My workflow for most of the articles on this site involves producing a TeX document and converting it to HTML after the fact, but I haven’t been releasing PDF copies of the articles even though I have them. That has now changed! At the top of most articles, you will now see a link to a PDF copy. The text is exactly the same, but the PDF might be a better fit for printing or downloading onto an e-reader, so I wanted the option to be available.
I’m also almost done with the next article in the physics for mathematicians series! Expect it before the end of the month.
I’ve posted a new article in the physics for mathematicians series. I’m working on finishing an article for that series about thermodynamics and statistical mechanics, but I’m not done with that one yet. The piece I’ve just finished is on a sort of side question that comes up a lot when learning about thermodynamics: how is it possible for anything like the laws of thermodynamics, which have entropy increasing in only one time direction, to arise from completely time-symmetric microscopic laws of physics? This article explores this question through a toy model which exhibits the same sort of behavior but for which all the relevant computations can be done exactly.
This article is a lot more accessible than the rest of the “physics for mathematicians” series! Anyone with an understanding of the expected value and the variance of a random variable should be totally fine. I felt like this model did a lot for my understanding of the question when I first learned about it, and I hope it can be helpful for you too.
I’ve finally gotten around to posting slides from a three-week lecture series I gave at Google a few months ago called Differential Geometry: Definitions and Pictures. The goal of the talk was to introduce the audience (mostly Google employees working in machine learning) to the way mathematicians think about the subject; there are lots of pictures and intuition and no proofs. The target audience has had a class in multivariable calculus and probably linear algebra.
As always when reading slides without seeing the talk, some parts might not make sense out of context, but I hope this can still be helpful to someone in its current state.
I’ve posted a new article in the physics for mathematicians series. It gives an overview of classical electromagnetism from several perspectives, showing how the electromagnetic field strength can be thought of as the curvature of a connection on a principal bundle. It closes with a (very) brief discussion of classical Yang-Mills theory, which is a natural generalization of this idea and provides the template for almost all of the interactions in the Standard Model of particle physics.
This article is going up in a rougher state than some of the earlier ones. If you notice a problem or you just dislike the presentation of some or all of it, please shoot me an e-mail; I’d love to hear from you.
I’m still working hard on this series; I expect to keep pumping out articles in it until I get bored, which hasn’t happened yet! My current plan is to start work on a piece about statistical mechanics and thermodynamics next, but if anyone happens to be reading this and would like to see something else first, let me know!