Group theory: course

Description

This is a one-semester course in modern algebra and groups.

Prerequisites

• Calculus 1-3,
• Linear algebra
• proofs.

Outline

• Review
  • Linear algebra
• Modular arithmetic
• Permutations
• Definition of group
• Homomorphisms of groups
• Subgroups
• Products of groups
• Quotients of groups
• Classification of abelian groups
• Rings and fields
• Transformation groups

• Group theory: test 1
• Group theory: test 2
• Group theory: final exam

Notes

Text:

• Contemporary Abstract Algebra by Gallian
• A First Course in Abstract Algebra Fraleigh. Chapters: 1. Groups and subgroups, 2. More groups and cosets, 3. Homomorphisms and factorgroups, 5. Introduction to rings and fields.

Further reading

• Introductory algebraic topology: course