Midterm topics: There will be four problems, each worth 5 points. Two problems will be theoretic (asking to prove something) and two will be computational (sort of -- for instance asking to determine the splitting field of a polynomial).  One should also expect topics on finite fields and cyclotomic extensions. The questions will be reasonable taking into account that you have only 50 minutes for the midterm. I finally decided not to include problems on Galois groups since we did not have enough time to work on them.