An Invitation to Abstract Algebra
Steven J. Rosenberg
 392 pages
 English
 ePUB (mobile friendly)
 Available on iOS & Android
An Invitation to Abstract Algebra
Steven J. Rosenberg
About This Book
Studying abstract algebra can be an adventure of aweinspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics.
To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout.
The book follows a single arc, starting from humble beginnings with arithmetic and highschool algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we canāand cannotārepresent the roots of polynomials.
The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory.
The presentation includes the following features:
 Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters.

 The text can be used for a one, two, or threeterm course.

 Each new topic is motivated with a question.

 A collection of projects appears in Chapter 23.

Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinksāperiod. This book is offered as a manual to a new way of thinking. The author's aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.