Practice exercises
13 fevereiro 2022, 13:02 • Pedro Resende
A list of practice exercises for the exam (shaped like a huge exam), many of them taken from Dummit&Foote, can be found here.
Note that (as stated in the beginning of the "fake exam"), the list of exercises does not necessarily cover all the material which may appear in tomorrow's exam, but it is nevertheless useful as preparation for the exam.
For instance, someone asked me whether questions about categories will appear in the exam. The answer is that some categorical concepts will be necessary even if no specific questions solely about categories exist. (For instance, in the "fake exam" there is a question about the endomorphism ring of a direct sum which needs the properties of the direct sum of modules both as a product and a coproduct).
Another question I received was about semisimple modules and representations. A bit of this, too, will appear in the exam.