The book "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand et al. is a pretty good introduction to thinking like a mathematician, and the content in that book furnishes the minimum required background for studying subjects like number theory and topology. Once you've...
I'm starting my first (official) year as a Ph.D. student. My Fall 2012 schedule looks like this:
Partial Differential Equations
Algebra I (category-oriented algebra)
Topics in Complex Analysis
For the Spring 2013 semester, I have to pick three among these five:
Algebra II
Functional Analysis...
I have a friend who, like me, is a Math major, although she started later than I did and as such, hasn't yet gotten into the core classes for her degree. She's frequently checked out my own personal library and I figured that, since the holidays are coming up, it might be cool to start her off...
I'd consider myself an average--if not below average--math student (my talent is more centered in English and the like). I survive because of my enthusiasm for the subject, not because of any real innate ability, and I've found that math is doable at pretty much any level of experience given...
I second the Axler recommendation. I'd also recommend Shilov and Friedberg. Friedberg is a bit more expensive than the other two, though, so you might just want to get Axler and Shilov which, together, cover a lot of topics with excellent exposition.
I believe that it's a misconception that it's difficult to find a job with a pure math degree. It's been my impression that a math degree is among the most marketable and versatile degrees around. Certainly with a Master's in math, your options expand even further.
Check out these links. I...
If you're planning on CS grad school, knowing more math would probably be quite helpful. I know my school's CS department recommends a solid background in linear algebra and discrete math (namely combinatorics and graph theory) to grad school hopefuls.
It honestly seems like you're in a win-win situation of sorts, assuming that "knows his stuff" implies "good teacher," but give the waitlisted class a try. It's been my experience that full classes are easy to get into with a bit of patience, so add that section to your shopping cart and check...
I'm a little bit of the latter, I'm sure, but neither semester is quite as bad as it looks. In the Fall, only the first three classes are really going to be difficult. Differential Equations is a low-level, nonrigorous course that I'm actually retaking in order to replace a mediocre grade from...
Fall 2011:
-Advanced Calculus I (Intro to Real Analysis I)
-Abstract Algebra I
-Advanced Linear Algebra (Grad class)
-Differential Equations
-Techniques of Problem Solving
-Introduction to Communications
Spring 2012 (Early, but I figured I'd post it anyway):
-Advanced Calculus II
-Abstract...
This was a month ago, I know, but I'm wondering how Artin's been working for you so far. I've been considering picking it up so I can really learn the material at a high level before my class this Fall.
I think the non-calculus-based Physics classes are for non-majors. At my school, any major even tangentially related to Physics (that is, Math, Computer Science, Engineering, and Chemistry) is required to take the calculus-oriented Physics sequence. Those classes are also likely to go more...
Honestly, it might benefit you to do some independent study in number theory, both because you'll get more practice with proofs and because number theory knowledge makes algebra easier--or so I've been told. "Elementary Number Theory" by Jones and Jones is an excellent book in that regard...
If your school offers a course to the effect of Intro to Discrete Mathematics or Logic and Proof in Mathematics, that would be a good one. Some people recommend holding off on such a course until second year (and in fairness, it tends to be difficult), but if you're exposed to that sort of...
That doesn't seem that bad. My only concern would be prerequisites. Have you really mastered everything you'll need for those classes? If so, I see no reason not to give that schedule a try. Worst case scenario, you drop a class and know your limits for the following semester.