Instructor: Mark Newman
Office: 277 West Hall
Office hours: Wednesdays 1:30-3:30pm
Email: mejn@umich.edu
This course will introduce and develop the mathematical theory of networks, particularly social and technological networks, with applications to important network-driven phenomena in epidemiology of human infections and computer viruses, the Internet, network resilience, web search engines, and many others.
Topics to be covered will include experimental studies of social networks, the world wide web, information and biological networks; methods and computer algorithms for the analysis and interpretation of network data; graph theory; models of networks including random graphs, preferential attachment models, and the small-world model; computer simulation methods; network dynamics.
A provisional outline of the course can be found here. Details may change, but this is reasonably accurate.
Students should have studied calculus and linear algebra before taking the course, and should in particular be comfortable with the solution of linear differential equations and with the calculation and properties of eigenvalues and eigenvectors of matrices. In addition, a moderately large portion of the course, perhaps three weeks, will deal with computer methods for studying networks. Although students will not be required to write computer programs, some experience with computer programming will be a great help in understanding this part of the course.
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 networks. There will be one mid-term and a final. The final will be on Friday, April 23 from 1:30pm till 3:30pm. Grade will be 40% on the homeworks, 25% on the mid-term, and 35% on the final.
There is no set text for this course because no one has written one yet. But there is a course-pack as described below, and we may read some research papers that address particular topics during the course. There are also a number of books that cover parts of the material quite well.
Course-pack: The course-pack contains a copy of the review article The structure and function of complex networks, M. E. J. Newman, SIAM Review 45, 167-256 (2003). Copies of the course-pack are available from Howard Oishi in the Complex Systems office (4485 Randall).
Books: A list of useful books is given below. None of them is required. However, if you want recommendations, I'd recommend for graph theory either Wilson (introductory) or West (more advanced), and for social network analysis either Scott or Wasserman & Faust. The Ahuja book is excellent if you're interested in the computer programming/algorithms side of things. Meyer is good if you need to brush up on your linear algebra.