Summer mathematics internship for high school students?

[huey910]

I am looking for summer internships this year. I originally wanted to try Wolfram but they require people who know computer programming or mathematica(which I would have to enroll into their summer camp to learn more about) so this seems to be out of the question. I wonder if I could shadow a lecturer or researcher at a University(Cambridge is obviously too ambitious because, let's face it, who would want a lower 6th student bothering them for days?) I have had brief interactions with Professor Imre Leader from Cambridge though - should I ask him whether there will be any slight chance that I might be able to get an internship or would it be just a waste of effort? Where else would be good places to get mathematics work experience? If this helps, my favorite branch in mathematics is abstract algebra.

 

[genericusrnme]

You could certainly try but I wouldn't put too much hope on it.

The best use of your time, imo, would be to pick up a few books on your local library and study from then for however many hours a day you'd spend shadowing someone. Off of the top of my head, I'll go ahead and recommend;
Introduction to Linear Algebra - G Strang
Modern Algebra with Applications - W Gilbert
How to Prove it - A Structured Approach - D Velleman

I'm assuming here you want to study mathematics at university here ofc.