I'm a math major and was wondering what to do over this summer, since I'm not going for any internships/have any fixated family agenda. I was thinking of working out a book, like Spivak, or work on a math-related project. In fact, some time back, I had planned on doing a project on the mathematics of crime-fighting. Sadly, that didn't turn out as expected. The reason was myself; I got demotivated rather quickly (feeling rather ashamed about it now). Initially, I was enthusiastic, but when it came to researching the concepts, and working out the math, I guess the lack of someone to spark off the ideas with, and share my thoughts, eventually put me off.
So, in order to not repeat the same mistake again, and to do something fun this summer, I'm looking for a study/project-mate; so that can bounce off our ideas and intuition, and learn something new in the process. I'm open to doing anything, as long it's interesting and challenging math that we'd both be comfortable with. Collaboration would be purely online, through email/other means which can be discussed. The stipulated time period would be May 20th - July 20th, but I guess that can be discussed as well.
The only factor I'm looking for, is an interest towards mathematics/analyzing stuff mathematically. Provided that, I don't think it'll be that hard to find something to work on, that's interesting for both of us.
As for my areas of interest, I'm interested in using math to solve real-world problems such as mathematical modelling using differential equations. At the same time, I'm equally interested in pure mathematics topics such as Analysis and Number Theory. Actually, you could say I've been more of a proof-oriented guy so far, rather than an applied math guy. But then again, it's just as I said at earlier: I'm open to doing anything, anything at all, as long as it is some challenging mathematics (of course, which is reasonably accessible to a freshman undergrad)!
My idea of a project is working on ANY problem that challenges me to think up something new mathematically, anything that prompts me to look up a new topic in math, and then come back to the problem and see how I can apply it there, i.e essentially a back-and-forth process between learning something new and applying it. The problem does not have to be practical; actually I've worked so far only in pure math.
Even if a project is not acceptable, I'd be happy to have someone to study a new math topic together with, or something like working out the problems in Spivak, or even learn some new problem-solving techniques in the spirit of Olympiad-math. Actually, it's all open completely from my end.
A grander idea would have been to build a small online team of 5-6 members, but I guess that's asking for much. So, anyone up for it?