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 high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we can―and cannot―represent 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 three-term 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 thinks―period. 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.

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