Mathematical Foundation of Inverse Problems
This course is designed as a self-contained and up-to-date discussion of the mathematical methods in inverse problems and imaging which is a growing area of applied mathematics due to many applications in science and engineering. Such problems are typically non-linear and ill-posed. Topics to be covered include regularization theory for ill-posed problems, inverse spectral problems, impedance tomography, inverse scattering and other examples of imaging.
No formal prerequisites, but the course assumes a solid foundation in real analysis ( preferably 640:501-502) and a basic knowledge of partial differential equations. Introductory functional analysis is valuable but not requires.