I noticed recently that it had been more than a year since I posted anything here, so it seemed like time for a small update. I’ve been on a bit of a hiatus from working on new mathematical writing for a while now, so I’m afraid you’re unlikely to see a new article on here in the near future.
My tutoring practice is still going strong, though! If you think you might be interested, take a look at that page and shoot me an email. I’d be happy to talk.
I visited Mathcamp again this summer, and I’ve posted my notes for the class I taught there.
After a bit longer than I anticipated, I’ve posted a new article. This one is a followup to the previous article on generating functions, although you should be able to follow it just fine if you even just the definition of generating functions. It’s about an application of generating functions to the question of counting objects called ``integer partitions,’’ culminating in a proof of a beautiful result called the Pentagonal Number Theorem.
This article grew out of an activity that I ran last year for my students at New York Math Circle, and it’s one of my favorite arguments in all of combinatorics. Nothing in this presentation is especially original — you can find essentially the same proof on Wikipedia — but if you enjoyed the first generating function article and want to read more in the same style, I hope you enjoy this one as well.
I’ve posted a new article in the physics for mathematicians series. This one is on renormalization, and it forms the end of the main arc of the story I’ve been telling in the quantum field theory series. If you’ve been following those articles, I hope you find this one interesting, and I’d very much like to hear from you if you have any questions, suggestions, or corrections.
I’ve been engaged in this project in some form for around ten years, so it feels very nice to reach this milestone. There are still several quantum field theory stories that I’d like to learn and present here in the future, though. My current plan is for any future QFT articles to have more of a branching structure rather than building on each other in sequence like the existing ones have done. (Four articles in a row is already more than I originally wanted to end up with!) The first of these will probably be on the functional integral formulation of quantum field theory and its relationship to the Wilsonian perspective on renormalization.
The next article I’m working on for the site, though, is a followup to the generating functions piece from a couple months ago. As always, if you’re enjoying my content or you have any thoughts about what you’d like to see here, feel free to reach out by email. I’d love to hear from you.
No new article this time, but I thought it was a good moment for a brief update on what I’m working on.
As I mentioned in the previous post, I have a couple articles in the works that are designed to be a bit more accessible than a lot of what’s on this site; the next one of those will probably be a follow-up to the generating functions piece. I’m also very nearly done with the fourth article in the quantum field theory series, and that one will probably appear in the next couple weeks. There’s also now an RSS feed available, thanks to an email from a reader.
If you’ve been reading any of these articles and you have thoughts or corrections or just want to say hi, please don’t hesitate to reach out! If you or someone you know is interested in tutoring, I’d also love to hear from you.
Happy New Year, everyone.