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For graduate schools in STEM which take students with a Bachelor's degree (BS/BE/BTech etc.) and graduate them with an MS and/or PhD, what do they assume about the student's prerequisite knowledge when designing courses, their difficulty and overall dynamics?

My question is pointed towards knowledge and not what is on the student's transcripts. For instance, a student might have "Linear Algebra" on his transcripts but might not remember Singular Value Decomposition very well.

Do they:

  • assume that student knows all the courses he has taken very well and build from there? (What happens to people who had a BS in allied fields? For instance a student may have a BS in Pure Math but enrol for a MS/PhD in Computational Math with little idea about a "compiler".)
  • assume he knows nothing and take him to proficiency?
  • anything in between?
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    This really varies among different universities, even in the same field. The assumptions for computer science PhD students at MIT or Berkeley are very different from the assumptions for computer science PhD students at the University of Southern North Dakota at Hoople. – JeffE Jun 24 '12 at 12:51
  • @JeffE, in that case, I'll direct my question to the Top 3 of the field. I assume there won't be much deviation within them? – user107 Jun 24 '12 at 13:55
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I agree with @aeismail's and @dmckee's answers, but let me add a different spin:

Students are admitted to strong PhD programs not on the basis of how much or what they know, but rather on their potential for successful research. Every program admits students from all over the world, who may or may not have undergraduate degrees in exactly the same field. Beyond a few fundamental concepts, it is not reasonable to assume that incoming graduate students have any specific prior knowledge.

That said, most courses for PhD students are generally taught as if the students have a strong undergraduate background in the same field. The definition of "strong undergraduate background" depends strongly on the graduate program; the expectations at the top PhD programs are generally extremely high. More importantly, PhD students in top departments are expected to have the intellectual maturity to recognize and correct weaknesses in their background, even if the missing material is not normally covered in a strong undergraduate program.

Also: Courses are arguably the least important part of any PhD program.

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    +1 Students are expected in my department to bone up on what they need - including reading up on or retaking classes that they've technically "done" but will be needing to use heavily. – Fomite Jun 25 '12 at 8:57
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    In my experience in chemistry, a lot of PhD programs give first year students exams to check their knowledge and see where they might need remedial classes. – scientifics Jun 25 '12 at 14:59
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They are coming to grad school, not some hand-holding, jolly the kids along, summer program.

It is assumed that if students arrive with a deficiency they will take the necessary remedial classes (often that means getting in with the upper-division undergrads) and if you have forgotten something they will do the necessary boning up.

They will be boning up on things from time to time for the rest of their lives, after all. Might as well get in some practice in school.

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In my experience it is not uncommon for first year grad classes to share a syllabus (and lectures) with an undergraduate class. The grad class often has some additional assignments (e.g., an extra or longer paper or additional problems in homework assignments).

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This is a very difficult question to answer, since there are so many disciplines and so many programs at so many universities, all of which have their own rules.

But in general, the standard master's program (or coursework phase of a doctoral program) is designed to take someone who has a bachelor's degree in the same field and bring them up to a level of competence sufficient to pursue graduate-level research in that field. Very little allowances, if any, are made for people coming from other disciplines and programs, and they're certainly not designed for someone starting with no knowledge whatsoever.

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