Math 3321 Review Test #1 Fall 2005

Dr. Cordero

- Give the
following definitions:
- Mapping (include the definition of domain, codomain, image)
- Onto mapping
- One-to-one mapping
- Composition of mappings
- Inverse of a mapping
- Invertible mapping

- State and prove Theorem 2.1.
- State and prove Theorem 2.2.
- Complete the following definitions:

- An
__operation__on a set S is ..... - A set S is
__closed__with respect to an operation if …. - An operation
on a set S is
__associative__if… - An operation
on a set S is
__commutative__if … - An element
is an
__identity__for an operation on S if … -
An element
is an inverse for

- State and prove Theorem 4.1.
- Give the
following definitions:
- Permutation
- Permutation group
- Abelian group

- State and prove Theorem 6.1.
- State and prove Theorem 6.2.
- State and prove Theorem 6.3.
- Give the
definition of
__subgroup__. - State and prove Lemma 7.1.
- State and prove Theorem 7.1.
- State as a theorem Problem 7.22. Prove your theorem.