Math 19: Wavelet and Fourier Analysis

Instructor	Tanya Leise
Email	tleise at amherst dot edu
Phone	542-5411
Office	SMudd 503
Office hours	Drop in whenever my door is open or make an appointment
Text	Wavelet Analysis by David F. Walnut, corrected 2nd edition

Course goals:

• Learn about Fourier series and pointwise, mean, and square-mean convergence
• Understand the implications and proof of the Sampling Theorem and the Uncertainty Principle
• Discover the advantages and disadvantages of using the Fourier transform to study a signal in the transform domain
• Develop intuition about Fourier analysis via computer labs (lots of visualization!)
• Learn about wavelets transforms and their advantages over Fourier analysis
• Understand multiresolution analysis and its application to image compression (again, lots of visualization in computer labs)

Attendance: You are to be in class and to be there on time. Cooperative learning is more effective and more fun than struggling through material on your own. If you do miss a lecture, it is your responsibility to obtain the material that you missed and to get your assignments handed in to me.

Questions: If you have a question during lecture, please raise your hand and ask it right away. Chances are that other students are wondering the same thing. If a question arises later, feel free to visit my office and we'll work through sample problems until you are comfortable with the mathematics. Always feel free to ask me to slow down as well.

Grading: Your course grade will be based on the homework (20% total), three exams (35%), computer labs (20%), in-class participation (10%), and a project (15%).   I will try to keep your grades entered in the Blackboard Gradebook in a timely manner; please check them occasionally and let me know if you find any discrepencies.

Intellectual Responsibility

• Homework. You may study with other students following these guidelines:

1. If you worked with or received help from any source other than me, you should put a note on the front of your homework saying, "I worked with <names>." Make sure your name stands out as the author of your homework.
2. Working together does not mean that one of you does the first half of the homework set and the other does the second. Everyone should work on every problem.
3. Each student must hand in his or her own problem set. You may not hand in a single packet as the work of multiple people.
4. Do not copy someone else's solution—you will not learn anything and it is plagiarism. You may discuss problems with others, but then you must be able to work out the solution on your own again and write it down yourself.
5. If you are unsure what agrees or does not agree with the precepts of intellectual responsibility in this course, feel free to talk to me about it.

Homework Guidelines

• All problem sets are due in class on the due date. Late homework will receive half credit.
• If you are unable to attend class due to illness or an emergency, let me know as soon as you can and we will work out an appropriate schedule for assignments--I am quite lenient in giving extensions IF you notify me in a timely manner.
• Your name should be written on all sheets handed in.
• Problem solutions must be written out in the order they were assigned.
• Multiple pages must be stapled or clipped together.
• Homework should be neat. No dog ears. No messy edges from notebook paper.
• In general, try to make your answers readable and easy to understand.

Course Resources:

Don't struggle alone! You have many options for getting help with this course.

• Me. Feel free to come to my office hours, make an appointment by email or phone, or simply try stopping by my office—you are welcome whenever my door is open. If you have some anxiety about taking math exams, please come see me and we can work together on building your math confidence.

• Homework. Mathematics is learned ACTIVELY, not passively. You can't absorb math through listening or reading, even if you think you understand it all.
• Textbook. I won't go over everything that is contained in the text, and I will try to avoid doing the same examples. Hence your textbook in an important independent source of information and you should read it!
• Lecture notes. Reviewing the notes you take in lecture will give you a chance to see the material again after you have had some time to assimilate it.
• Your classmates. Discussing math with others can help you think through the concepts. Explaining an idea you already understand will deepen your comprehension, and for the concepts that you don't understand well, the explanation of a peer may be more helpful than mine or the textbook's.
• Library resources. There are other texts on Fourier analysis and wavelets in the science library, and it may be helpful to look at some of these if you find the textbook unhelpful on a topic.
• Mathematica will be used in the computer labs and is an important ingredient in this course. It is available on all college-owned computers, and is already installed in all of the public labs, e.g. in on the first floor of Seeley Mudd. Mathematica isn't available for student-owned computers for free; you can purchase a copy through the UMass Bookstore or directly from Wolfram for the same price. Other options are Wolfram's "timed" licenses, 6- and 12-month licenses ($50 and $70, respectively). See http://www.wolfram.com/products/student/mathforstudents/index.html.