I am posting this question in the aftermath of the earlier posting in this link. Here are what I would like to know more about master and PhD thesis:
(1) I understand that schools' math departments have different policies and guidelines, but what is the generally accepted purpose of a master thesis?
(2) Now switching to PhD level: I often heard the term "original research" done by PhD candidates. What exactly does it mean? Does it mean solving an open question? Discovering new theorems?
(3) And I am curious to know this: If Ivy League PhD candidates are expected to break new ground in their thesis, what are generally expected of candidates at the bottom-of-the-ranking schools like these schools? In particular, am curious about this: Are the same yardsticks applied to both?
Thank you for your time and effort.
POST SCRIPT: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I am surprised that this posting was voted for getting closed. I believe that it is suited to be posted here since Academia SE is for wide variety of disciplines, and therefore only a few of them are math-related. Also, I have sharpened the focus of question (3). Thank you.