Hello everyone. I am currently in my third year (junior year I think it's called in the USA) of undergrad, as a maths major, hoping to get into a masters program. I go to a small university. I looked at some universities graduate school's websites, and I've seen quite a few that say they do not accept students with a masters into their Phd programs. This seems a bit odd to me, it's certainly not the case at my university; is this standard? I mean, I seriously doubt I'll know by the end of next year which area I want to specialise in, so I'll want to do a masters first. Is there anything wrong with this route? Also, I suspect my background is quite weak for a typical undergrad. What kind of courses should an undergrad looking to get into grad school have? I've taken the calculus sequence. As for real maths, I have taken: linear algebra; a little abstract algebra (mostly group theory); real analysis in one variable, at the level of Rudin. At the end of this academic year you could add complex analysis in one variable, from Conway. My background looks suspiciously weak to me, especially when I look at the undergrad curriculum for Princeton (a family friend went to Princeton). Next year, my final year (senior year?) I will be taking only maths courses (which is typical at my uni). That said, I can probably add multi-variable analysis and abstract algebra to the list of courses I know, by going through the books myself, before my senior year. Does this sound sufficient? I know very little about what my senior year courses are going to be like. As for non-math courses, I have taken: Two years of physics (general physics; EM and QM) Applied maths (numerical analysis; ODEs, PDEs, mathematical methods, GR) First year stats As you can probably tell, my uni has a good applied maths program; I'm not so sure about the pure maths program. The physics program is also good from what I hear. So, is my background sufficient, or weak? Is taking masters instead of going straight into a Phd program a good ora bad idea? Thanks for your help.