Welcome to the Category Theory Study Group!
For over 30 years Professor Michael Miller has been teaching advanced mathematics courses through UCLA’s Extension program. He’s built up a following of 20-30 “regulars” who are always augmented by several welcome newcomers. As a camaraderie has built up among the participants over the years (and because Mike only teaches in the Fall and Winter quarters) many of his regular students choose a subject or two to study as a group throughout the Spring or Summer months. (Past groups have delved into Lie Groups, Quantum Mechanics, and Algebraic Geometry among others.)
This year a group of us has settled on the vibrantly growing field of category theory and we invite you to join us.
Exercise Your Brain
Whether you’re a professional mathematician, engineer, physicist, physician, high schooler, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of this study group, not to mention the camaraderie of others including some of the “regulars” from Dr. Miller’s classes who all have widely varying backgrounds (literally from actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Only a very few in the group have dabbled directly in the subject area in the past, but there’s enough depth and diversity in the group already that we should be able to get fairly far into the subject by ourselves.
Even if it’s been years since you last took Calculus or Linear Algebra, we will all help you get quickly back up to speed in studying mathematics. (One should note that the text we’ve chosen doesn’t have any significant prerequisites, though at least a passing knowledge of high school set theory might help.)
If you’re interested in mathematics, physics, computer science, programming, quantum mechanics, quantum information, or even string theory, this is one of the topics that is rapidly becoming de rigueur for delving in deeply and being able to understand them better. And naturally, it’s simply a beautiful and elegant subject for those who have no need to apply it to anything, but who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the group by the way.)
If you’re not sure what you’re getting into (or are scared a bit by the general description), I highly encourage to come and join us for at least the first few meetings before you pass up on the opportunity.
“I’m putting together a study group for an introduction to category theory. Who wants to join me?” – Chris Aldrich
In some sense, we’re using this website as a means of communication between ourselves, but we’re also hoping to leave it behind to help other students (and autodidacts) in the future. So whether you’re in the initial “peleton,” or you come across this in the future after we’ve all come and gone, feel free to sign up and add your own thoughts and comments to these pages.
“The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.”
– David Spivak’s course description from his MIT class using his textbook Category Theory for the Sciences
For a brief introduction to what we’re undertaking, please take a peek at the following pages, or browse through the menu:
and the following initial posts:
For those who need an introduction to the subject or some motivaton, you might find Ilyas Khan’s article Category Theory – the Bedrock of Mathematics? interesting. Though it tends a tad toward the technical side (so don’t let it scare you away – besides there’s a group of us here to help you!), it does show a little of the depth and breadth of what is going on in the subject.
Want to join us? You can register as a participant to be allowed to add your own content here, or you can simply add your thoughts as comments to existing pages and posts.
We look forward to welcoming you to the set of students who are studying category theory.