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