Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Prerequisite

Permission of the instructor

Books

The required textbook for this course is available online:

Spivak, David I. Category Theory for Scientists, 2013.

The following book is also recommended:

Awodey, Steve. Category Theory. Oxford University Press, 2010. ISBN: 9780199237180.

The Goal of This Class

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. Either of these will open up and clarify our thinking on a subject, and if category theory can help us do that consistently, then we should all be prepared to consider the class a success.

However, it is possible that the class will fail this test. That is, in order to be really honest we must be willing to acknowledge that maybe category theory is not useful in expanding scientific thinking. But we will only admit defeat if we first make a good faith effort to prove its usefulness to ourselves and find that we come up short.

To that end, I am requesting your help. I have written a book with several scientific applications, but it could use many more. Once you understand a mathematical topic we discuss, look into your field to see how it might apply there. Such an application might be obvious and "on the surface" or creative and "deep", but anything of the sort will be useful to us. I want you to tell me what resonates with you, what works for you, what expands your thinking. You can express this in class or in written correspondence.

I also want to hear from you what is missing. If we are to make a powerful impact on our thinking, we should be on the lookout for what we'd hope to find but seem to miss. We admit from the beginning that category theory is not intended to provide formulas that take in initial data and make predictions about the future. This is the domain of differential equations, linear algebra, and other well-known subjects in applied mathematics; it is not something we are attempting to improve upon with category theory. Instead we look into the possibility that some of the very structure of our thinking can be adequately represented and articulated in the language of category theory. To the degree that it can, the infusion of mathematics into our thinking will afford additional rigor, which should lead us to new insights. Be on the lookout for such openings. The overall point is that your engagement is very important for our success. Please speak up often in class and come to office hours.

Grading

Attending lecture is mandatory. Class participation is 33% of your grade. It's crucial that you ask questions when you don't understand.

Homework is also worth 33% of your grade. It will be collected weekly. Late homework will generally not be accepted. Just turn in what you have when the homework is due.

The rest of your grade is based on your final project. This can either be an oral presentation or a publishable document. See the Projects section for more details.