A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)

Category: Mathematics
Author: Charles C Pinter
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by Gene_Parmesan   2020-07-09
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....

by tzs   2019-07-12
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...

by tzs   2017-08-19
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/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/...

by GregBuchholz   2017-08-19
Thanks. I'll start looking into algebraic geometry and abstract algebra.

https://www.amazon.com/Algebraic-Scientists-Engineers-Mathem...

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