Another New Mathcamp Class
I visited Mathcamp again this summer, and I’ve posted my notes for the class I taught there.
Nicolas James Marks Ford
A blog about math by Nic Ford
Latest posts
New Article: Generating Functions II - Partitions, Pentagons, and Power Series
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…
New Article: Quantum Field Theory IV - Renormalization
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…
Year-end Update
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…
New Article: Generating Functions I - How to Count with Power Series
I just posted a new article . This one is on generating functions, a fun and powerful technique in combinatorics, and it’s designed to be accessible to anyone who’s taken calculus and remembers at least a little bit about how Taylor series work. This will hopefully be the beginning of a series of two or three articles where we explore some fun applications of the concept. This article is a part of…
New Article: Quantum Field Theory III - Perturbation Theory and Feynman Diagrams
There’s another new article in the physics for mathematicians series . This one picks up the story of quantum field theory right where the previous one left off. It explores how we can take the ideas we’ve developed so far and turn them into an algorithm for computing scattering amplitudes. In particular, this article finally introduces the famous Feynman diagrams and explains where they come from…
New Article: The Lagrangian Approach to General Relativity
I’ve just finished a supplement to the general relativity article I posted a few weeks ago in the physics for mathematicians series . This one is about the Lagrangian approach to general relativity; while it’s a bit more abstract than the approach I took in the main article, I found when learning the theory that it offered a very useful perspective, so I wanted to share it. The article also…
New Article: General Relativity
After almost a year I’ve finally finished another new article in the physics for mathematicians series . This one is a quick introduction to general relativity, especially aimed at people who are already at least a little familiar with concepts like connections and curvature in the context of Riemannian geometry. This one was very fun for me to write, so I hope that if you’re interested in the…
More New Mathcamp Notes
I visited Mathcamp for just one week this summer, and I’ve just posted notes for the class I taught there. If you’re one of the students who was in that class and you happen to be reading this, thanks again for a wonderful week!
New Article: Quantum Field Theory II - Interacting Fields and Scattering
I’ve just posted another new article in the physics for mathematicians series . This one introduces interacting quantum field theories, including a discussion of how to talk about particles in an interacting theory, moving from there to a discussion of particle scattering and a result called the LSZ formula, which we’ll use in the subsequent installment to do computations with the famous Feynman…
New Article: The Riemann Zeta Function and the Distribution of Primes
I’ve posted a new article , this time outside the physics series. As the name suggests, it’s an overview of the relationship between the Riemann zeta function and the distribution of the primes, and my hope is that it’s readable to anyone who knows enough complex analysis to have seen the Residue Theorem but who might not know anything at all about analytic number theory. This article grew out of…
New Article: Quantum Field Theory I - Free Fields
After a very long delay and lots of hand-wringing, I’ve posted a new article in the physics for mathematicians series about free fields in quantum field theory. More than any other article in this series I am posting this one without being completely satisfied with the quality of the exposition, but it’s been long enough that I thought it was better to stop delaying and just get it out there,…
New Mathcamp Notes
This year was the first in a long time that I’ve taught at Mathcamp full time, and I’ve just posted notes for two of the classes I taught there this summer. If you’re one of the very small number of people who are still interested in the quantum field theory article I’ve been promising for years, I have good news: I have actually, finally written most of the first post, and I anticipate having it…
Bean and Nothingness Released, and Other News
I’m pretty sure my audience here is small and mostly already knows this, but just in case I’m wrong: the video game I’ve been working on since 2012 has finally been released! Right now it’s only available for Windows (Mac and Linux versions are likely coming pretty soon) and you can get it right here on Steam . This has been a labor of love for the four of us who’ve been working on it and we’re…
Tutoring Services Available
A bit over a year ago, a friend of mine connected me to his cousin who was interested in learning some of the math he never had a chance to study in college. That meeting inspired me to start working as a tutor for adults interested in proof-based mathematics, which I have been doing ever since. I have room for a couple more students, so I’ve just put up some more information about the work I do.…