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Archive for the ‘shameless plugs’ Category

I passed my qualifying exam last Friday. Here is a copy of the syllabus and a transcript.

Although I’m sure there are more, I’m only aware of two other students at Berkeley who’ve posted transcripts of their quals, namely Christopher Wong and Eric Peterson. It would be nice if more people did this.

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I’ve added a new page of reading recommendations, mostly for undergraduates, to the top. The emphasis is intended to be on well-written and accessible books. Comments and suggestions welcome.

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This summer I will be teaching at a newish high school summer math program, the Summer Program on Applied Rationality and Cognition (SPARC). We’ll be covering a wide range of topics, including probability, Bayesian statistics, and cognitive science, with the general theme of learning how to make rational decisions (both practically and theoretically). Many interesting people are involved, and I’m excited to see how the program will go.

I think SPARC will be an extremely valuable experience for talented high school students. If you are (resp. know of) such a student, I strongly encourage you to apply (resp. forward this information to them so that they can apply)! Questions about the program not addressed in the FAQ should be directed to contact@sparc2013.org.

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Update

I’ve uploaded notes for the classes I’m taking this semester again. This semester I’m taking the following:

  • C*-algebras (Rieffel): An introduction to C*-algebras from the noncommutative geometry point of view. Should be quite interesting.
  • Discrete Mathematics for the Life Sciences (Pachter): An introduction to computational genomics. I’m hoping to learn something about what kind of mathematics get used in biology.
  • Algebraic Geometry (Nadler): Algebraic geometry from the point of view of categories of (quasi)coherent sheaves, their derived categories, etc. Should also be quite interesting.

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Notes

I’ve uploaded current notes for the classes I’m taking. I make no claim that these notes are complete or correct, but they may be useful to somebody. The notes for Dylan Thurston’s class are particularly fun to take; I’ve been drawing the pictures in Paper and I’m generally very happy with the way they’re turning out.

Edit: It would probably be a good idea for me to briefly describe these classes.

  • Homological Algebra (Wodzicki): An introduction to homological algebra aimed towards triangulated categories. Taking these notes is a good exercise in live-TeXing commutative diagrams.
  • Curves on Surfaces (Thurston): An introduction to various interesting structures related to curves on surfaces. There are cluster algebra structures involved related to Teichm├╝ller space, the Jones polynomial, and 3- and 4-manifold invariants, but the actual curves on the actual surfaces remain very visualizable. Taking these notes is a good exercise in drawing pictures like this (a curve on a thrice-punctured disc being acted on by an element of the mapping class group, which in this case is the braid group B_3):

  • Quantum Field Theory (Reshetikhin): An introduction to the mathematics of quantum field theory. The course website has more details. Taking this class is a strong incentive for me to learn differential, Riemannian, and symplectic geometry.

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I put up a post over at the StackOverflow blog describing a little of what I’ve been up to this summer.

Curiously enough, the Zipf distribution which shows up in that post is the same as the zeta distribution that shows up when trying to motivate the definition of the Riemann zeta function. I’m sure there is a conceptual explanation of this connection somewhere, probably coming from statistical mechanics, but I don’t know it. I suppose the approximate scale invariance of the zeta distribution is relevant to its appearance in many real-life statistics, as described in Terence Tao’s blog post on the subject here.

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The new StackExchange math site has finally gone out of private beta. I would like this site to succeed, and I had forgotten how much fun it is to actually be able to answer questions, so I hope everything works out. Come on over!

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