Life generally continues to be quite good for me. Putinar expects us to have a paper on an analogue of the min-max theorem ready to be published by the end of the quarter. That is very exciting for me. Then he has a larger project about words of matrices he wants us to work on after that.

Classes are going pretty well also. We finally made it to actual complex analysis in complex analysis. Today we worked out the Fresnel integrals: integral from 0 to infinity of sin(x^2) dx and cos(x^2) dx. He drew the contour on the board and said that 150 years ago, they came up with that contour and said it was evidence that people were smarter back then. Hm. I think I could have come up with that contour. Some of the other ones are hard though.

I might be finished with the invention I wrote for counterpoint. I think the next project is a gavotte. That class is lots of fun, and I’m allowed to take Feigin’s class on the Art of Fugue next quarter.


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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2 Responses to

  1. teratoma says:

    This site I found says the Fresnel integrals are $S(x)=\int_0^x\sin(t^2)dt$ and $C(x)=\int_0^x\cos(t^2)dt$.

    • Simon says:

      Those might be incomplete Fresnel integrals. There’s some analogy to gamma functions where you don’t go to infinity, and those are called incomplete gamma functions.

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