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FWIW (and I know you're not making this claim) I don't believe Math 55 is a good example of how mathematics should be taught at large, nor do I think calling it

FWIW (and I know you're not making this claim) I don't believe Math 55 is a good example of how mathematics should be taught at large, nor do I think calling it an intro class accurately conveys what it is. It's effectively the compression of an entire undergraduate degree into a single freshman course. I say "effectively" because the material covered depends heavily on who's teaching it, but certainly anyone coming out of Math 55 can pick up any undergraduate math content trivially. For example, undergraduates who have taken it are generally explicitly prohibited in course descriptions from taking further undergraduate mathematics classes (because it would be free credit for retreading the same ground) and can only take graduate courses from then on out. It's strongly self-selecting and as a result can afford to cover a truly insane amount of ground. The overwhelming majority of people who take it drop out (the usual dropout rate from people who take it in the first week is probably > 90%), but the people who stay almost all get As. And you will need to be almost entirely self-motivated because a lot (maybe most) of your waking hours will be thinking about math. There's a very small minority of students for whom this is an optimal way of learning. For most students this is the quickest way to make them run screaming away from mathematics even faster than they already do.

C-x_C-f 5y ago
> For example, undergraduates who have taken it are generally explicitly prohibited in course descriptions from taking further undergraduate mathematics classes (because it would be free credit for retreading the same ground) and can only take graduate courses from then on out. Not at all, you are only prohibited from taking "freshman courses"[1]—that's what 55 is supposed to cover (definitely not all of the undergrad math curriculum), though some professors go beyond that. Many students go on to take at least some undergrad courses, with those in the 140's range being mathematical logic gems with no real counterpart in the graduate department. [1]Students from Math 55 will have covered in 55 the material of Math 122 and Math 113. If you have taken 55, you should look first at Math 114, Math 123 and the Math 131-132 sequence. https://legacy-www.math.harvard.edu/pamphlets/courses.html https://legacy-www.math.harvard.edu/pamphlets/courses.html
- dwohnitmok 5y ago
  I wonder if the pamphlet's changed or I'm misremembering. I distinctly remember Math 123 and Math 114 both explicitly excluding Math 55 (It's also worth stating that Math 122 and Math 113 are definitely not freshman courses). But regardless I'd be very surprised to learn a Math 55 student took Math 114 or Math 123. I would also be surprised (although less so) to learn of a Math 55 student in the 130 series. The Math 140 series have only become more serious courses in the last 10 - 15 years or so IIRC. The 240 series was generally where to go for serious mathematical logic courses (and generally is where you would go after e.g. a first 140 series course in set theory anyways).

C-x_C-f 5y ago

> For example, undergraduates who have taken it are generally explicitly prohibited in course descriptions from taking further undergraduate mathematics classes (because it would be free credit for retreading the same ground) and can only take graduate courses from then on out. Not at all, you are only prohibited from taking "freshman courses"[1]—that's what 55 is supposed to cover (definitely not all of the undergrad math curriculum), though some professors go beyond that. Many students go on to take at least some undergrad courses, with those in the 140's range being mathematical logic gems with no real counterpart in the graduate department. [1]Students from Math 55 will have covered in 55 the material of Math 122 and Math 113. If you have taken 55, you should look first at Math 114, Math 123 and the Math 131-132 sequence. https://legacy-www.math.harvard.edu/pamphlets/courses.html https://legacy-www.math.harvard.edu/pamphlets/courses.html

dwohnitmok 5y ago
I wonder if the pamphlet's changed or I'm misremembering. I distinctly remember Math 123 and Math 114 both explicitly excluding Math 55 (It's also worth stating that Math 122 and Math 113 are definitely not freshman courses). But regardless I'd be very surprised to learn a Math 55 student took Math 114 or Math 123. I would also be surprised (although less so) to learn of a Math 55 student in the 130 series. The Math 140 series have only become more serious courses in the last 10 - 15 years or so IIRC. The 240 series was generally where to go for serious mathematical logic courses (and generally is where you would go after e.g. a first 140 series course in set theory anyways).