Introduction to Mathematical Modeling

Basic information

Workload: 

60 hours

Prerequisite: 

Does not exist.

Syllabus: 

Models of population growth. Malthus - geometric progression / exponential function. Malthusian catastrophe - arithmetic progression versus geometric progression. Growth by Fibonacci numbers. Regression - linear and exponential (optimization as a black box). Calibration of the exponential model with real data (IBGE census, for example). Logistic model of population growth - differences equation. Calibration of the logistic model with real data. Oscillatory behavior; chaos. Schelling's segregation model in Social Sciences. Computational experiments. Principles of micro-economy: Consumer choice. Firm theory. Balance. Elements of game theory: Duopolies and the models of Cournot and Bertrand. Player with complete information: rational; best-reply. Player with incomplete information: Reinforcement Learning / Relative Payoff Sum.

 

Teaching Plan

Bibliography

Mandatory: 

  • Moacyr Alvim Silva. Mathematical Models in Social Sciences, lecture notes. 2014;
  • John Maynard Smith. Mathematical Ideas in Biology - Cambridge University Press, 1968;
  • Howard Weiss. A Mathematical Introduction to Population Dynamics. IMPA. 2009.

Complementary: 

  •  Fragelli Cardoso, R. Introduction to Economic Theory. Mimeo, 2008  Dixit, Avinash K. Thinking strategically: the competitive edge in business, politics, and everyday life. W.W. Norton & Company - 1991;
  •  Noam Nisan. Algorithmic game theory. Cambridge University Press. 2007;
  • Ralph Teixeira, Augusto Morgado. Probability Theory. FGV / EPGE, 2009;
  • Mark Newman. Networks: an introduction. Oxford University Press, 2010