07: available
|
Impartial combinatorial games:
- Read: Ferguson, Part I, sections 1, 2, and 6
- Topics: examples of combinatorial games: take-away, nim, green hackenbush;
how to win at nim using *n and binary addition; Sprague-Grundy theorem
- Homework 08: available
|
Two-player general-sum noncooperative games:
- Read: Poundstone, Chapters 6 and 12
- Topics:
payoff matrices for general-sum games;
goal-dependent strategies;
the prisoner's dilemma and variations;
communicating through repeated play;
natural selection of survival strategies
- Homework 09: available
|
Two-player general-sum cooperative games:
- Read: Ferguson, Part III, section 4
- Topics: solving TU and NTU games; Nash bargaining axioms;
the Nash arbitration function
- Homework 10: available
|
Many-player cooperative games:
- Read: Ferguson, Part IV, sections 1,2,3
- Topics: coalitions;
value/power functions;
multiplayer payoff matrices;
payoff vector, group and individual rationality, stable and unstable solutions;
Shapley axioms and computing the Shapley function
- Homework 11: available
|
Problem Session:
- Extra problems: not yet available
|