Hacker News Reader

Comment by BinaryIdiot | Hacker News Reader

This really reminds me, it's been two decades now since I've taken _any_ Algebra. I'd really love to go re-learn it from the basics on up. I mean, I still remember a lot of it here and there but some sort of refresher course up to doing more advanced would be awesome.

Any recommendations?

View on HN

Hell yes! I love hearing about people interested in abstract algebra and wholly support your endeavor! Here is a pretty decent resource on relevant texts:

http://www.cargalmathbooks.com/#Abstract%20Algebra

That page in general is pretty gold for math texts in general.

Also, #math on freenode has lots of algebra-strong users on it, though depending on your luck some can be less helpful than others. I love chatting about this kind of thing with people, so if you would like an ad hoc mentor/study-buddy I would be more than happy to help. Feel free to email me at the address in my profile.

Good luck!

Hi there, the email field doesn’t show up - you need to put it in your about section for people to see it :)

Uff. Thanks! Done.

Cool, thanks for the info! I'm going to check out that list.

I think Linear Algebra is traditionally recommended, since you can readily apply a lot of geometric intuitions while picking up the mathematical ones. The drawback is that you have to make sure you're not cheating yourself of the mathematics by over-relying on the geometry.

Sheldon Axler's acclaimed "Linear Algebra Done Right" is freely available as a download [1] through July due to the pandemic. I've not read it (yet!), but I've heard so many good things about it I feel comfortable recommending it off the cuff. :)

(Recommendation: try not to focus too hard on the matrices! They're just convenient representations (syntax!) for the actual things we care about: linear transformations. It's less geometrically intuitive, but it lays a much better foundation for algebraic widgets other than vector spaces. Use the wealth of geometric intuitions to jump-start your mathematical sense.)

I don't have a lot of recommendations for other algebra topics, unfortunately. My class textbook for abstract algebra was Dummit & Foote, which I found very dry and lacking in intuition. Aluffi is perfectly servicable if you feel good about your linear algebra; just don't feel like you have to complete every exercise.

Also, I'm a sucker for order theory, so if you're up for something a little less algebraic, pick up Munkres' Topology. I'm consistently surprised at how often topological and order-theoretic intuitions come up in software development. There's a close connection between topology and logic, so perhaps I shouldn't be so surprised -- but I haven't studied Stone duality at all, so it shall remain surprising for now.

[1] https://link.springer.com/book/10.1007/978-3-319-11080-6

Sheldon Axler's acclaimed "Linear Algebra Done Right"

Seconded. Highly recommended.

Sheldon Axler book for some reason is hugely hyped in HN always when this topic comes up.

But I do wish for a more comprehensive book on Algebra covering the entire breath of the field.

Matrix Analysis by Roger A Horn, seems a good book with most of the knowledge of matrices covered. Could be helpful for people working with Graphics.

I wonder whether HN has heard of "Linear Algebra" by Hoffman and Kunze. I learned from it as an undergraduate and remember it being told that it was a classic. Another more abstract book is by the great Halmos: "Finite Dimensional Vector Spaces". Both books will stretch and entertain you.

Reply on news.ycombinator.com