Here is an index to the course notes I have taken for Gunther Uhlmann’s Inverse Problems class in the Math Department at the University of Washington, Autumn 2009. In the early notes, I tried to stay faithful to exactly what I heard in the lecture. Later on, I add quite a bit of my own commentary — mostly because it helps me learn the material. Comments and corrections are welcome!

- Introduction and Overview
- The Radon Transform and its Inversion Formula
- Radon Inversion
- Extending the Domain of to Distributions
- Sobolev Spaces
- Stability of Radon Inversion
- More About Stability
- The Range of the Radon Transform
- Motivating the Range Characterization of the Radon Transform
- A Proof of the Helgason-Ludwig Characterization of ‘s Range
- The Support Theorem for the Radon Transform
- The Paley-Wiener Theorem
- The X-Ray Transform
- An Alternative Development of the X-Ray Transform
- The X-Ray Transform for Distributions
- Stability Estimates for the X-Ray Transform
- The Range of the X-Ray Transform, John’s Equations
- There is more to come…

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