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We had a discussion on this when Stephen's last post showed up here: https://news.ycombinator.com/item?id=6041726 https://news.ycombinator.com/item?id=6041726
by jcurbo 13y ago
We had a discussion on this when Stephen's last post showed up here: https://news.ycombinator.com/item?id=6041726 https://news.ycombinator.com/item?id=6041726
I've been looking into this myself and I have a similar background as you (elementary calculus and linear algebra; I also took number theory as part of a math minor). So far it looks like I should pick up a bit of abstract algebra/topology (rings, fields, groups, etc) then I should be able to start off on the shallow end of category theory and work from there. At the same time I need to improve my understanding of how monads, monad transformers, monoids, functors, etc work in Haskell from an operational standpoint; I have a basic understanding now but I'd like to dig deeper.
The thread I linked above has a lot of links to books and stuff like Reddit's r/haskell and other places, that you can sort through to see what works for you. I have yet to make that determination for myself, but there's plenty to choose from. I actually picked up a copy of Benjamin Pierce's "Basic Category Theory for Computer Scientists" a few years ago based on someone's recommendation, way before I got into Haskell, and didn't make the connection until I picked up his book on type theory recently (while researching a paper on FP) and thought his name looked familiar.
Ultimately I'm hoping to be able to get deep into type theory and go through that Homotopy Type Theory book that came out recently.
- davidcuddeback 13y agoThanks for the response. I was interested in the answer to this question as well. I read through the thread [1] that you linked to, and seems like the consensus is the same thing you said: it's best to learn abstract algebra and topology first. Does anyone know of some good sources for those topics? The other threads are understandably focused on category theory. As for category theory, after reading through that thread [1] and the Reddit thread [2] that it links to, I think Conceptual Mathematics: A First Introduction to Categories [3] will be my first read on category theory (but probably followed by the Rosetta Stone paper). That book receives some strong recommendations as a first book in the Reddit thread [2]. [1] https://news.ycombinator.com/item?id=6041726 https://news.ycombinator.com/item?id=6041726 [2] http://www.reddit.com/r/haskell/comments/1ht4mf/books_on_category_theory_for_beginners/ http://www.reddit.com/r/haskell/comments/1ht4mf/books_on_cat... [3] http://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categories/dp/052171916X http://www.amazon.com/Conceptual-Mathematics-First-Introduct...
- jcurbo 13y agoNot a problem. I'm interested in the abstract algebra question too, as I haven't actually done any research yet. Perhaps someone should start an r/categorytheory. :)
- davidcuddeback 13y agoThis might become a recursive rabbit hole.
- davidcuddeback 13y agoDigging deeper into the HN thread that you linked to, I came across this discussion [1] on Reddit which is focused more on the abstract algebra question. They recommend Algebra: Chapter 0 by Aluffi (Amazon [2] or PDF [3]). [1] http://www.reddit.com/r/math/comments/1eiyid/category_theory_prereqs_does_alg_geometry_come/ http://www.reddit.com/r/math/comments/1eiyid/category_theory... [2] http://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/0821847813?tag=duckduckgo-d-20 http://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathe... [3] http://www.mimuw.edu.pl/~jarekw/pdf/Algebra0TextboookAluffi.pdf http://www.mimuw.edu.pl/~jarekw/pdf/Algebra0TextboookAluffi....