I'm the second-year college student in the Mathematics Faculty. I'm having difficulty in finding orientation for self-study. Can anyone show me the course of Mathematics in some universities in the world, from the first-year to the the final year as well? I'm following Rudin for analysis and J. Kelly for general topology, and I'm going to learn Complex Analysis, Euclidean Geometry, and Differential Equations. But I want some courses for self-study. And of course, textbooks for it. It's my first time to have question and my English is not so good. Thanks for your answer.
You want to understand the term OpenCourseWare. Here are schools that partake (and you can search their websites for courses on your needs).
From this site, these are some of the large universities that partake, with this listing being roughly in the order of adoption of OCW principles.
Massachusetts Institute of Technology (MIT)
University of California, Berkeley
University of Pennsylvania
University of Michigan
Differential Equations http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/index.htm
As another example, at Princeton, you have: http://www.virtualprofessors.com/category/mathematics
This effort has also gone global, for example Oxford: http://www.maths.ox.ac.uk/notices/opencourseware
You could also look at the Khan Academy for some of these items: http://www.khanacademy.org/
There is also this site and it claims to also have math, but I have not spent enough time there yet: http://www.open.edu/openlearn/science-maths-technology?seeall=1
There are many wonderful books in these areas too, so you might want to peruse your closest library. There are probably free books online in these areas too that you can search out.
Remember, patience, practice, persistence! Enjoy!