This summer I finished my BSc maths degree at Imperial College London and ranked around top 5% of the class.
I was considering the idea of applying to some US universities like Stanford, Harvard, etc., but they don't do master's applications, just straight up PhD ones for mathematics. I quite like the idea of doing a PhD, so it is not a big problem for me, but I was wondering about my chances here, coming off a BSc and applying straight to a PhD sounds like a big reach.
Has anybody had similar experiences and know if it's even worth trying?
Thanks for all the help.