I will be applying to college in the 2015-2016 school year, and I am hoping to gain admission to some of the top schools in the country (MIT, Caltech, Stanford, Harvard, Princeton, etc). I understand that there is a section on the Common App where you explain what you did over the summer before senior year. I am very interested in mathematics and physics and I want to do either theoretical physics or pure mathematics as a profession. So in previous years, I have attended some math summer camps in the U.S such as USA Canada Mathcamp. Another summer I launched a weather balloon into near-space with electronics and a camera, but this was kind of an easy project that I did with my friends for fun.
As far as this summer, I have a dilemma. I totally forgot about the deadlines for applying to summer camps in math/science and so that is out of the option. It is probably too late to apply to interships as well.
My plan for the summer as of now is to simply prepare for math olympiads, teach myself abstract algebra, and teach myself introductory quantum mechanics using the Feynman lectures. But all of this is self studying and I’m not sure if this will be accepted or looked upon favorably by the admissions commitee. After all, there is no way that they could check that I studied this stuff. Also, I fear that this might appear less impressive than what some of my peers are doing: community service in another country, orchestra tour in Asia, doing research at lab, etc.
I suppose I could try to enter one of the science fair competitions (intel, seimens, etc) and start a project but this takes up a lot of time and to be honest I would rather study abstract algebra.
I understand it’s quite late to be thinking about what to do over the summer (school just ended for me), but it is what it is. It’s probably too late even to apply for an internship at some tech company.
So my question is: (1) will colleges look favorably upon what I plan to do this summer, and (2) if not, can anyone suggest some things I could do over the summer?
tl;dr:
Will colleges look unfavorably on my self studying physics and math over the summer before junior year, instead of doing some program or community service in another country or research at a lab or something like that? I thought I would do this summer what I enjoy doing: sitting down and thinking about math and physics for hours on end. If colleges would not consider this favorable, does anyone have any suggestions of things I might do over the summer to impress colleges?
BTW: when I say things to do over the summer I am excluding things like vacationing in another country (which I am doing) because colleges don’t care about this obviously.