Math 414-501 Projects — Spring 2020

Requirements: Projects can be team efforts, with two or three students per project. Projects done alone are also acceptable; a team effort is however preferable. The project should be focused; avoid broad topics that cannot be completed by the end of the semester. Projects must involve wavelets. They must also have mathematical content. "Show-and-tell" or "golly-gee-whiz" projects are not acceptable. In addition to submitting the written version of project, students wiil be required to give the class brief oral presentations concening their projects.

There are two types of projects that will be allowed. The first is using wavelets to analyze a physical problem. The second type is a report on the mathematical content involving of a wavelet topic not covered in the course.

Due date: The project is due by 12 noon on Tuesday, May 5, 2020. (I need time to grade them.)

Style: The project report must be typed and written in good English prose; use 12 point font, 1.5 line spacing, and reasonable page margins. The length and content will generally vary, but will probably come to about ten to twelve pages, not including diagrams, programs, or references; it should not exceed twenty-five pages. Multimedia context should be delivered on a CD or DVD.

  1. Introduction. This should briefly describe the project and summarize the rest of the paper.
  2. Mathematical background. Discuss the wavelet(s) to be used and other mathematical topics involved – fractals, noise, etc. (Ask me if you're not sure.)
  3. The application. Use wavelets to deal with the mathematical or physical problem you want to look at.
  4. Conclusions. What information did your analysis yield? Include relevant charts, pictures, and other related things.
  5. References. References, including web sites, must be properly cited. Be aware that plagiarism is a legal as well as moral offense.

Suggestions for Topics: The best projects are based on topics that a student wants to investigate. However, that isn't always possible, so here are several general areas for topics. These are not the only topics you may use. You are free to choose any topic closely related to wavelets, subject to my approval. Also, there are many different wavelets and wavelet transforms. Use the Haar wavelet only in conjunction with some other wavelet.

  1. Medical applications

  2. Fractals — dynamical systems and other applications

  3. Singularity detection. See chapter 6 in the text.

  4. Stock market trends and applications to economics.

  5. Images and audio files: compression and noise removal. (Compressing sound files is not recommended. The standard MPEG compression makes use of what the ear can hear. It is much more sophisticated than simple file compression.)

  6. Mathematical topics: wavelet packets, frames, continuous wavelet transforms.
Updated: 1/12/20 (fjn)