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 relative to an operation on S if ….
- 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.