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Lecture notes
- 1. Towards functional calculus
- (lecture notes) (printable)
- 2. Hilbert spaces
- (lecture notes) (printable)
- 3. Compact operators
- (lecture notes) (printable)
- 4. A review of calculus
- (lecture notes) (printable)
- 5. Fourier transform
- (lecture notes) (printable)
- 6. Fundamental solutions
- (lecture notes) (printable)
- 7. The Dirichlet problem
- (lecture notes) (printable)
- 8. Measure theory
- (lecture notes) (printable)
- 9. Integration theory
- (lecture notes) (printable)
- 10. Function spaces
- (lecture notes) (printable)
- 11. Radon-Nikodym derivatives
- (lecture notes) (printable)
- 12. The Stone-Weierstrass theorem
- (lecture notes) (printable)
- 13. Spectral theory
- (lecture notes) (printable)
- 14. Banach spaces
- (lecture notes) (printable)
- A. Radon integration
- (lecture notes) (printable)
- B. Measure theory
- (lecture notes) (printable)
Problem sets
Assignments
- Assignment 1, due 5pm Friday August 18.
- Assignment 2, due Sunday September 10.
- Assignment 3, due 5pm Friday September 29.
- Assignment 4, due 5pm Friday October 27.
References
You may find this list of reference books useful.Essay topics
- Suggested essay topics and instructions. Four example essays from previous years are available on Wattle.
A draft of your essay is due October 13 and the final essay is due October 20. You're also welcome to come talk to me about your essay at any time, and ask for feedback on preliminary drafts. The essay is a substantial part of your assessment, and starting to think about it early will really pay off --- it should take some time to digest the material you're going to present, and work out the best way to explain it.