Here are the features of an advanced graduate mathematics course:

  • 24 hours of optional lectures over the course of the term;
  • No homework, labs, guided assignments, quizzes, tests, previous year exams, or sample solutions;
  • A concise syllabus;
  • A list of recommended reading with about 5 items, with titles such as a Harvard University Press textbook;
  • The final exam lasts three hours and consists of several problems with sub-items.

What would be an advisable way to properly prepare for the exam?

  • What is the course topic? – Ryan Sep 29 '14 at 19:42
  • For example, "Non-smooth differential geometry". – Jake Sep 29 '14 at 19:50
  • The course did not begin yet, but I assume that problems will be on topics discussed in lectures, like usually. There might be some slightly more specific information once the course begins. – Jake Sep 29 '14 at 19:52
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    Remember that you can, and in this case probably should, assign YOURSELF some homework to make sure you understand and can work with the material. – keshlam Sep 29 '14 at 21:18
  • Try to find students who've taken similar classes from this professor before. – mkennedy Sep 29 '14 at 21:23

Hopefully you went to lecture - in my experience, in courses like this, the best you can hope for is that the professor draws questions directly from the lectures notes/questions that he raised during lecture. You can attempt to read the books, but there's probably too much material there. Focus on the lectures notes, and hope the prof is just trying to test "how smart you are", i.e., just doesn't give you a bunch of hard questions tangentially related to any material discussed in class.

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In my experience, a study method in this case would include the following

  • Be present at all lectures if possible.
  • It is especially important to be present at the first and last lectures, where key information about the course and the exam is likely to be conveyed.
  • A good idea in such a case is to record the lectures in audio or audio and video format, to have a reference to every detail; an alternative would be to write everything down verbatim.
  • Read the textbook, if the course has one, or at least the one or two of the items from the reading list, cross-referencing the material with the syllabus. Some relevant material may be skipped with careful discretion without substantial decrease in quality of exam preparation.
  • Make a notebook, which summarizes all important items from the lectures and the literature, such as all major theorems, formulas, concepts, and other items that can be expected on exam.
  • Find problem sets, which fit well the course syllabus. For example, those can be end-of-section problems in the items from the reading list or problem sets from a similar course offered elsewhere. Also, students that took the same course before might still have exam problem statements.
  • As you work through lecture notes, reading list, problem statements, and problem solutions, highlight and annotate the items of relevance to the exam (to the extent of that being possible), so you can quickly go over it later and recall auxiliary information that is not in the text.
  • Add all concepts and patterns from problem solutions, as well as, preferably, all concepts and patters from the relevant material in the reading list, to the notebook.
  • Ask the instructor if there are any questions in regards to preparation for the exam.
  • Before the exam, go over the lecture notes, reading list items, and especially the notebook. In particular, reread the entire notebook several times the day before the exam and several times about one hour before the exam.
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