MAE 298, Winter 2008 (CRN: 29857)
Network Theory and Applications
Computer NetworksBiological NetworksTransporation Networks
Instructor: Prof. Raissa D'Souza
Email: raissa at cse.ucdavis.edu
Office: 1101 Mathematical Science Building
Teaching Dr. Soumen Roy
Assistant: Email: sroy at cse.ucdavis.edu
Office: 1228 Mathematical Science Building
Lectures: Mon & Weds 2:10-4:00pm, 176 Chem
Office hours: Soumen Roy, Tues 2-3pm
Prof. D'Souza, Tues 4:30-5:30pm (or by appt suggested)












Overview:
We are beginning to understand how pervasive network structures are in the world around us, from the Internet and the power grid, to social acquaintance networks, to biological networks. This course is intended for graduate students interested in learning about modern perspectives on networks, and should allow students to incorporate network theory into their own research. This course will cover General Techniques and Selected Applications. Applications will reflect student interest, thus the later material comprising the course content is still TBD.

Prerequisites:
Familiarity with: linear algebra, basic statistics, calculus, ordinary differential equations, using computer software.

Course structure: Lectures, bi-weekly problem sets/paper reviews and a class project.

  • Topics: This course assumes no prior knowledge of networks. We will begin with basic concepts about networks and the mathematical tools for their analysis, developing key metrics for characterizing the structure of a network. We will then examine several models of network growth (random graphs, preferential attachment, small-worlds). Emphasis will then shift to network function and algorithms, such as the Page Rank algorithm for ranking web pages, and also decentralized search and routing in social and information networks. The next topics to be covered will reflect student interest.

  • Paper reviews: For these assignments, you are required to provide a short summary (one or two paragraphs) and a review of the strengths and weaknesses of the paper. The goal of these reviews is to help you synthetise the main ideas and concepts presented in each paper. Note, not all students will review the same papers. Based on your interests, you will choose the papers.

  • Project: Students work individually or in small groups on a course project. The projects will complement and extend the lecture material. The project may include simulation and modeling, network visualization, creating software for network analysis, or analysis of a real-world network (such as a transportation, social, biological or ecological network). Here is a list of potential project topics.

    • Resources: There will be no required text for this course. The content will largely come from articles and class notes. Several technical texts, covering aspects of network theory, are available and might be worth purchasing.

    The course will begin with excerpts from the following:

  • The Structure and Function of Complex Networks, by M. E. J. Newman, SIAM Review 45 (2), 167-256, 2003.

  • Random Graph Dynamics, by Rick Durrett.