Found in 6 comments on Hacker News
This is several days late, but I had this tab open along with many others and I'm finally getting to it.

What is it that you find challenging about math? If it's the actual computation/calculation -- the part where you are finding a numeric answer -- don't worry, that's nowhere to be found in abstract algebra (or any higher level math). Pure math (of which abstract algebra is a part) is about the study of patterns more than anything that has to do with numbers.

In fact, the name "abstract" refers to the fact that it's concerned with abstract collections of things -- for instance, groups. You'll study sets of operations on groups -- if you are able to identify Collection X as a group, you immediately know you can apply theorems a, b, c, etc. to it. For these reasons, the sort of things you are likely learning in pre-alg on Khan Academy don't have much direct applicability.

I think it's an enormously beneficial subject for programmers to study, maybe the only math course beyond the standard discrete math that I think should be required. (I want to add category theory, but I don't feel I can as I only have the barest grasp of the fundamentals myself...) As with all pure math courses, it will quickly move beyond the depth/level you can actively use in programming, but the mind-expanding it does is really great at encouraging the sort of abstract thinking the OP's post is about. It has strong relations to generics, interfaces, polymorphism, etc.

As for how to get into it, I used this book: https://www.amazon.com/Book-Abstract-Algebra-Second-Mathemat....

tzs · 2019-02-25 · Original thread
For abstract algebra, take a look at Pinter's "A Book of Abstract Algebra" [1]. It's a Dover republication, so is not expensive. It has a lot of exercises...in many chapters more than half the pages are exercises.

It does not provide answers to every exercise--maybe 10% tops--but a lot of the exercises are small and should not be any problem. These are often in a group, where he takes something that would be one hard exercise in another book and breaks it down almost to the level it would be if were part of the main text, leaving just small thing for you to fill in as exercises.

There are a few recurring themes throughout the exercises, where he applies the material of the chapter to some specific application in several exercises (e.g., error correcting codes if I recall correctly), and subsequent chapters continue with those themes in their exercises.

[1] https://www.amazon.com/Book-Abstract-Algebra-Second-Mathemat...

tzs · 2017-07-26 · Original thread
I typically have several books in progress. I'll read a chapter from whichever one I'm in the mood for when I have some time for reading. Currently in progress:

"A Book of Abstract Algebra: Second Edition" by Charles C. Pinter [1].

"How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg [2].

"Guns, Germs, and Steel: The Fates of Human Societies" by Jared Diamond [3].

"Introduction to Analytic Number Theory" by Tom M. Apostol [4].

"Algorithmic Puzzles" by Levitin and Levitin [7].

I've also got a 46 books in my Safari Library queue, although only about half a dozen are actually in the in progress state.

In addition to the above, I'm about 3 years behind on Analog, the science fiction magazine. Those are all on my Kindle and I'm slowly trying to catch up.

Recently finished:

"Moonwalking with Einstein: The Art and Science of Remembering Everything" by Joshua Foer [5].

Probably going to pick up soon:

"The Greatest Story Ever Told--So Far" by Lawrence M. Krauss [6]. Flipped through it at a bookstore and there were some very interesting things in it.

[1] https://www.amazon.com/Book-Abstract-Algebra-Second-Mathemat...

[2] https://www.amazon.com/gp/product/B00G3L6JQ4/

[3] https://www.amazon.com/Guns-Germs-Steel-Fates-Societies/dp/0...

[4] https://www.amazon.com/Introduction-Analytic-Number-Theory-A...

[5] https://www.amazon.com/Moonwalking-Einstein-Science-Remember...

[6] https://www.amazon.com/Greatest-Story-Ever-Told-So-Far-ebook...

[7] https://www.amazon.com/Algorithmic-Puzzles-Anany-Levitin/dp/...

bmer · 2016-05-22 · Original thread
This book was far too wordy for me. I found a better compromise by reading two these books in parallel:

* Burns' "Groups: A Path to Geometry": http://www.amazon.com/Groups-Geometry-R-P-Burn/dp/0521347939

This was the main read. It's approach is to take the reader through group theory by presenting it as a series of problems. Discussion is limited mainly to historical notes.

* Pinter's "A Book on Abstract Algebra": http://www.amazon.com/Book-Abstract-Algebra-Second-Mathemati...

While going through Burns' book, if I needed more of a discussion on a certain topic, then Pinter's book always felt like it comfortably quenched my desire. Here is someone's discussion on why Pinter helped (along with a proposed litmus test for group theory texts): http://math.stackexchange.com/questions/1469294/recommendati...

pjungwir · 2014-10-16 · Original thread
I have a C hobby project I worked on during a couple flights the other week, but if I flew again I'd probably bring this:

http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathemat...

. . . along with paper for working the exercises.

Fresh book recommendations delivered straight to your inbox every Thursday.