few questions =)

[kurt.math]

Hi,

I am an Australian and i am going to try out for a few camps next year and the year after. I will be trying out for Ross, ISSYP, SSP and mathcamp. I just have a few questions regarding mathcamp.

I have looked at the 2009 classes and found there are extremely interesting classes such as multivariable calculus, Elliptic curves, algebraic topology, ring theory and Galois theory. I was wondering what is the level of difficulty of these classes, and how deep do they go, is it mathematically intense or do they just use words to summarize the topics?

Also, I will most likely be starting university mathematics through distance education while still in high school (i will be in my second last high school year). Is there any rule stating that i can not go because of that (but let me convey to you that i will still be a high school student when i apply for the camps).

Thank you for helping

[archimedes1]

No classes are just summaries; there is real mathematics going on in each one. For quick overviews and brief tastes of different areas, Mathcamp has colloquia on weekends.

Many campers take courses with a college during the school year, so it shouldn't prevent you from coming.

[kurt.math]

[calc rulz]

The answer is very much that real mathematics does go on. We rigorously prove everything in these classes, and the problems are as difficult as one might expect in a normal college math class. E.g., last year in algebraic topology, we rigorously proved homotopy lifting and the existence of a universal cover, or this year in ring theory, we proved Wedderburn's theorem on semisimple rings and the classification of modules over a PID. Usually, the class must go quite fast and/or not cover everything that a full college class might cover, but we are doing serious mathematics.

[Darmani]

[calc rulz]

Ehhhhhhh okay so by sketch of the proof of Fermat's Last Theorem you actually mean sketchiest of sketchiness sketchier sketchy proofs. The first three days required complex analysis and group theory, and we legitimately proved dimension formulas, the Fourier expansion, and some facts about Hecke operators.

The last two days, we learned Galois representations under the assumptions that if you know what a Galois group is, what a homomorphism is, and what a vector space is, then you know what a Galois representation is . Now just assume a significant graduate background in algebraic geometry and homological algebra, and you can prove Fermat's Last Theorem.

Back to Darmani's point, it is true that Mathcamp classes often move faster than college because you only have a week or two to cover a large amount of material.