I'm an Italian mathematics student who wants to apply for a strong PhD program in pure mathematics in USA. Of course, like everyone (I think), my dream is to get in a top school, just to make the idea, my dream school is UCLA. Of course, every PhD applicant to schools like that has a perfect GPA end high GRE/Toefl scores, therefore recommendation letters apart, I guess that the level of applicants is pretty uniform. My question is this:
Does holding a Master's Degree really help me to get in top schools like UCLA?