M435 Projects in Applied Mathematics

Fall 2008

This course provides students with an opportunity to explore a range of mathematical techniques and applications via in depth projects. In 2008 four projects will be selected from the following topics:

Iterated Singular Value Decomposition, Missing Data and the Netflix Competition
Nonlinear Modeling and Predicting the Stock Market
Image Analysis and Deblurring
Topology Preserving Mappings and Voice recognition
Linear Programming and Game Theory
Simulation Modeling
Numerical simulation of differential equations

Prerequisites: M229 and preparedness to program in Matlab. Note that in Fall 2008 we are waiving the M340 or M345 or M355 requirement.

Instructor: Professor Michael Kirby, Kirby@math, Weber 211.

Office Hours: M, W 3:00-3:50.

Weekly Schedule including due dates and topics will be posted here.

Grading policy

The final grade will be determined the evaluation of

4 reports (submission in LaTeX required) 80% (20% each)
class participation 5%
final report presentation 15%

Groups

All work will be done in groups. The groups will generally be different for each project. Each group will receive a single grade for each project.

Project Reports

The duration of each project will be approximately 3-4 weeks. Each group will submit a jointly written single report.

Sample Report Outline

General Introduction to the Problem

qualitative problem description.
why is it interesting?

Modeling Approach

This generally includes several steps:

Quantitative problem formulation (discrete or continuous?)

Variable identification

Parameter identification

For example, in a simulation model it is useful to identify a small number of parameters to vary. Simulations are run (many times) for each set of parameters and predictions are made.

Mathematical Theory

Can a simplified version of your model be solved analytically? Is your approach linear or nonlinear? Can you make predictions about long time behavior?

Computational Questions

How does the complexity of the problem scale with the number of variables or parameters under investigation? Can the algorithm be parallelized?

Results

Use Figures embedded in the text and cited in the text.

Interpretation

Predictions, added value.
Weaknesses of the approach

Conclusions and Summary

Answer the questions:

what did you learn about this question that you could not have discovered without your mathematics?
if you had 3 months to work on this problem what would you do?

Appendices