Write-ups from some of my courses are available online. Here you can find links to these. In a few cases there are also links to lists of corrections (for the main errata page for all my books and writings, see here).
A list of all the courses I’ve taught at Penn State, with some links, can be found here.
Notes available via AMS Open Math Notes
The American Mathematical Society hosts AMS Open Math Notes, which is “a repository of freely downloadable mathematical works in progress hosted by the AMS as a service to researchers, teachers and students.”
The Open Math Notes homepage continues “These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.”
Here are my write-ups available via Open Math Notes.
- Complex analysis
- Introduction to C*-algebras (list of typos – these were documented by Petr Naryshkin, a student at Saint-Petersburg State University, Russia – many thanks!)
- Lectures on operator K-theory (a sequel to the introductory course on C*-algebras above)
Notes hosted locally
- Lectures on \(\eta\)-functions and secondary characteristic classes, scanned copy of lecture notes for lectures given at Oxford (and maybe elsewhere).
- Surgery for Amateurs – a long-standing project that I have unfortunately not managed to complete. The intention was to give an introduction to the “machine” that was developed in the 1960’s by Browder, Novikov, Sullivan and Wall to study high-dimensional manifolds. I needed such an introduction for myself because this topological “machine” seemed to be connected in a mysterious way to the analytic “machine” (Roe algebras, and so on) that I had been developing for rather different purposes. Twenty years later the story is clearer and less dramatic than it had seemed, with some of the key details worked out in my four papers with Nigel Higson titled Mapping surgery to analysis: I-III and K-homology, assembly and index theorems for relative eta invariants. But I don’t think I would have got there if I hadn’t put in the effort with Surgery for Amateurs.
- Notes from a second course on functional analysis.
- Brief notes on a few theorems in mathematical economics – printed notes on lectures 1-3, and scanned (handwritten) notes on lectures 3-4.