I am a high school soph - planning to pursue my interest in math over the summer. Considering 3 options and would like input on which one is best to pursue my interest while improving my college admission chances for selective colleges.
Option#1: A summer program - last year as a freshman I got admitted into programs like PROMYS, AwesomeMath and Mathcamp. I went to one of them, loved it. As a repeat camper, I think I will be able to get admission. Advantage of the camp is I will get exposure to do smart people and might be able to get some math research exposure. this camp costs a bit but parents are willing to pay if I really want to go.
Option#2: do an online course. Currently, I am on my way to complete the most challenging courses offered at school: Calculus AP + Stats AP. But by doing an online course this summer, I will be able to go for a DE class in a nearby college which could potentially show my interest/expertise in math to potential colleges. This also enables me to do some summer volunteering. So far my volunteering hours are not many and this will help add some - can volunteer at a math teaching program. this option does not cost anything.
Option#3: this is not in hand yet but can do an internship with a prof at a local college - got a favourable response but this is not yet confirmed. This is more open-ended but could potentially lead to a research project that I can contribute. I can at least gain researching skills and a potential reco from this prof. This option also does not cost anything.
Which one you think is the best for furthering my interest in math and also to improve my chances in getting into a top-20 college.