Abstract Algebra: Let G be a finite group. (1) If |G| is even, show that G has an odd number of elements of order 2. (2) If G is abelian, we compute the sum of the elements of the group (where group multiplication is written as addition).
Includes course on Group Theory (problems and solutions at website) and Ring Theory, and Field Theory. For Prerequisites on proofs and sets, see the Math Major Basics course.