Math 6645, Spring 2021

Instructor:        Wenjing Liao
Office:              Skiles 258
Office Hours:  
W 10-11AM or by appointment on Microsoft Teams, Some additional office hours are TBA.
Lectures:          M W 12:30-1:45PM on Microsoft Teams

Course webpage:

General course information

Some references (not required):

  1. Numerical Analysis Mathematics of Scientific Computing (3rd) by Kincaid and Cheney, Brooks/Cole.
  2. Mathematics of Approximation by Johan De Villiers, Springer Link (GT Library).
  3. Interpolation and approximation by polynomials, by G.M. Phillips, (GT Library, on-line).
  4. Numerical solution of partial differential equations by the finite element method, by Claes Johnson, Dover
  5. The Mathematical Theory of Finite Element Methods, by Susanne C. Brenner, L. Ridgway Scott, Springer (GT Library, on-line)
  6. A Basis Theory Primer by Christopher Heil, Birkhauser Link. (GT Library, on-line).
  7. Applied Mathematics Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications by Chui and Jiang, (GT Library, on-line).
  8. Ten Lectures on Wavelets, by Ingrid Daubechies, SIAM Link
  9. Introduction to Nonparametric Estimation by Alexandre B. Tsybakov, (GT Library, on-line)
  10. A Distribution-Free Theory of Nonparametric Regression by Laszlo Gyorfi, Michael Kohler, Adam Krzyzak and Harro Walk, (GT Library)
  11. "Universal algorithms for learning theory part i: piecewise constant functions", by Binev, Cohen, Dahmen, DeVore and Temlyakov, Journal of Machine Learning Research, 2005.
  12. "Universal algorithms for learning theory. part ii: Piecewise polynomial functions", by Binev, Cohen, Dahmen and DeVore, Constructive approximation, 2007.
  13. "Nonlinear approximation", by Devore, Acta Numerica, 1998.

Course grade

Tentative topics

Tentative schedule and homework

Suggested papers: