CS-235. Problem Set 1

Due Thursday Jan. 25

 

In all the problem sets "Ex. C.N" or simply "C.N" stands for the Exercise from Shoup's book, from Chapter C, number N (in the book they are numbered as "C.N" as well).

  1. subscribe to csmail
  2. Ex. 1.1
  3. extra credit: Ex. 1.5
  4. Prove all the properties listed in Theorem 8.3 for a group (interpreting "+" as the group operation and "-" as the inverse). The commutativity is used only in (iii) and (viii) - restate (iii) in a way that does not require the group to be abelian (for all, except (viii) prove the properties for any groups - abelian or not)
  5. Ex. 8.2
  6. For any groups G1 and G2, prove that  G1 x G2 is a group.
  7. Ex. 8.4