I am currently a second year undergraduate mathematics student in the Netherlands, with a 4.0 gpa (8/10 average grade) and I'm looking to apply for graduate school (In the USA) starting in the fall of 2015. I have a couple of questions though.
-In my country it is required to get a master's degree before doing a PHD, and write a huge (one year) Thesis at the end. Basicly everyone gets a Masters degree (tuition is 2k/year), even the people that dont want to do research. It seems that the preferable option in the USA is to do graduate school, which basicly the master's and the phd combined. Is getting a master's degree first looked down upon in the US?
-I am going to be writing a Bachelor Thesis this summer/fall, is this an important part of the application?
-My undergraduate program is quite extensive, covering differential geometry/algebraic topology/complex analysis/measure theory/functional analysis/logic&axiomatic set theory, and I will also be taking 3/4 graduate courses (commutative algebra/algebraic geometry/harmonic analysis) next year. It seems that math undergraduate programs in the USA generally dont cover as much (from reading about it online). Is this true?
-Are all PHD's fully funded, or will I still have to pay tuition?
-Will I need to get a special visa to work in the USA (I know I will need one to study)?
-It is expected of foreigners to also take the GRE?
I could also take the safe route, and do a Master's degree in my country and then try to apply for a PHD program afterwards, and I might. But it seems beneficial to do my Graduate studies somewhere else then my bachelor, and my country is quite small so the differences will be neglible.