Do you know of any really good Abstract Algebra websites with lots of examples?

[nontradstuden]

Hi. I've just failed my first test in my Abstract Algebra course... I'm sure I scored a zero.

So... needless to say, I need help. Do you know of any good websites with lots of examples? Or even a really good book with lots of problems? The textbook we're using is 'A First Course in Abstract Algebra, 6th ed.' by Fraleigh. I'm so lost I need help ASAP.

Thanks for your suggestions.

I'm drowning here... D:

 

[Deveno]

a site I've always been fond of is:

http://dogschool.tripod.com/

usually, it's the basic concepts that throw people for a loop...abstract algebra isn't even close to any OTHER kind of class labelled "algebra" you might have encountered before (with the possible exception of some ways of presenting linear algebra...but there, the usual emphasis is on "linear" not "algebra").

Fraleigh isn't that hard a text (you could be using Dummit & Foote), but i suspect it's not the book itself that is giving you problems, but rather some gap in what the book is assuming you already know, that you don't. it's hard to say what that "gap" is, and how long it's been there (it could be you stopped paying attention to definitions in grade-school, and focused on computation. if there suddenly stops being something definite to compute...you'd be lost).

ideally, you'd find a tutor, who can give you one-on-one guidance with your particular stumbling blocks (or use up a LOT of your instructor's time, out of class. some teachers are up for that, some...not so much). the trouble with any on-line site, is the same as the trouble with any book: if you don't understand it, you can't very well ask it: "what do you mean?"

 

[nontradstuden]

@Deveno


Thanks for your reply. You're right. I think I've been focusing on computations only for the last X amount of years...

I feel like I understand the definitions i.e. isomorphism (one-to-one, onto, compatible operations), but when he gives us a weird problem to prove, I don't know where to go with it. But I've had this gap for so long that it may be time to switch majors... or get very little sleep until I graduate X years from now...

Thanks again!

 

[Deveno]

unfortunately, saying "you're having trouble with a weird problem" isn't, in and of itself, very illuminating.

we are allowed to help with problems here, weird or otherwise, but we can't just do them for you. the deal is: we'll give you a good solid kick in the right direction, and then it's your turn.

there's a lot of very smart and talented helpers here, some of them are full-fledged instructors in their own right.

i don't know what your major is, and i don't know what changing it would entail for you. but if it were, mathematics, for example, you can be at least comforted that not all of math is like abstract algebra. some people don't much care for algebra, but are like ducks to the water with analysis, or probability, or geometry.

 

[epenguin]

Outsider's semi-informed view

Maybe these smart and talented helpers should be telling students what is the point of abstract algebra? Perhaps motivation is part of this and other students' problem.

:shy: Would it be true to say that it is about mathematical structure? I.e. math is not a collection of facts like Pythagoras' theorem but that or other theorems within a structure of deduction from postulates. That or other theorems may be true within some axiom sets, false in others, meaningless in yet others - and, possibly motivating, more obvious in some than others? Particular systems are put in wider context. Also abstraction unites and relates apparently different things , matrices and graphs, vectors and polynomials?

For this reason abs. algebra has come to influence the terminology and language also of more applicable fields. So when you study vector spaces you will hear of field, groups and rings.

Well I'm saying that as an outsider - the talented helpers will say if there is anything in it. I, quite long ago in one of my scientific butterflights alighted on and went through a book of abstract algebra and have one or two. It was quite fun for a time to discover that x - x = 0 (or maybe it was x + (-x) = 0 ? Stuff of that kind.) was not, in some systems considered either taken for granted as obvious, nor axiomatic, but was something you could, and had to, prove. After a bit the fun palled because it seemed anodyne - did not seem to lead to the specific structures which are also part of the fascination and usefulness of math, like say the solution of cubic equations or there can be only these 5 Platonic solids etc.

The point of it is that it is abstract and the trouble with it is that it is abstract. Or the other way round.

If motivations are the problem you might dip into whatever is most of interest to you - no obligation to wade through everything - in "Applications of Abstract Algebra" by George Mackiw used from $3.22 at Amazon.

 

[micromass]

Fraleigh is one of the easiest texts on the subject, so I doubt you will find easier.

You obviously have a problem, but I don't know what it is. Maybe you're having some misconceptions about the subject.

It's allowed here to make a thread asking about some conceptual information. So you are perfectly ok to ask "what is an isomorphism". Besides giving the definition, we might be able to tell you how you should threat it. Intuitively, an isomorphism identifies structures. For example, I might have a structure {a,b} with a+a=a+b=b+a=b+b=a. And I might have a structure {0,1} with 0+1=1+0=1+1=0+0=1. These two structures are the same, their elements are only called different. Indeed, if I rename a and 1 and b as 0, then I see that I have the same thing. The act of renaming things is an isomorphism.

Besides asking conceptual questions, it is vital to make many exercises. The more exercises you solve, the better you will become. Certainly if you lack intuition in the subject.

 

[cryptofreq]

Abstract Algebra is the course where I crashed and burned way back in 1993 when I was a mathematics major. 23 years or so later I'm studying to be a math teacher after I retire from the US Army. I have to take this particular course to make up for a few math deficiencies. I guess the pass always catches up to you. Thankfully I feel that I'm a bit more mature to handle these topics - guess I was hung up on the computation portion of math and couldn't wrap my brain around these "abstract" topics. I also have a take a course in non-euclidean geomtry as well. Does anybody off hand know of some good websites that I can use for studying before I take this class?