What Should I Focus on When Preparing for Graduate-Level Algebra I?

[futurebird]

I'm getting ready to take grad level Algebra I. My adviser gave me a book to read over the summer. He said "read the first 50 pages." I audited undergrad Algebra I, but I'm wondering what concepts should I focus on for my self-study preparation?

1. What are the hardest things to understand about Algebra I. I'm talking about concepts like "compactness" in Analysis (that took a few days for me to really grasp.)

2. What are the most important theorems? You know the big ones you really need to know.

3. What is "cool" or "fun" about this subject? What can I look forward to?

Are there any internet resources or books you would recommend?

My plan right now is to read the first 50 pages. Memorize the definitions. Do the problems I can find answers for on the web and maybe learn two of the important proofs by heart. (not memorize them, but so I can pretty much do them on my own.) I hate feeling overwhelmed, and since my undergrad degree was in Drama (yes Drama) I often find I need to do a lot of back-tracking to fill in my gaps. (but this is getting better after my first year.) So, I want to be extra prepared and lessen the misery. If possible.

 

[mathwonk]

go to my website http://www.math.uga.edu/~roy/

and download the 80006a notes: course outline.

if interested download the rest of the notes.

or my more detailed 843-4-5 notes.

these were actual notes from a grad algebra I course taught at various times over 1-2 semesters.