Abstract Algebra is it too much?

[SMA_01]

I'm an undergrad math major, and this is my first semester taking upper level math. I'm currently taking Abstract Algebra, and feeling pretty intimidated. I mean, I feel out of the loop, I'm trying hard to understand, but I feel overwhelmed, like maybe it's too much for me. Is it normal to feel like this? My other classmates don't look like they're struggling with the material, but then again, I haven't really asked them...I'm reading the text (we're using Fraleigh), but it seems unclear at times. Does it get more "understandable", should I be worried?

 

[HallsofIvy]

Have you considered asking other students in the class to study with you and/or work on homework together? Not only is "small group" studying a generally good idea, here it will let you see how others are dealing with the class.

 

[jedishrfu]

Maybe you could read the Wikipedia article on it to get a big picture that might help.

When I was an undergrad physics student I took the same course and with the same Fraleigh. It was tough mostly because I didn't know how to do proofs well. My prof would always say if you throw enough mud at the wall some of it will stick.

 

[SMA_01]

HallsofIvy- Thanks, I haven't actually, but will consider that. Although, I am not too good at the group studying arrangement...

Jedishrfu- I'll look into that, thanks

 

[nonequilibrium]

Hey SMA, I took my first Abstract Algebra course last year and I had the exact same feelings. I could understand every line from a logical point of view, but I didn't understand it, i.e. I didn't see the underlying story. I saw that what was written down was true, but I for the life of me couldn't figure out why someone would write it in the first place, and the concepts never came to life in the course.

I struggled it for a whole semester and when I started studying for the exams I felt a bit better, but didn't feel a real understanding. But after really focussing one last time deeply on it, I suddenly, somewhere, made a snap, and suddenly I could start playing with it and I had developped a feeling for the concepts. I started feeling like I understood it :)

Don't fret! Abstract Algebra is indeed quite unlike anything you've encountered before, just keep paying attention, making exercises, thinking about how the things relate (and I didn't obsess about it or anything; I spent a lot of time on it, but not overshadowing much).

Enjoy ;)

 

[conquest]

The 'small groups' approach is generally a good idea for all courses actually!
I am currently grad student mathematical physics and for me it allways helped to realize that most of the things in abstract algebra are generalizations of things that are quite familiar for R and C. Like the notion of primes and even the group axioms etc. I think if you check the history books it certainly evolved in that way (just like a lot of other braches of mathematics e.g. differential geometry)

So if you feel lost just think back to the parallel concepts in R and C.
Also with subjects like this a 'real' understanding just takes a while to build. even now I sometimes suddenly realize I finally completely understand some of the concepts!

 

[homeomorphic]

I'm probably going to sound like a cocky bastard, but I took an abstract algebra course from that book, and I thought it was almost too easy. Although, I took another graduate level one using Dummit and Foote and although I did really well, it wasn't easy--lots of hard problems. And, I took abstract algebra after doing analysis and topology, so by anyone's standards, it would have been easy by comparison.

I attribute my success as a math major to two things. Well, maybe more than two things, but I'll just focus on two major ones. One was that I read Tristan Needham's Visual Complex Analysis. That clued me in on how to try to think about math. What kinds of things needed to be done and just how far you could go with intuition. Another factor was that I had been an EE major for a long time before I switched to math and got a lot of practice thinking about math and physics in an intuitive way. So, I was really thinking the way that Needham showed me to all along, but he just showed me how to take it to the next level. Before I did all that, I wasn't all that great at math. I got a C in linear algebra when I took it the summer after freshman year. Partly because I was late (like 15 minutes) for a test, more than once, but still.

Had I not been so well prepared, it might not have been so easy for me. So, you could interpret my post in a negative way, but also what I'm suggesting is that maybe there's a reason why your classmates aren't having as much trouble. Maybe they are better prepared.

 

[nonequilibrium]

And, I took abstract algebra after doing analysis and topology, so by anyone's standards, it would have been easy by comparison.

Not my standards! I think algebra is harder than analysis or topology.
But for the rest nice post :) I got Needham's book from the library when I was taking complex analysis but didn't thoroughly read it (just parts of chapters here and there), but it indeed looked very refreshing! I should give it another go. Thanks for reminding me.

 

[homeomorphic]

Not my standards! I think algebra is harder than analysis or topology.
But for the rest nice post :) I got Needham's book from the library when I was taking complex analysis but didn't thoroughly read it (just parts of chapters here and there), but it indeed looked very refreshing! I should give it another go. Thanks for reminding me.

I don't know what's harder than what, but the specific class I took was much easier, and I think most people would agree if they had taken the same classes in the order that I did.

There are some abstract algebra books out there that look pretty nice, although I haven't read them.

Charles Pinter, A Book of Abstract Algebra. Visual Group Theory by Nathan Carter. And there's Hermann Weyl's old classic, Symmetry.

Another comment I could make is that I noticed a lot of the other math majors seemed to catch up to me after a while. When I started taking upper division classes, no one could touch me, but then, after a while maybe the strong survived, but also people who had not done as well as I did were catching on, so at some point I wasn't always the top student anymore.

And then I went off to grad school, and I'm getting my *** kicked. Looks like one more year of that. If you really want to be humbled, go for a PhD. That's what happens to most of the cocky bastards. We get knocked off our high horse in due course, too.

 

[mathwonk]

try the free notes on this page:

http://www.math.uga.edu/~roy/number #4. abstract algebra notes. math 4000.these were written by an expository genius ( maybe on bad day). ok, ok, but they are free.

 

[chiro]

And then I went off to grad school, and I'm getting my *** kicked. Looks like one more year of that. If you really want to be humbled, go for a PhD. That's what happens to most of the cocky bastards. We get knocked off our high horse in due course, too.

You're lucky, that happened to me last year (C*-Algebras) in undergraduate :)

Having said that, it's a good experience to have your arse handed to you on a plate because if you have a good attitude and still want more pain, then that is a good sign (as bad as that sounds).

I think though if someone was able to do every form of pure math and found it easy, then they deserve to have a big head, because umm they kinda do :).

 

[conquest]

I don't know what's harder than what, but the specific class I took was much easier, and I think most people would agree if they had taken the same classes in the order that I did.

Well if you're talking abstract algebra one should include things like algebraic topology and algebraic geometry. In my experience there a lot of branches of mathematics out there and they all get very complicated and interesting if you put algebraic in front of them.
What I trying to say is I like algebra! =)