I really don't have an answer to your financial aid question. With my school, all I had to do was apply to financial aid as I do every year, then talk to the study abroad office and they handled everything. The programs tuition comes out of my normal tuition in my home school, and the aid I...
I've never actually taken a course, but I've self studied it for about 7 months now. Granted, this is the only rigorous, proof based part of math I've ever done, but I've never enjoyed studying anything more than this.
I started with Understanding Analysis by Stephen Abbott, then I moved on to...
Well the only thing I can offer any advice on is the Advanced Calculus. I used this book
http://community.middlebury.edu/~abbott/UA/UA.html until a couple months ago to get me started on Analysis. It covers pretty much all the things you listed under analysis in a very friendly manner. I...
That actually seems right to me.
This is actually the line of reasoning used to explain that sup{L(f, P´)}=inf{U(f, P`)}
Since for any partition P, U(f,P) is greater than or equal to L(f,P') for any partition P', it follows that U(f,P) is an upper bound on {L(f,P)} From this, it follows that...
Back in September of Last year, I started studying this book to get me started on proofs
https://www.amazon.com/dp/1420069551/?tag=pfamazon01-20
I certainly wouldn't say its the best book of its kind, but it did help me tremendously. It covers basic logic, set theory, relations, functions...
Fall 2012
Infinite Sets (<-- A special topics class at my school)
Abstract Algebra (First course)
Geometry (Audit)
Topology (First course)
I can't wait!
Also, I'll be studying some Analysis from Principles of Real Analysis (by Aliprantis and Burkinshaw) this summer.
I felt almost that same way before as well. Just a year ago when I was in High school, all of the Math I saw seemed so dry and dull. It was all "memorize this, plug this into this, [insert step three here], etc,..." I hated it. But then I started studying what I call the "real" math. The "kind"...
My college has similar requirements, and I'm taking that class this semester. From what I understand, the Calculus requirements are not really content requirements; rather, they are "Mathematical Maturity" requirements. So I think you'll be okay even if you've forgotten most of Calculus or...
Ironman, I sometimes struggle with the same thing. I do a proof, one which I feel is especially hard for me at the time, and in the end, like as soon as I finish it, I'm sitting there wondering whether or not whatever I did was correct. Usually what I do in these situations is examine every...
It did mention mention metric spaces briefly after proving what I'm guessing is a special case of the Baire Category Theorem, that R is not the countable union of no where dense sets. I'm about half way through though, so I don't know if I will ever see metric spaces again in that book.
Would...
Recently, I started learning Analysis from the Stephen Abbott Understanding Analysis book, and I feel like I can finish it within the next month. So I was wondering, what other book should I study after this one? With an intro to analysis, would I be ready for an intro to Topology? If so, which...