Two of my classmates dropped out of a math graduate program. One of them actually quit right in the middle of class, saying "This is not fun anymore!". It was a Group Theory class on Galois Fields. She became a real estate agent. The other flunked his qualifiers & decided to quit the program and become a pilot (!!) instead of retaking the exams.My prof said attrition rates in math were super high.Its just not everybody's cup of tea, I guess.
Among undergrads, sometimes people switch because profs demean you. Once when I was a TA, the Algorithms prof wrote an email calling a student "bozo" because he couldn't figure out shell sort ( its a stable sort algo ). Unfortunately the student was cc'ed in the email & took it badly & switched.
Galois Fields was when I realized I just didn't want to be a mathematician. I like math, but you can only be a professional mathematician (as opposed to a numerical modeller or some other applied mathematician) if you tackle the stuff that's so hard no other mathematician in the world can do it, or esoteric enough that only a few other mathematicians have bothered trying.
No, it is unstable. The striding means that two equal elements can easily be reordered. For example, after 2-sorting [(2,a), (1,b), (1,c)] by the first component you get [(1,c), (1,b), (2,a)].
I'm 100% with you on that one. That was my biggest stumbling block in college, simply remembering basic algebra. The online resources were more effectual than my professors on teaching a subject.