Reddit reviews A First Course in Abstract Algebra, 7th Edition
We found 8 Reddit comments about A First Course in Abstract Algebra, 7th Edition. Here are the top ones, ranked by their Reddit score.
Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.
Amazon search for Dover Books on mathematics
There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Pre-Calculus / Problem-Solving
Calculus
Linear Algebra
Differential Equations
Number Theory
Proof-Writing
Analysis
Complex Analysis
Functional Analysis
Partial Differential Equations
Higher-dimensional Calculus and Differential Geometry
Abstract Algebra
Geometry
Topology
Set Theory and Logic
Combinatorics / Discrete Math
Graph Theory
P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
My first introduction to group theory/abstract algebra came from this book by Fraleigh (for God's sake don't pay $120 for it). As I remember, it started pretty basic so take a look.
I'm also a big fan of Dummit & Foote as AngelTC mentioned.
When I first took abstract algebra a couple years ago, we worked out of Fraleigh's A First Course in Abstract Algebra. My classmates and I thoroughly enjoyed it. Well written, well paced, and all around an enlightening introductory read about my most favorite field of math :)
I think it's perfectly tractable for any interested student with a good command of algebra.
Edit: Oh I misread the question. If he's already gone through these elementary parts of abstract algebra, that's about the entire undergraduate coursework I had. The one quarter of graduate algebra I ended up taking went over the orbit-stabilizer theorem, free groups, then dove right into module theory and homologies. We worked out of Artin and Rotman.
Actually now that I think about it, maybe module theory would be a good stepping off point from these parts. I know it gave me a cool new view and appreciation of linear algebra
Ok this is not going to be very original, but I'd start getting a foundation in algebra, linear algebra and analysis. My suggestions for those topics are Fraleigh, Gilbert Strang's Video Lectures (I'd suggest Heuser for learning analysis but that's german and won't help you).
I guess the most important thing to remember is that you don't have to understand everything when you read it for the first time. Try to get a feel for functions and matrices, sets and maps, etc, because you'll need those all the time.
Good Luck!
> Given, my professor is horrible
Well, that definitely doesn't help.
> rings, fields, ideals, irreducibles, etc have without exception come off as some bullshit definitions that a mathematician dreamed up one day to grind out a speculative paper to meet his tenure quota. I don't see anything fundamental in any of this...
It might just be because you're in an intro class. I'm taking my second semester of abstract algebra, and the material on rings is starting to come together for me a lot more - things like seeing the rational numbers being the field of fractions of the integers, or the complex numbers as the algebraic closure of the real numbers. But also, there's the fact that those concepts are general enough that we can look at any field and construct its field of fractions or algebraic closure, etc.
> what's the utility of the definition of "irreducible element" for example? OK so you can't reduce it into non-invertible elements, fine. Who cares if something is invertible.
Is this your first real abstract math course? If so, it's possible that it may just not be your thing. The definition of irreducible elements might not help you build a bridge or fly a plane, but it's a tool that lets you ask questions about the abstract structure of rings. Irreducible polynomials can't be factored, which is interesting (kind of by definition, but hey). If you have a polynomial ring (so long as it's got a multiplicative identity and is commutative), the ring you get by taking its quotient by the ideal generated by any irreducible polynomial is actually a field! Or you can look at splitting fields of irreducible polynomials, and start talking about the construction of the finite fields...
You might not say there's much utility to that, but who needs utility? That's not what abstract algebra is for! It's fun because you get to start with some basic axioms and then explore all the enormously complicated structure they imply. I find it absolutely fascinating.
> It occurs to me that I don't understand the material and that's what's making me so frustrated. I've read through all of the relevant chapters in the assigned textbook (Gallian) repeatedly. What text were you using?
Yeah, I think part of the problem is that these concepts can take a while to sink in. I suggest giving it a break for a month or two after the end of this semester, but come back and give abstract algebra another shot later. Maybe in the summer, or in the fall. After you've given your brain time off to integrate all the knowledge you've just crammed in there, everything will make a lot more sense and you'll get a lot more enjoyment out of the subject. I can testify to that - my first semester of algebra was okay, but I'm loving my second semester now.
We're using A First Course in Abstract Algebra, by Fraleigh. It's an excellent book, I highly recommend it.
Fraleigh is a little bit easier to wrap your head around. Get an old edition (or find it at the library), obviously.
Also, I highly recommend Herstein's Topics in Algebra. Again, try to get it from a university library.
I've got a few recommendations:
A First Course in Abstract Algebra. The importance of this subject in mathematics cannot be overstated, even if it seems very counterintuitive. Most number theory problems are solved through advanced algebra. This book examines most aspects of groups, rings, and fields, and many major applications of them. Anyone can read the first chapter, but you're going to have a very bad time if you don't get each chapter DOWN before the next one. This subject matter took me two of the hardest classes ever to get through, so don't be discouraged.
Like I said elsewhere, Rudin's Principles of Mathematical Analysis. Starting from basic set theory, it provides a thorough construction of the concept of real numbers, followed by sequences, series, single-variable calculus, multi-variable calculus, touches on standard and partial differential eqs, and VERY basic functional analysis. Again, a short but extremely dense book, anyone can do it, but not easily. Don't take shortcuts, and it will massively expand your mathematical literacy.
Neither of these requires much set theory, but if you're having problems there is this book. It is what it looks like, but the first few chapters are logic so you can probably skip them. It's an easy read and it seems to me that set theory is very similar in operation to logic.
There's a good explanation of introductory quaternion theory in this book, which sets it in the larger context of group and field theory.