Midterm Exam

Abstract Algebra

Winter 2005

Hunsicker

Definitions: Define all of the following terms. (5 points each)

1) Greatest common divisor

2) Well ordering principle

3) Group

4) The group Zn

5) Function, domain, range, image

6) Bjijective function

7) The group Sn

8) Cycle

Theorems to state (5 points each):

9) Euclidean algorithm

10) Disjoint cycle theorem

Theorems to (state and) prove (15 points each)

13) Properties of divisibility

14) Subgroup theorem

Proof techniques to explain (10 points each)

16) Proof by induction

17) Proof by contradiction