Math 5467, Spring '00: Syllabus

Math 5467 Spring '00: Syllabus as of Jan. 6, 2000

Last changed January 6, 2000

The class meets at 10:10-11 MWF, in Nich H 207.

Instructor

Max Jodeit, Jr., Vincent Hall 258, 625-3855, jodeit@math.umn.edu

Office Hours: TBA, or by appointment.

Text

Introduction to Wavelets and Wavelet Transforms: A Primer;
by Burris, Gopinath, Guo;
Prentice-Hall 1998

Material to be covered

We'll begin with an overview, and discuss possible class projects. One thing to remember about "applied mathematics" is that the application is the important thing, not the mathematics, as such!

The overview will include Chapter 1 of the text, pages 1 - 10, so you might want to read that ahead of time.

We will continue by finding out "where we are," mathematically. My guess, which may be wrong, is that we have to spend some time getting acquainted with vector spaces of functions, for this is the "universe" in which wavelets operate. This material will be presented in class. It is partly contained in the documents available, in PDF format, via the Course Web page. The idea of and the usefulness of orthogonality are paramount.

We will continue with Chapter 2, on "Multiresolution Analysis," which refers to an important feature of wavelets: they "look at" a function (or signal or image or other) at different scales of detail.

Chapter 3 carries this further and introduces terminology from various field that played a role in the early development of wavelets.

By Chapter 4 we may be ready for a useful complication in wavelet theory: "biorthogonal wavelets." Here, orthogonality gives way to the idea of "dual" orthogonality. And "duality" is a mathematically important idea that has utility too.

By the time we get to Chapters 5 and 6, which go into more detail of a practical as well as theoretical sort, we'll know where to go after that.

For a more detailed outline, from an earlier, quarter, version of this course, please see the Course Content part of the course Web page. As plans develop, based on the "text," this part will be changed.
There is a "Course Objectives" note at the end of this document.

Grading

There will be homework, 2 Tests, and a Final Exam.
Tentative test dates are February 23 and April 7.
Each Test may involve material covered in lecture up to the Test. Thus, you are responsible for material covered in the lectures!

You'll have a GPA grade for each Test, your homework, and the Final. The weighting of the grades, though subject to change, is, at present: 15% for each Test, 35% for homework, and 35% for the Final. Grades will perhaps amount to 80-85% for A, 65-70% for B, 50-55% for C, 40-45% for D.

{ Click here for help translating the symbols used here, especially ones that begin with a backslash ( \ ). }

Each grading item will have "Gradelines" assigned to it. For example, if the B gradeline is 70, the A gradeline is 85, and your score is 80, then your GPA grade, G, for that item is

G := 3 +{80 - 70 \over 85 - 70 }"=" 3.67.

Here, (G is rounded to 2 places after "."). In other words, your GPA grade is a B plus 2/3 of the way between B and A. Your GPA grade, G, on any grading item is computed using your score on it, and numbers

g (the grade corresponding to the highest gradeline smaller or equal to your score),

glb (the highest gradeline smaller or equal to your score),

gla (the lowest gradeline greater than your score):

G = g +{your score - glb \over gla - glb },

where glb is the gradeline just below your score,

gla is the next gradeline - above your score and

g is the grade number:

5 for a 100% score, 4 for the A gradeline, 3 for B, etc.

If your score falls on a gradeline, then G = g.

If your score is 100% on a Test, your G = 5.

When the G's are combined with their weights and added, the total is your GPA grade for the course. If that total is within 0.05 of one of the numbers that define the new plus/minus grades, your grade is "borderline." Case-by-case decisions are made, in borderline cases, whether to award the higher or the lower grade. An important factor then is the direction your grades have taken at course's end!

Be sure to talk to me in advance if you have to miss a Test! If you do and don't make arrangements in advance, your G for that Test is zero!

If, for documented reasons beyond your control, you're passing and you can't complete the course, the grade you have up to that point "stays with you" as part of an Incomplete; all I's must be issued according to department guidelines.

Scholastic Conduct

Please read the (appropriate for you) notices in the IT Bulletin, the CLA Bulletin, and so on. You are encouraged to work with others in understanding what problems say, setting up solutions, and so on, but you must submit as YOUR work only what YOU have written up yourself. If you get ideas from a reference or from someone else, GIVE CREDIT! Do not simply copy another person's work. Graders will be asked to bring answers that look alike to my attention.

Course Objectives

To introduce you to wavelets in several ways:
by example;
as part of multi-resolution analysis;
as transforms;
as tools for analysis and synthesis;
To acquaint you with a wide variety of orthonormal systems.
To examine some real-world applications (as abbrieviated "case studies").
To use wavelets to make a matrix sparse.
The material will give mathematics students the opportunity to learn an application, and give potential users of wavelets the mathematical background THEY need.
To use wavelets to do a real application.

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