this class gave me trauma

i'm surprised that greene has high ratings in some of his other classes since every negative thing you might've seen/heard about his lecture style is true, and him having a "nice" personality probably contributed to his higher ratings even though his demeanor is more so a result of him not personally caring if the students are suffering; greene's old school in that he expects you to self-study outside of class but he's also contrarian in that he evidently doesn't believe in teaching anything coherent in class: we somehow got through the syllabus with 2 weeks left to spare because he skipped over/rushed through so much stuff (in spite of this class supposedly being foundational for other math classes), and then the rest of the class got even worse because greene wasn't constrained to the syllabus anymore (ex. we were expected to know stuff from analysis even though that class isn't a prerequisite)

if you thought the professors you've had so far were good but felt like they could've been better, then you should take greene's class to lower your expectations, otherwise run

It is clear from the get-go that Greene's area of interest is not algebra. The lectures are very disorganized, and he will skip across topics or talk about a graduate-level topic in Algebraic topology without motivating such discussions. His tests are mostly rehashings of the homework or the practice tests, so that does make it easier.