I do’nt doubt that getting into ivy leagues for masters is far from a piece of cake, but I would like to know whether it is as hard as getting into for undergraduate studies.
Though the ranking isn’t an absolute indicator, I saw that UM-twin city is ranked higher than Columbia U for chem. E graduate programs. Does it mean it will be harder to get into UM-twin than Columbia U for chem. E grad programs?
The Ivy League is a sports conference. That’s all. The Ivy universities also happen to be considered good undergraduate schools, which is unrelated to their being part of a sports conference.
None of that has anything to do with the strength of a school’s graduate program.
Like you said, ranking is not an absolute indicator of difficulty in gaining admission, but as a general rule, yes, higher ranked programs will be more difficult to get into, within reason. However, at the graduate level, things like research experience and fit with a particular program or faculty member are important, and these are difficult to quantify.