Hey n_student. Like you, when I was a freshman I also had no experience with things like proofs. In fact, I had never had any experience with proofs until an analysis/introduction to proofs class in my junior year. Needless to say, I had a lot of trouble with even the simplest of proofs at...
Well, the transpose of
\begin{bmatrix}A & B \end{bmatrix}
would actually be
\begin{bmatrix}A^{T} \\ B^{T} \end{bmatrix}
if I am not mistaken, so you would have to require A and B to be symmetric as well for the transpose to work.
I don't think this is what you were looking for, but after...
I was able to get by the first few, more computational courses without putting in much effort outside of class, but you will probably need to learn to teach yourself in the upper level, more proof-based courses.
The thing is, you will learn more by practicing working through problems/proofs...
I hate to disappoint, but I actually haven't looked at it yet, sorry.
I thought I would have plenty of time to study it this summer but I'm taking 3 courses that are fairly work intensive, although not particularly difficult.
I also chose to start studying Topology first, and that's also been...
These links will be very helpful, thanks a lot. I try and do a lot of self-studying but there's always an issue of not knowing if I'm doing everything right or if I really understand everything.
I ended up buying Artin's book as well as Rudin's book on Analysis and Munkres' book on Topology since I'll be taking those two courses next fall.
I also considered Dummit and Foote as well as Jacobson and still might get one or the other. Again, thanks for the responses.
Starlit, don't worry about it. Like you, I never needed to study in high school and I really, really screwed up in my first semester at college.
I'm a junior now and I'm doing very well. You're going to have invest more time into studying/reading on your own, but as long as you remain...
Wow, lots of replies. Thanks guys. :biggrin:
The text that we used was the one by Fraleigh, but I don't like it too much. I found the exercises in the book were lacking in difficulty, at least up to where I left off.
We covered groups, group actions, rings, homomorphisms, quotient...
I have just finished my first course in Abstract Algebra. I was wondering if anyone could recommend a book that goes deeper into the subject. We covered groups and rings, but not much else after that.
Also, this is a really cool forum.