Discovering abstract algebra
Author(s)
Bibliographic Information
Discovering abstract algebra
（AMS/MAA textbooks, vol. 67）
American Mathematical Society, c2021
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Note
Includes index
Description and Table of Contents
Description
Discovering Abstract Algebra takes an Inquiry-Based Learning approach to the subject, leading students to discover for themselves its main themes and techniques. Concepts are introduced conversationally through extensive examples and student investigation before being formally defined. Students will develop skills in carefully making statements and writing proofs, while they simultaneously build a sense of ownership over the ideas and results. The book has been extensively tested and reinforced at points of common student misunderstanding or confusion, and includes a wealth of exercises at a variety of levels. The contents were deliberately organized to follow the recommendations of the MAA's 2015 Curriculum Guide. The book is ideal for a one- or two-semester course in abstract algebra, and will prepare students well for graduate-level study in algebra.
Table of Contents
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
by "Nielsen BookData"