Math 76 W09

Topics in Applied Mathematics

Professor Rockmore

__Syllabus __

(will be updated as we progress)

__**Special Notes: __

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**(1)
****Tuesday, 1/6 – No class **

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

**(3) ****3/4 –
Final Projects are due**

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__ __

__Week 1__:

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**1/6 – No Class**

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**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, ÒA brief history of generative models for power law and lognormal distributionsÓ

__Suggested Readings:__

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

Albert-L‡szl— Barab‡si 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, ÒOn the use of GIS dataÓ

** **

**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**

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** **

**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

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**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