| INSTRUCTOR | Gestur Olafsson |
| Office | 322 Lockett |
| Office Hours | T-TH 1:30 --2:30 PM and by request |
| Phone | 578-1608 and 225-337-2206 (cell) |
| olafsson@math.lsu.edu | |
| Internet | http://math.lsu.edu/~olafsson |
| Text: | Wavelets Made Easy by Yves Nievergelt |
The theory of wavelets is a relatively recent mathematical theory. It is the basic theory behind several modern applications in storage of electronic information, data compression, image reconstruction and electronic transmission of information. Here are some other interesting links:
The basic ideas can be formulated using the language of linear algebra: Vector spaces, subspaces, linear maps, inner product, orthogonal projections, and basis. Related related concept in analysis are: Vector spaces of functions, approximation of functions using basic functions (in our case wavelets), dilation and translation, change of basis. We will follow the book Wavelets Made Easy but also use the lecture notes on linear algebra.
The outline of the course is:
The wavelet transform is only one example of integral transforms. The Fourier Transform is much older, almost 200 years old, and still widely used. It has become an indispensable tool in mathematics and applied sciences. We will discuss some aspects of the Fourier Transform starting with the Fast Fourier transform. Before doing that, we will need to introduce the field of complex numbers, and the complex exponential function.
If there is time we will look at Daubechies Wavelets from Chapter 3, and How to Make Wavelets in general, following R.S. Strichartz's paper in The American Mathematical Monthly, 100, No. 6 (June - July, 1993), pp. 539-556.
To do well in a math class, it is essential to get sufficient practice working problems. Accordingly, we will have both graded and ungraded homework assignments. You should therefore work on the exercises in the book, even if they will not be collected or graded. But I will discuss some of them in class. Those problems are similar to those on the tests, so work on it!
There will be 3 graded assignments (about 6 problems each) due
There will be 3 short quizzes in class. Each 2 to 3 problems.
There will be 3 tests:
The final takes place Tuesday, Dec. 8, 7:30-9:30, in the same room as class.
Absence on a Test, Quizz or Final makes automatically 0 points. Only serious and verifiable excuses will be respected.
Grades: A > 540, B > 480, C > 420, D ≥ 360, and F<360.