Discovering Abstract Algebra

ISBN-13: 9781470464424 / Miękka / 2021 / 199 str.

Jr John K. Osoinach

Spis treści

• Group theory: Introduction
• Binary operations
• Groups
• Subgroups and generating sets
• Applications of subgroups
• Types of groups: Quotient groups
• Cyclic groups
• Direct products
• The isomorphism theorems
• The symmetric groups
• Alternating groups
• Ring theory: Rings
• Commutative rings
• Fields
• Quotient rings
• Linear algebra: Vector spaces
• Linear transformations
• Field theory: Extension fields
• Algebraic extensions
• Intermediate group theory: Group actions
• The Sylow theorems
• Appendices: Relations and functions
• Matrices
• Complex numbers
• Index