
Oral exams
On this page, I collect some advise for the preparation of
oral exams and state my expectations.
Preparation
You should carefully go through the lecture notes (if available),
your notes taken during the lectures and a textbook. This important step
has to be accompanied by other types of learning:
 Talk about mathematics, in particular with your fellow students!
Try to imitate an oral exam with your fellow students by asking
each other questions about the lecture.
 Use the index of books or lecture notes! For any entry
you should be able to give a precise definition. You should also be able
to relate the entry to an important proposition. You can use the index to
find good questions you can ask to yourself.
 Go through the problem sets for the lecture. Read all problems,
if possible aloud! Check whether
 1) you have understood all mathematical notions appearing in the
problem and whether you can give their definitions.
 2) you have understood the problem: look at examples, drop
a prerequisite and try to find a counterexample. Finding an
example or a counterexample is a crucial way of learning!
 3) whether you remember the important idea, the most important
propostion that entered into the solution of the problem!
It is fine, if you still have the time to solve the problem
a second time. But never forget step 1)3)!
The exam
 Usually, there are 5 minutes of exam per weekly hour (SWS) of
lecture. Twenty minutes
are a rather short time to get a fair appreciation of your abilities and
knowledge.
There is no reason to worry, if an exam should take longer.
 The subject of the exam is, as a rule, the full collection of
subjects of the lecture and the problem classes accompanying the
lectures.
 At the beginning of the exam, you can suggest two or three
theorems or subchapters as starting points. The mathematical content of these
suggestions should be reasonably disjoint. Do not expect me
to ask you to reproduce the proof of the theorem you suggested.
You should rather have well understood the theorem itself:
the notions entering in it, its consequences, applications, examples or
counterexamples.

My emphasis is on testing your understanding, not on factual knowledge.
If it becomes evident that you have done your best to really understand
the mathematical content, this is more important than having been able
to reproduce certain proofs by heart.
 In general, there is no need for individual advise before an oral
exam.

