MATH 3319 - Abstract Algebra I

Description

This course introduces the fundamental structures and concepts of abstract algebra, with a focus on group theory, and provides an introduction to rings and fields. Topics include classification of groups, the Isomorphism Theorems, Lagrange’s Theorem, and applications from number theory. Proof-writing and problem-solving are integral components of the course.

Learning Objectives

• Identify group theoretic concepts, such as subgroups, cyclic groups, cosets, normal subgroups, quotient groups, direct products, and homomorphisms.
• Apply theorems and techniques of group theory, including classification of small-order groups, the Isomorphism Theorems, and Lagrange’s Theorem.
• Demonstrate a basic understanding of other abstract algebraic structures, including rings and fields.
• Develop coherent mathematical arguments using direct proofs, proofs by contradiction, and other standard proof techniques.