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gunnervi comments on Replace the Symbol with the Substance - Less Wrong
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I wonder what the takeup would be on a university that promised it would NOT give exams, NOT award certificates, and NOT even publically confirm you ever studied there. But in all other regards it would teach you through two degrees and a PhD, if you could manage the work.
Even I might go to a university like that, in the expectation that the other professors and students would be far enough above the norm to make it worth it. Though strictly private exams are important; they tell me how well I'm doing. And it would also need to not have some ridiculous system of course prerequisites, because I'm not going to waste that time. Also, why assume that this university is going to teach only to the PhD level?
Being currently subject to a system of ridiculous and often inaccurate course prerequisites, I think that the correct model is to list what concepts (depending on the school and department, listing texts that students are expected to be familiar with or courses they are expected to have taken may be appropriate) students are expected to know before taking the course in question - they can choose to ignore the prerequisites if they so desire.
The only reason I see for "hard" prerequisites (it is mandatory to take course A before course B) is safety courses (I don't know if this is ubiquitous, but at my university, there is a safety course that permits access to the student shop and (I think) is a prerequisite for all courses that require use of the machine shop - this is far more efficient than, say, every course that requires it taking time to give students safety training (as this would grow redundant for students taking large numbers of these courses)