> when i was in graduate school for mathematics, it indeed felt that i had been lied to in undergraduate school.
I'd be interested to hear more about that. Standard US undergraduate mathematics curriculums are aggressively non-"the whole truth", but they rarely lie. (Sometimes there'll be less attention than a professional mathematician might like on checking hypotheses, but, in my experience, they're always there for someone who cares to check.) What lies did you feel like you'd been told?
(I mean, of course, content lies. Implicit pedagogical lies like "what you see and do in undergraduate mathematics classes faithfully represents the graduate and research mathematics experience" are unfortunate, and won't go away as long as the audience for math courses is made up much more of people who want to apply it in other disciplines than people who want to be mathematicians, but I think they are of a different character.)
I'd be interested to hear more about that. Standard US undergraduate mathematics curriculums are aggressively non-"the whole truth", but they rarely lie. (Sometimes there'll be less attention than a professional mathematician might like on checking hypotheses, but, in my experience, they're always there for someone who cares to check.) What lies did you feel like you'd been told?
(I mean, of course, content lies. Implicit pedagogical lies like "what you see and do in undergraduate mathematics classes faithfully represents the graduate and research mathematics experience" are unfortunate, and won't go away as long as the audience for math courses is made up much more of people who want to apply it in other disciplines than people who want to be mathematicians, but I think they are of a different character.)