I posted a similar question at the following link yesterday; since, however, the focus of the question was different, I'm posting this question in a separate post.
It seems as if I'll be taking the next year off and studying a lot of mathematics on my own and apply to graduate schools in the next cycle. There's a lot of advice both on this website and Academia StackExchange for such students. However, I'd like to know how can students who have studied material outside of class better convince the admissions committee of the work they have done thus far. I know it's generally difficult to do this as an international student; the situation must be different for U.S citizens, I suppose.
Assuming I don't get to take courses which I'll be self studying over the next few months, how should I go about making sure the admissions committee take due notice of the work I have done, and more importantly, they can recognize it, if not verify it completely. Of course, I will keep in touch with my math adviser. In addition, what else can I do? Say, I am studying abstract algebra on my own in the summer, working out problems in, say, Dummit and Foote's book. Should I, perhaps, make a website (a Google site), periodically type the solutions to the work I have done and post it online, so when I apply to graduate schools, I can refer admissions committees to this portfolio of sorts.
In a nutshell, I'd like to know, especially for students who have gone through such a process/situation, of the list of best possible set of actions one can do to make sure the work one has done outside of class is duly considered, if someone who is interested in mathematics schools doesn't have a large number of math courses.
I have an additional query: I'll be taking next year off, but I'll be able to visit my college. Even though I won't be enrolled in classes, preferably with the instructor(s) who already know me, sit in their classes, work on problem, and perhaps even take exams. even though I won't get a grade, I could ask the instructor to mention in the letter that I completed this task. She could also comment on how well I did relative to my peers. Thoughts?