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Category Theory and General Nonsense
(Taught in Splash Spring 2016)
In this course, I teach the basic components of category theory, focusing on objects, maps, and compositions of maps. From here, we learn about their application in commutative diagram proofs, which can be used to demonstrate so many different results that mathematicians have jokingly called them "general nonsense". In reality, the methods of category theory are remarkably intuitive and simple to learn, precisely because they reveal the contentless form of mathematics itself, drawing the interest of countless mathematicians, philosophers and scientists. Any math course that you've taken had ideas provable using these techniques, whether it was logic, geometry, algebra, or calculus. Learn them, and amaze your teachers by showing them your clever "nonsense proofs".