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

  • Matlab Code
  • Background information or theory

 

 

Sample Latex Report

 

 

More About LaTeX

 

To create your report edit the file sample.tex and modify the text.  Equations appear as

\begin{equation}

\label{myfirstequation}

y= \int_{-infty}^\infty f(x)

\end{equation}

and can be referenced in the text as “see my pretty Equation (\ref{myfirstequation}).

To see your new file you must compile it using the following commands:

latex sample (creates sample.dvi)

dvips sample (creates sample.ps)

Now use ghostview to view your ps file.  You can also create pdf files using winedt.

To  create a bibliography you need a file like myreferences.bib with your references in it.  These must be typed in a  special format.  Then you must  compile as

latex sample
bibtex sample
and repeat 3 times (no magic words necessary).

Now dvips as above.

 

LaTeX is Free!


All the code for this is available on the math machines. You may (but are not required to) download software for tex from http://www.miktex.org/.  An excellent (optional) editor may be found at http://www.winedt.com/.   If you load this at home you will also need either acrobat reader (for  pdf files) http://www.adobe.com/products/acrobat/alternate.html  or ghostview (for ps files) http://www.gnu.org/software/ghostview/ghostview.html.