problems in mathematics Where can i find long and interesting problems related to analysis (or to mathematics in general) in order to prepare for the Phd qualifying exams (outside of usa) 
i don't want research problems, but enough difficult for self training and that can be solved in some hours.
 A: I know I'm late, but in case somebody else, like me, gets here looking for the same answer as you: 
Problems and Solutions in Mathematics looks quite advanced and meets your topic requirements.
The cambridge tripos archives, should also meet your needs...
You Also have Problems and Theorems in Analysis I & II. 
At Slightly lower level (regarding required knowledge, not difficulty), you have "Berkeley Problems in Mathematics". Also, as you speak French "Agrégation Externe de Mathématiques" could be a good warm-up.
I'll start training on those alongside my job, for the same reason as you.
Hope it'll help some people.
A: Do you speak French?
Polytechnique, Centrale
(look for Mathematiques 1 & 2)
A: Most universities have their PhD qualifying exams posted on their websites. For example:
University of Florida
http://gma.math.ufl.edu/past-exams/first-year-analysis/
UCLA
https://www.math.ucla.edu/grad/handbook/quals
Stanford
http://mathematics.stanford.edu/academics/graduate/phd-program/phd-qualifying-exams/
To name a few. I googled "phd qualifying exams math." It appears the page at the University of Florida also has qualifiers for Measure Theory, Complex Analysis, and Functional Analysis.
A: I'm not sure what exactly you seek, but do you know the Berkeley problems in Mathematics?
