David Feldman

College of the Atlantic

Fall 2008

Tu/Fr 1:00-2:25

James Gower Seminar Room

- Lecture 1: Introductory examples and questions. [One slide per page] [Four slides per page]
- Lecture 2: Basic network properties. [One slide per page] [Four slides per page]
- Lecture 3: Erdos-Renyi model. [One slide per page] [Four slides per page]
- Lecture 4: Watts-Strogatz model. [One slide per page] [Four slides per page]
- Lecture 5: Introduction to Preferential Attachment. [One slide per page] [Four slides per page]
- Lectures 6-8: Probabilities and Stochastic Processes, Power Laws and Long Tails . [One slide per page] [Four slides per page] (Updated 7 Oct. 2008.)
- Lectures 9-1: Community Discovery and Higher-Order Structures [One slide per page] [Four slides per page] (Updated 28 Oct. 2008.)

Network structures are ubiquitous in the world around us: communication networks, transportation networks, networks of friends and acquaintances, and biological networks, to name just a few. In this class, students will learn about the mathematical similarities and abstractions that under-lie these examples. Additional examples will be drawn from molecular biology (gene regulation and protein interaction networks), economics (trading networks, relations among firms, and strategic interactions on networks), computer science (computer networks and the world wide web), and ecology (food webs). The last decade has seen an explosion of work in the theory and applications of networks to an enormously wide range of problems. Students who successfully complete this course will: gain a broad introduction to recent work in this field; understand the strengths and weaknesses of network modeling; and be able to apply networks and network analysis in a variety of settings.

In the first part of the course, we will focus on empirical descriptions of network structure. We will then turn our attention to dynamics of networks: how do networks form and grow, and how are these growth rules related to global structure? Finally, we will consider algorithms and dynamics on networks. In this latter part of the course we will learn about the spread of diseases and computer viruses on networks, how to detect community structure in networks, and how Google's PageRank algorithm works.

Evaluation will be based on several problem sets, three short literature reviews to be posted on the course blog, and a final project on a topic of the student's choosing.

Intermediate/Advanced. *ES* *QR* Pre-requisites: at least one college-level mathematics class and permission of instructor. Lab fee $10.