capstone course math 4490 -4700 fall 2008. the course logistic students work in groups on a project...
TRANSCRIPT
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