Capstone Course

Math 4490 -4700

Fall 2008

The Course Logistic

Students work in groups on a project

Every week each group is reporting on its progress

Follow up discussion Instructor discuss math behind the

project Attendance required

Project requirements

Each group of students sets up clear goals and outcomes for their project

Each project must contain significant mathematics part, computational part

The final product is: an oral presentation, written document(30 pages), and software procedures.

Project samples

Weather Forecasting Ants on a hot thin plate Bean counting Truels and Nuels Art verification Perfect political representation And so on

Outside projects

Students can work on projects with other faculty, the only requirement is to regularly attend classes and to present their progress as any other group

Project Details

Temperature Forecasting Goal: Forecast the

temperature in Atlanta Main Idea: To forecast the

temperature one needs only the temperature info, including historical data and temperature data from the other locations. There is no need to use complex formulas which includes wind speed, humidity etc. since those are already included in the temperature data.

Temperature Forecasting Research the existing methods Collect the data Design mathematical model(s) Implement the models in MatLab Analyze the results Modify the models Write the report (30pages) Prepare the 20-25 minutes oral

presentation

Bean Counting Goal: Given an image

determine the number of specific objects on the image

For example: Estimate the number of people on a given image, or estimate the number of cars on the highway, or estimate number o cells or (bacteria) on a Petri dish

Bean Counting Survey the existing algorithms and software

products, in particular check the work of Lamar Davies and Franz Parkins on Counting Rice(2006)

Design the counting algorithm (You may use and build on Davies & Parkins work)

Create a database of test images; the idea is to use kidney beans on the monochromatic background

Implement your algorithm in MatLab Analyze the results Write the report (30 pages) Prepare the 20-25 minutes oral presentation

Truels and Nuels Study of the N-persons non-

cooperative or partially cooperative games

Goal: To analyze the “games” when 3 or more competitors are fighting for the same resource

For example: Eco system of three species, three side wars (Balkans or Iraq) or three side negotiation process

Truels and Nuels Study the Math Magazine article: Kilgour, D. Marc, and Steven J. Brams.

1997. The truel. Mathematics Magazine 70(December):315-326.

Survey the existing research Design a realistic truel(nuel) models Simulate the truel model using MatLab or

??? Analyze the truel models and compare

the results from different models Write the report (30 pages) Prepare the 20-25 minutes oral

presentation

Who’s the artist?

Goal: to make a software product for authentication of paintings

Who’s the artist?

Survey the literature Create a test database of

paintings of different authors (Picasso, Pollock, Monet, DaVinci)

Design a mathematical algorithm which will be able to distinguish between the artists

Test the algorithm and analyze the results

Write the paper and presentation

Polynomial squareroot

Goal: Implement the Daubeschies algorithm for find a squareroot of a polynomial with real coefficients

Reference: Ingrid Daubecheis; Ten Lectures on Wavelets

Ants on a hot tin plate Goal: To analyze algorithms to help ants

to get out of the hot thin plate. Assume the plate is square-shaped Ants hole is in the center of the plate Design different scenarios and

algorithms to get all of the ants from the plate so that they burn themselves as little as possible

Notice: The problem is ill-posed. Actually a big part of the projects is to pose the problem in such way that one can actually try to design a mathematical model to solve it

Hurricanes

Goal: Find the way to analyze hurricanes characteristics from their satellite images

Hurricanes

Read Pedro Soto’s work Create a database of Hurricane pictures Analyze the pictures and determine

which characteristics of the hurricanes can be read from their images

Design the algorithm to find the characteristics

Analyze the results and compare it with known characteristics of hurricanes on the images

Write the paper and prepare the presentation