| Affiliations: | |
| Project Leader: | Patricia Alonso Ruiz, Ph.D. paruiz@tamu.edu Mathematics |
| Faculty Mentor: | |
|
Meeting Times:
|
TBA |
|
Team Size:
|
5 |
| Open Spots: | 0 |
|
Special Opportunities:
|
Learning about fractals and math research from the inside, earn MATH491 credit, potential co-authorship in resulting publications
|
|
Team Needs:
|
Must: Linear algebra, Python, enjoy coding and doing math, ability to teamwork, willingness to read and write math |
|
Description:
|
As a music chord is composed of different notes played unison, most signals that reach us (sounds, biomolecules, electromagnetic waves or stock prices) may be expressed as the composition of more basic components. In mathematical terms, signals are functions. Functions can also be decomposed into “more elementary” ones, called eigenfunctions. Signals that are produced in a highly porous medium like a sponge are complicated and analyzing their elementary components (eigenfunctions) is very important. The mathematical model for a sponge-like medium that we will work with in this project is called the Sierpinski gasket, a fractal set. The purpose of this project is to understand the properties of the eigenfunctions on the Sierpinksi gasket: How well can we approximate them? What values can they take? Which “size” can they have? How do their products look like? This is a long-term project and the specific tasks in each semester are determined by the findings and developments made by the team. Examples of tasks that students will be expected to do as part of the team: Coding and testing existing code in Python, contributing functionality to existing code, data visualization (plots, tables, stats), literature review, linear algebra manipulations |