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Abstract Algebra (MNS)


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Category Theory (CT) as it stands in modern day mathematics is done in a rather abstract fashion. I learned a substantial part of it from the classic text called "Category theory for working mathematicians" by one of its pioneers Saunders Mac Lane. It can hardly be read without any foundation of Abstract algebra. Incidentally, I stumbled into the textbook by David I. Spivak on CT around a year ago and got introduced to an apparently impossible idea of teaching CT to a set of audience having no formal mathematical training beyond elementary Linear Algebra. Inspired by this excellent text on CT, I started contemplating on offering an advanced undergraduate course on CT to both the students from the department of MNS and those from the department of CSE. In Summer 2020, BRAC University created the platform for me to take up this challenge of teaching basic Category Theory to students who do not have formal abstract algebra background. One may naturally then come up with the question: "OK, then fancy topics of CT can be learnt without knowing abstract algebra at all?" The answer to this question is actually NO. Spivak's textbook is designed in such a way that a student gets familiarized with the necessary Abstract Algebra tools along the way. The best part is that it doesn't disallow the students without an Algebra background to take part in the course.

Another interesting feature of the text by Spivak is how he connects various abstract categorical tools using the conceptual framework of "ologs" applied in knowledge representation, data storage etc. Following Spivak, we will always try to support our abstract category theoretic constructions with more down-to-earth examples of "ologs" whenever possible.

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