Instructor: Mark Newman
Office: 322 West Hall
Office hours: Tuesday 1:30-3:30pm
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; spectral methods and random matrix theory; maximum likelihood methods; 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 September 29, November 3, and December 10.
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.
Textbook (required): Networks: An Introduction, M. E. J. Newman, Oxford University Press, Oxford (2010)
In addition to this required text, 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:
|Wednesday, Sept. 3||Introduction||Chapter 1||Info sheet|
|Monday, Sept. 8||Classes of networks||Chapters 2 through 5|
|Wednesday, Sept. 10||Basic mathematics of networks||6.1-6.11||Homework 1, Data set||Homework 1 handed out|
|Monday, Sept. 15||Centrality, transitivity, assortativity||Chapter 7|
|Wednesday, Sept. 17||Network structure and degree distributions||8.1-8.6||Homework 2, Data set||Homework 1 due, Homework 2 handed out|
|Monday, Sept. 22||Computer algorithms 1||Chapter 9|
|Wednesday, Sept. 24||Computer algorithms 2||10.1-10.4||Homework 2 due, no new homework this week|
|Monday, Sept. 29||Midterm 1||In class, usual time and place|
|Wednesday, Oct. 1||Random graphs 1||12.1-12.5||Homework 3||Homework 3 handed out, due Oct. 15|
|Monday, Oct. 6||No class|
|Wednesday, Oct. 8||Random graphs 2||12.6-12.8|
|Monday, Oct. 13||No class||Fall Break|
|Wednesday, Oct. 15||Configuration models 1||13.1-13.4||Homework 4||Homework 3 due, Homework 4 handed out|
|Monday, Oct. 20||Configuration models 2||13.5-13.8|
|Wednesday, Oct. 22||Configuration models 3||13.9-13.11||Homework 5||Homework 4 due, Homework 5 handed out|
|Monday, Oct. 27||Generative models 1||14.1-14.2|
|Wednesday, Oct. 29||Generative models 2||14.3-14.5||Homework 5 due, no new homework this week|
|Monday, Nov. 3||Midterm 2||In class, usual time and place|
|Wednesday, Nov. 5||Partitioning and community structure||11.2-11.8||Homework 6||Homework 6 handed out|
|Monday, Nov. 10||Maximum likelihood methods|
|Wednesday, Nov. 12||The expectation-maximization method||Homework 6 due, no new homework this week|
|Monday, Nov. 17||Spectral methods|
|Wednesday, Nov. 19||Random matrix theory 1||Homework 7, Data set||Homework 7 handed out, due Dec. 3|
|Monday, Nov. 24||Random matrix theory 2|
|Wednesday, Nov. 26||No class||Thanksgiving|
|Monday, Dec. 1||Percolation||Chapter 16|
|Wednesday, Dec. 3||Epidemics on networks||17.1-17.8||Homework 7 due|
|Monday, Dec. 8||Network search||Chapter 19|
|Wednesday, Dec. 10||Midterm 3||In class, usual time and place|