Abstract Algebra, Spring 2007,
Midterm Exam Study Guide
The midterm exam with be Thursday, March 1.
It will cover chapters 1 and 2 of Landin, with the majority
of the problems coming from chapter 2.
- About 40-60% of the exam will be closed book, closed note. This
potion of the exam will ask for basic definitions, theorems and
examples, and possible some true false statements.
- You should know the
following definitions: equivalence relation, group, abelian group,
cyclic group, order of a group, order of an element, subgroup,
permutation, symmetric group (on a finite set), orbit, cycle, alternating group,
coset, normal subgroup and factor group.
-
You should know the examples
of the dihedral group, the Klein 4 group and the cyclic group Z_4.
- You should know the statements of the following theorems from Chapter
2: Theorem 1-page 59, Theorem 9-page 70, Theorem 11-page 72, Theorem
14-page 78, Theorem 16-page 80, Theorem 20-page 89, and Lagrange's
Theorem-page 110. You need not remember the Theorem number, and the closed
book portion of the exam will not ask for the proofs.
- The other 40-60% of the exam will be open
book, and you can use three pages of notes that you wrote
yourself. Many of the problems on this portion will be chosen from the
suggested problem, or be very similar to the suggested problems. The
list of suggested problem can be found here
and it is recommended that you review them to study for the exam
and possible include some of them in the notes you bring to the exam.