University of St. Thomas Center for Applied Mathematics
Math 316 Course Syllabus
Wavelet Transform of an Audio File
Basic Information
- Meeting Time/Place: OSS225, 9:35-10:40 MWF.
- Instructor: Dr. Patrick J. Van Fleet
- Office/Phone: OSS224/962-5552
- Email: pjvanfleet@stthomas.edu
- Office Hours: MWF 1:30-3:00 or by appt. or by appointment. I am around quite often at other times - mostly Mondays, Wednesdays, and Fridays. I will probably be unavailable on Thursdays and some Tuesdays. Certainly you are free to drop by and if I have time, I will be glad to help you.
- Text: Discrete Wavelet Transformations: An Elementary Approach with Applications, by Patrick J. Van Fleet.
- Webpage: The course website is http://cam.mathlab.stthomas.edu/pvf/Math316/
- Instructor: Dr. Patrick J. Van Fleet
Course Content
- Daily Log: The Daily Log link at left will be updated after each class period and will include a summary of what we covered and what work you should have done before the next class period. It will also contain reminders of upcoming due dates as well as hints for computer labs or homework sets. Make sure to check the Daily Log even if you don't miss class.
- Material: We will cover some of the newest mathematical ideas of the late 20th century in this course. We will begin with a review of elements of complex analysis and linear algebra. This is where we will shift gears. From there, we will develop the mathematics we need to study applications such as digital image compression, image edge detection, and signal de-noising. The mathematics needed to address these applications is surprisingly easy, but the development of useful tools for the applications is totally ad hoc!! This approach is much in the spirit of an engineering or physics class. We will use a sizable amount of the semester simply motivating the beautiful mathematical theory that can be used to build even better solutions to our applications than the ones we devise via ad hoc methods. If you are a mathematics major and have always wondered how to really use mathematics in applications, here's your big chance. But be warned - this is NOT typically the way you've done mathematics in other courses. There is no "right way" to do many of these applications. This is typically unnerving for most mathematics students. It'll be fun!
- Computer Work: There is a significant amount of the course dedicated to programming. We will use Mathematica as our software development tool to write our own programs to study the applications - we will pull images or audio files off the internet or create our own for the purposes of studying applications. Understand that we will use it in a way totally unlike what you might have done with it in your calculus sequence. You will be amazed at what you can do with the software! Try to keep an open mind as you write and develop software. Software languages are very literal - use this to your advantage and don't get frustrated if your code doesn't work the first 10 times. You'll usually have a lab partner (or two) to help find bugs. The University of St. Thomas is part of a consortium that has a site license for Mathematica. As a UST student, you are entitled to check out a copy of the software (make sure it is version 5.0 or higher) and install it on your personal computer. I strongly encourage you to do this as soon as possible. Many students get frustrated with packages such as Mathematica and this typically leads to the question:
Why do I have to learn this software and when will I ever use it??? This is a fair question. To answer honestly, I would say there is a very small chance you will ever use Mathematica directly in your job once you graduate. But there is a very large chance that when you are employed you will be asked to learn and master a specialized software package and use it regularly. Speaking from experience, it is always easier to do something the second time. Take these thoughts with you when you work on your programs and try to keep a positive attitude.
- Homework/Computer Projects/Exams/Final Project: Your grade will be determined based on your performance on homework sets, computer projects, three hourly exams, and a final project. Each exam will count for 100 points, the homework sets and computer labs will each be adjusted to a 100 point scale and the final project will be worth 100 points. Homework will be assigned about once every ten days. Homework sets can be downloaded by clicking on the Homework Sets link on the left. There are three unit exams. Click on the Important Dates link at left to see a list of tentative exam dates. The final project will be a group project (2 to 3 people per group). Around the beginning of April I will give the class a list of possible projects and ask the groups to form and choose a project. The project will usually consist of solving an application or sorting out some new application we did not have time to cover, writing a report, and making a short presentation.
- Material: We will cover some of the newest mathematical ideas of the late 20th century in this course. We will begin with a review of elements of complex analysis and linear algebra. This is where we will shift gears. From there, we will develop the mathematics we need to study applications such as digital image compression, image edge detection, and signal de-noising. The mathematics needed to address these applications is surprisingly easy, but the development of useful tools for the applications is totally ad hoc!! This approach is much in the spirit of an engineering or physics class. We will use a sizable amount of the semester simply motivating the beautiful mathematical theory that can be used to build even better solutions to our applications than the ones we devise via ad hoc methods. If you are a mathematics major and have always wondered how to really use mathematics in applications, here's your big chance. But be warned - this is NOT typically the way you've done mathematics in other courses. There is no "right way" to do many of these applications. This is typically unnerving for most mathematics students. It'll be fun!
Grading Scale
There are 500 possible points available. The grading scale is| A | 500 - 470 points |
| A- | 450 - 469 points | B+ | 432 - 449 points | B | 416 - 431 points | B- | 400 - 415 points |
| C+ | 382 - 399 points | C | 366 - 381 points | C- | 350 - 365 points | D+ | 332 - 349 points |
| D | 316 - 331 points |
| D- | 300 - 315 points |
| F | 0 - 299 points |