I'm an undergrad (liberal arts) that is planning on applying to math PhD programs and eventually being a math professor (hopefully). Many people have told me to go straight into PhD programs. This seems to be more or less the norm in the US, but looking at the sites of schools like UWaterloo, UBC, Simon Fraser, etc., it seems like they highly recommend having a masters first.
Is the masters in Canada similar to the first couple years of PhD programs in the US and then the PhD is equivalent to the dissertation portion of the PhD, or are you expected to a masters and then a full 5-7 year PhD program?
Also, how do the applications compare to the US?