Instructor: Mark Newman
Office: 322 West Hall
Office hours: Wednesdays 1:30-3:30pm
Email: mejn@umich.edu
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, criticality and fractals, computational complexity, and numerical methods. Depending on progress the class may also address information theory, game theory, or network theory. Examples studied will include population dynamics, evolutionary theory, epidemiology, simple models of markets, opinion formation, and self-organized systems such as forest fires and avalanches.
A firm command of calculus and linear algebra is a requirement. In particularly, students should be comfortable with the solution of linear ordinary 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.
There is currently no textbook on the market that covers this subject broadly at the level of this course, so there will be no required text. However, portions of the course are very well covered by a number of books that you may, optionally, take a look at. In particular, for nonlinear dynamics the course will follow the first few chapters of S. Strogatz, Nonlinear Dynamics and Chaos. There will also be some handouts addressing particular topics.
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 Thursday, October 25 from 10am to 11:30am. The final will also be in-class and will be on Friday, December 14 from 4pm till 6pm. Grade will be 35% on the homeworks, 30% on the mid-term, and 35% on the final.
Here is a brief outline of the expected content of the course. Details may change, but the general outline will be mostly as here: