Instructor: Mark Newman
Office: 322 West Hall
Office hours: Monday 2-4pm
Email: mejn@umich.edu
Quick links:
This course will introduce and develop the mathematical theory of networks, particularly social and technological networks, with applications to network-driven phenomena in the Internet, search engines, network resilience, epidemiology, and many other areas.
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 and preferential attachment models; community structure; percolation theory; network search.
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 moderate portion of the course, perhaps two weeks, will deal with computer methods for analyzing networks. Some experience with computer programming will be a great help in understanding this part of the course.
There will be weekly graded problem sets, consisting of questions on both theory and applications. There will be three midterm exams but no final. The midterms will be in class at the usual time on October 19, November 16, and December 12.
There will be reading assignments for each lecture. The assignments are listed on the schedule below. Students are expected to do the reading for each lecture in a timely manner.
Course packs (required): There is no textbook for this course but there will be two course packs, which will be available from Dollar Bill Copying on Church Street. The first course pack will cover the first part of the semester up to the first midterm exam; the second course pack will cover the remainder of the semester.
In addition to the course packs, a list of other useful books is given below. None of them is required, but you may find them useful if you want a second opinion or more detail on certain topics.
General books on networks:
Books on specific networky topics:
Date | Topic | Course pack reading | On-line resources | Notes |
---|---|---|---|---|
Tuesday, Sept. 5 | Introduction | Chapter 1 | Info sheet | |
Thursday, Sept. 7 | Technological and social networks | Chapters 2 and 3 | ||
Tuesday, Sept. 12 | Information networks and biological networks | Chapters 4 and 5 | Homework 1 handed out | |
Thursday, Sept. 14 | Basic mathematics of networks | 6.1-6.10 | ||
Tuesday, Sept. 19 | Paths, components, and the graph Laplacian | 6.11-6.14 | Homework 1 due, Homework 2 handed out | |
Thursday, Sept. 21 | Centrality | 7.1-7.2 | ||
Tuesday, Sept. 26 | Transitivity and assortativity | 7.3-7.7 | Homework 2 due, Homework 3 handed out | |
Thursday, Sept. 28 | Computer algorithms | 8.1-8.4 | ||
Tuesday, Oct. 3 | Paths and flows | 8.5-8.7 | Homework 3 due, Homework 4 handed out | |
Thursday, Oct. 5 | Statistics and errors | Chapter 9 | ||
Tuesday Oct. 10 | Real-world network structure | 10.1-10.2 | Homework 4 due, no new homework this week | |
Thursday, Oct. 12 | Degree distributions and power laws | 10.3-10.7 | ||
Tuesday, Oct. 17 | No class | Fall Break | ||
Thursday, Oct. 19 | Midterm 1 | |||
Tuesday, Oct. 24 | Random graphs 1 | 11.1-11.5 | Homework 5 handed out | |
Thursday, Oct. 26 | Random graphs 2 | 11.6-11.8 | ||
Tuesday, Oct. 31 | Configuration models 1 | 12.1-12.5 | Homework 5 due, Homework 6 handed out | |
Thursday, Nov. 2 | Configuration models 2 | 12.6-12.8 | ||
Tuesday, Nov. 7 | Configuration models 3 | 12.9-12.11 | Homework 5 due, Homework 6 handed out | |
Thursday, Nov. 9 | Generative models 1 | 13.1, 13.2 | ||
Tuesday, Nov. 14 | Generative models 2 | 13.3-13.6 | Homework 6 due, no new homework this week | |
Thursday, Nov. 16 | Midterm 2 | |||
Tuesday, Nov. 21 | Community structure 1 | 14.1-14.2 | Homework 7 handed out, due Dec. 5 | |
Thursday, Nov. 23 | No class | Thanksgiving | ||
Tuesday, Nov. 28 | Community structure 2 | 14.4-14.6 | ||
Thursday, Nov. 30 | Percolation | 15.1-15.5 | ||
Tuesday, Dec. 5 | Epidemics on networks | 16.1-16.3 | Homework 7 due | |
Thursday, Dec. 7 | Network search | Chapter 18 | In class, usual time and place | |
Tuesday, Dec. 12 | Midterm 3 | In class, usual time and place |