Complex Systems 899, Winter 2006: Theory of Complex Systems

Time: Tuesday and Thursday, 10-11:30am
Room: 229 Dennison

Instructor: Mark Newman
Office: 277 West Hall
Office hours: Wednesdays 1:30-3:30pm


This course is a math-based introduction to the theory and analysis of complex systems. Methods covered will include nonlinear dynamics, both discrete and continuous, chaos theory, stochastic processes, game theory, criticality and fractals, and numerical methods. Examples studied will include population dynamics, evolutionary theory, genetic algorithms, epidemiology, simple models of markets, opinion formation models, and cellular automata.


A firm command of calculus and linear algebra is a requirement. In particularly, students should be comfortable with the solution of linear differential equations and with the calculation and properties of eigenvalues and eigenvectors of matrices. In addition, a moderate portion of the course, perhaps three weeks, will deal with computer methods and algorithms. Some experience with computer programming will be a great help in understanding this part of the course, and students will be required to perform some numerical calculations, which means either writing programs or using standard numerical software such as Matlab or Mathematica.

Text book

We will use the book Modeling Complex Systems by Nino Boccara. It's not required that you buy a copy of this book, but you may find it useful. There will also be some in-class handouts covering particular topics in greater depth. A table of contents for Boccara's book can be found here. This book review from Physics Today is also informative and was written by a former University of Michigan postdoc from the Center for the Study of Complex Systems.


In addition to reading assignments, there will be weekly graded problem sets, consisting both of theory questions and of problems demonstrating applications of theory to example systems. There will be one mid-term and a final. The mid-term will be an in-class exam on either the Tuesday of the week after Winter break or the Thursday. The final will also be in-class and will be on Monday, April 24 from 4pm till 6pm. Grade will be 40% on the homeworks, 25% on the mid-term, and 35% on the final.


Problem sets


Here is a brief outline of the expected content of the course. Details may change, but the general outline will be mostly as here:

Mark Newman