This will be a class which focuses less on computation and more on themes surrounding abstraction and "naive foundations" in the sense of "amenable to how people think". Our starting point will be what we might think sets and functions are intuitively, before abstracting away desirable features, placing an emphasis on the morphisms (functions). Along the way, we will look at examples of ideas like universal properties, adjunctions, and functorial semantics which have proved to be powerful techniques both as organizational tools and devices that aid in exploring new topics. The eventual goal is to develop a picture of categorical structures, like elementary toposes and modules over monads, and how they help contribute towards a conceptual unity which lets us focus on what the non-trivial/formal content of a construction is.
Building this categorical machinery will also provide us with the language and tools to have a discussion on topics like questions of identity/equality, how certain invariants we assign to a collection of objects like topological spaces or representations end up having certain algebraic structures, what it means to have a collection of "spaces" or "algebras", and dualities between them.
The class will be run similar to a discussion rather than a lecture style class. To help facilitate discussion, people are encouraged to have questions either from the reading or a related question of their choice prepared before class; no more than one is required. The reading workload is about 10 to 20 pages per week.
We will try to keep the prerequisites to a minimum. It would be nice to have some familiarity with what is usually covered in Math 55. The bare minimum should probably be at least some exposure to matrices and proof by induction.
There are no exams. The text being used for the class has exercises if some people prefer to use those to check their understanding, but we do not require them to hand in any problem sets. There will be a short report due, allowing people to explore a math topic of their own liking.
Attendance is mandatory. Please send an email in case you cannot/could not be at class.
Section | Facilitator | Size | Location | Time | Starts | Status | CCN(LD) | CCN(UD) |
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Section 1 | Dennis Chen and Samuel Hsu | 20 | 45 Evans | [W] 5:00PM-6:30PM | 02/13/2019 | Open | 23107 | -- |
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