Math 76 W09

Topics in Applied Mathematics

Professor Rockmore

Syllabus

(will be updated as we progress)

**Special Notes:

(1) Tuesday, 1/6 – No class

(2) 1/27 – Final Project Proposals are due

(3) 3/4 – Final Projects are due

Week 1:

1/6 – No Class

1/8 – Introduction:

(1) What are complex systems?

(2) Network Basics and Examples

(3) Linear Algebra Review

Required Reading (on BBD):

P. Anderson, More is different

Miller /Page, Chapters 1 and 2 (Intro to the notions of agent-based modeling) (Note: I will give a Xerox of Chapter 1 to give you time to get the book).

Schelling: Chapter 1

Jackson, Chapters 1 and 2 (Note: I will provide a Xerox of Chapter 1 to give you time to get the book).

M. Newman pp 1-20. (basics of different kinds of networks, various important related statistics, topics of interest)

Assignment 1 (due 1/15) – retrieve from BBD

Week 2 (1/13 -- 1/15) -- Continuation of network basics:

(1) random graphs

(2) measures of clustering and connectivity; Community finding

(3) power laws

(4) Visualizations – MDS/Principal Components Analysis

(5) Agent-based Modeling

Note: We will use the x-hour this week.

Required Readings:

Page/Miller Chapters 3, 4

Schelling: Chapter 2

M. Newman, Power Laws, Pareto distributions and Zipf's law arXiv:cond-mat/0412004v3 [cond-mat.stat-mech]

M. Mitzenmacher, “A brief history of generative models for power law and lognormal distributions”

Suggested Readings:

F. Chung, A whirlwind tour of random graphs, www.math.ucsd.edu/~fan/wp/randomg.pdf.

Albert-László Barabási and Eric Bonabeau, Scale-Free Networks, Scientific American 288, 60-69 (2003)

Jackson, Chapters 3, 4.1, 4.2

Assignment 2: due 1/22

Week 3 (1/20 – 1/22) – Betweeness measures; centrality/HITS algorithm – hubs and authorities

1/20 – special presentation, first half of class, J. Chipman, “On the use of GIS data”

Required Readings:

Page/Miller, Chapters 5,6

M. Girvan and M. Newman, Community structure in social and biological networks, PNAS | June 11, 2002 | vol. 99 | no. 12 | 7821-7826

M. Newman, Mixing patterns in networks, Phys. Rev. E 67, 026126 (2003) [13 pages]

Suggested: M. E. J. Newman, A measure of betweenness centrality based on random walks, http://arxiv.org/pdf/cond-mat/0309045

Assignment 3: due 1/29

Week 4 (1/27 – 1/29) - Information Cascades/Epidemiology

Required Reading: Page/Miller Chapter 7

Recommended Reading:

Jackson, Chapters 3, 4.1, 4.2

1/27 – Final Project Proposals are due

Week 5 (2/3 – 2/5): Beginnings of Spectral analysis and the Laplacian, the PDM

Assignment 4: due 2/12

Week 6 (2/10 – 2/12): Spectral Clustering, connections between random walks and clusters

Assignment 5: due 2/19

Week 7 (2/17 – 2/19): Multidimensional Scaling, allometry

Week 8 (2/24 – 2/26): Collaborative Filtering and recommendation networks – notions of collaborative filtering and its uses. Item-item or User-user models. Uses in Amazon, Jester, on-line dating. Connections with Latent Semantic Analysis.

Week 9 (3/3 – 3/5, 3/10): Final Project Presentations