I’ll start off with a clarification. My students are engineers in the sense that they are PhD students and postdoc in control theory. So they’re very well acquainted with certain sections of modern mathematics: dynamical systems, optimization, some differential geometry, but not so much abstract algebra. The experience with linear algebra is interesting, because itContinueContinue reading “Teaching category theory to engineers (part 4)”
Category Archives: Math
Teaching category theory to engineers (part 3)
I have heard the requests to start posting lecture notes. I’ll get to it soon. These posts are my reflections on the experience of putting this course together and how the students respond. I’ve committed one of the cardinal sins of teaching category theory. I never mentioned the fact that the naming convention for categoriesContinueContinue reading “Teaching category theory to engineers (part 3)”
Teaching category theory to engineers (part 2)
Last time, I mentioned that I would have changed up how I presented the initial information. A few people couldn’t make it to the first lecture. So I offered to show up an hour early this week and essentially give the first lecture again. As you might expect, the second time around was much better!ContinueContinue reading “Teaching category theory to engineers (part 2)”
Teaching category theory to engineers (part 1)
I’m currently teaching an informal course in category theory at Caltech. As I’m currently writing, I’ve given one lecture so far. One of the goals here is to get them up to the point where they could *begin* to read current research in applied category theory. So I hope they could pick up a paperContinueContinue reading “Teaching category theory to engineers (part 1)”
Posets inside of categories
A poset can be thought of as a category with the property that each hom-set is either empty or singleton (technically that’s a preorder, but I’ll skip that for now). There’s also a category of posets. In my work lately, I’ve actually wanted to point at an object in a category and say “this oneContinueContinue reading “Posets inside of categories”
Adjoint School 2023
Category theory has been “applied” in one sense or another since the beginning. Eilenberg himself studied automata theory. But the applied category theory community as it currently exists formally coalesced in 2018. All at once, we had the first instance of the Applied Category Theory conference, the accompanying Adjoint School, and the announcement of theContinueContinue reading “Adjoint School 2023”
Delooping, and internalization vs enrichment
Originally I was planning to write a post called something like “monoid facts everyone should know”, but I’m going easy on myself and giving you just one fact for now. If you ask someone for the definition of a monoid, there are two sorts of answers you’ll get: it’s a set equipped with an associativeContinueContinue reading “Delooping, and internalization vs enrichment”
A different string presentation of monads
My intention with this blog post is not to teach what a monad is, and it’s not to teach how string diagrams work. I just want to share some strings I drew to represent monoidal monads. This post is the first part of a series of posts where I present a diagrammatic language I usedContinueContinue reading “A different string presentation of monads”
Combinatorics, Lecture 1 (26 Sep 2019)
John Baez is teaching a course on combinatorics this quarter. I’m taking detailed notes and texing them up. I’m also going to start blogging them. Credit to Tim Hosgood for the pictures. Prehistory of the course Larry Harper taught this course in the past. John is going to be talking about combinatorial species. He previouslyContinueContinue reading “Combinatorics, Lecture 1 (26 Sep 2019)”
What is the Grothendieck construction like?
This is my best attempt at an intuitive introduction to the Grothendieck construction. I’ll give you the definition, but not before warming up to the idea. I’ll start with the earliest conceptual ancestor I could come up with: addition. Numbers, Addition What am I going to tell you about addition that you don’t already know?ContinueContinue reading “What is the Grothendieck construction like?”
Joe Moeller 