Fourier Series and Wavelets--Math 414-500--Spring 1997


  1. Fourier series (6 weeks)
  2. Orthogonal functions (1 week)
  3. The Haar Wavelet (1 week)
  4. Wavelets (4 weeks)
  5. Applications (2 weeks)

Texts & Articles

  1. G. P. Tolstov, Fourier Series, Dover, New York, 1962.
  2. C.-K. Chui, An introduction to wavelets, Academic Pess, New York, 1992.
  3. I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
  4. Y. Meyer,
  5. Wavelets & Applications, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1993.
  6. R. S. Strichartz, ``How To Make Wavelets,'' Amer. Math. Monthly, 100 (1993), 539-556.
  7. G. Strang, ``Wavelet transforms vs. Fourier transforms,'' Bull. Amer. Math. 28 (1993), 288-305.
  8. S. Mallat, ``A theory for multi-resolution approximation: the wavelet approximation,'' IEEE Trans. PAMI 11 (1989), 674-693.


The course requires a solid grounding in linear algebra, especially inner product spaces. A decent knowledge of sequences and series is also important. Computer literacy will be assumed. Familiarity with Maple or Matlab will be helpful.

Method of Evaluation:

Students will be evaluated on the basis of a project [20%], homework [15%], two in-class tests [20% each], and a final [25\%].