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Abstract Algebra, 3rd Edition

David S. Dummit, Richard M. Foote · 4 HN comments
HN Books has aggregated all Hacker News stories and comments that mention "Abstract Algebra, 3rd Edition" by David S. Dummit, Richard M. Foote.
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Amazon Summary
This revision of Dummit and Foote's widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the student's understanding. With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year. Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.
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Hacker News Stories and Comments

All the comments and stories posted to Hacker News that reference this book.
The best resource I know of is the textbook I bought for the course I took on group theory and ring theory [1]. It’s pretty expensive and the exercises are very challenging but if you’re a self-motivated student, you can learn a TON of abstract algebra from this one book. You may want to review some linear algebra before you dive in, if you haven’t done so in a while. You can find solutions to many of the exercises online though I can’t vouch for their accuracy.

[1] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

For self study of abstract algebra, I recommend Dummit & Foote. I used it as a supplement to my undergrad algebra classes and found it to be very useful. This is in contrast to some books like Artin which leave a lot to the readers, while not necessarily bad, are sometimes difficult for self-study.

[0] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

trentmb
> For self study of abstract algebra, I recommend Dummit & Foote. I used it as a supplement to my undergrad algebra classes and found it to be very useful.

Because you used it as a supplement.

dkarapetyan
I've learned from both in various undergrad and grad courses and I have to say I like Artin better. Dummit & Foote is a little too dry. I recommend Artin and Dummit & Foote as a supplement.
Most people like the Dummit & Foote book; it tends to be loaded with examples rather than a lot of dense symbolic arguments:

http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/...

When I learned it, though, it was from this Dover book, which is more affordable:

http://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathem...

I'm soon starting my trek through every problem in the algebra text that Harvard's PhD prelim recommends for study:

Abstract Algebra by Dummit and Foote http://www.amazon.com/Abstract-Algebra-David-S-Dummit/dp/047...

I've started the first section of the first chapter, but that was only in a few hours of spare time. I'll be posting solutions by chapter soon and post my stories/insights on Hacker News. Here's section 1.1 (except the last problem, 36):

http://therobert.org/alg/1.1.pdf

Comments are appreciated. Better now than when I start the real journey. :)

brl
Do you want a hiking partner? How fast are you planning on going?
technoguyrob
That'd be great! I'm planning on spending a few weeks full-time on this (8 hours a day, or more if I can handle it). That should be a minimum of one section a day, but hopefully more, even a whole chapter on some days. It doesn't matter how fast, though, as if either falls behind we can just compare those solutions. Email me at technoguyrob[at]gmail[dot]com.
brl
At that pace I think I would definitely be holding you back. Maybe I'll try to tackle something a bit less steep, like Mount Fraleigh.

Have you already studied some abstract algebra, or would you mainly be learning it through this project?

technoguyrob
You can still read through my solutions and point out all my errors if you like, though. ;)

I've already had a couple classes, but I've never felt intimately comfortable with it. With several programming languages, I don't even need the occasional googling, nearly all the libraries (and of course basic syntax) are already in my head. When doing commutative algebra and Noetherian rings, I found myself looking back at ring theory for various properties about rings. Same goes for homological algebra: I had to keep going back to properties of modules. I understand it in more in terms of theorems and facts rather than mathematical intuition and maturity, and my goal is to change that around.

Xlp-Thlplylp
Note on the problem that a group G of even order contains an element of order 2. Partition G into classes {{x,x^{-1}|x\in G}. This is a partition since inverses are unique. For x\in G, call {x, x^{-1}} the class of x. At least one other element x besides the identity has a class of size one. Otherwise, the order of G would be 1 + 2*(# of classes of size 2) which is odd. Hence there is an x with x != 1 and x = x^{-1}; i.e., an element of order 2.
technoguyrob
Thanks, that's exactly the kind of comments I was looking for. That was exactly what I thought in my head, but it came out very distorted and ugly on paper. I'll update the solution later. Do you want credit?
Xlp-Thlplylp
Credit for this is optional. Another way to see obtain a partition of G is to observe that the relation x ~ y if and only if x = y or x = y^{-1} is an equivalence relation on G. The equivalence classes induce the partition above. The point is that any two equivalence classes {x, x^{-1}},{y,y^{-1}} are either disjoint or equal, and their union is G. But this is obvious (the word 'obvious' means "I thought of it.")
jfarmer
D&F was my sophomore-year college algebra textbook so all I can say is, good luck!

It gets very hard very quick and some of the questions are intentionally above virtually everyone's head.

technoguyrob
Cool, you're from the University of Chicago. What (math) field was your thesis in?
jfarmer
Chicago math students don't have to write theses. I guess they figure it's enough just to get through the curriculum.
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