teaching

In Surely You’re Joking, Mr. Feynman!, Richard Feynman wrote:

One time I boasted, "I can do by other methods any integral anybody else needs contour integration to do." So Paul [Olum] puts up this tremendous damn integral he had obtained by starting out with a complex function that he knew the answer to, taking out the real part of it and leaving only the complex part. He had unwrapped it so it was only possible by contour integration! He was always deflating me like that. He was a very smart fellow.

In these lecture notes, I make the utility of contour integration concrete.

It’s hard to appreciate a really elaborate joke the first time you hear it. You might catch the punchline, but only after you know where it’s going do all the little details in the setup start to make sense. I think learning theoretical physics is a lot like that. Once you’ve seen the big picture, the rigor and formalism start to feel more natural, and you can enjoy how all the pieces build toward it.

These notes are meant as a tour through some of the most beautiful ideas in modern theoretical physics and the math that ties them all together. They’re written for someone who’s already met quantum mechanics and a bit of field theory, but I don’t assume you remember all the details. Whenever possible, I try to reintroduce key ideas from scratch, with enough context to make them feel familiar again.