By extending the familiar concepts of arithmetic, this course introduces abstract algebraic structures. Topics include an introduction to number theory; group theory, including the classification of all finite abelian groups; rings, integral domains, and fields.
- Be able to write well-structured and logically correct mathematical proofs.
- Understand divisibility in the context of the integers and modular arithmetic.
- Understand the basic properties of groups and rings.
- Understand the role of functions in abstract algebra including the concepts of homomorphism and isomorphism.
- Understand the structure of finite abelian groups.
- Be able to read and understand mathematical proofs.