An Invitation to Abstract Algebra

Abstract algebra is a profound and useful field that is part of the shared language of many areas, both within and outside of mathematics. This book takes a rigorous approach and expects the reader to understand and create proofs and examples. It follows a single arc, starting from humble beginnings with arithmetic and high-school algebra and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we can represent the roots of polynomials. The presentation includes exercises, a one, two, or three-term course, and a collection of projects. The authors aim to instill the desire to understand the material, encourage more discovery, and develop an appreciation of the subject for its own sake.

Format: Hardback
Length: 372 pages
Publication date: 22 December 2021
Publisher: Taylor & Francis Ltd

Abstract algebra is a captivating and profound field that spans various areas within and outside of mathematics. It is a beautiful and useful language that unites different disciplines. To embark on this journey of discovery, some prior experience with mathematical reasoning is beneficial. This text assumes a rigorous approach, requiring readers to understand and create proofs and examples throughout. The book follows a single arc, beginning with arithmetic and high-school algebra and gradually introducing abstract structures and concepts. It culminates with the achievements of Niels Henrik Abel and Evariste Galois in understanding the representation of polynomial roots.

The mathematically experienced reader may notice a bias towards commutative algebra and a fondness for number theory. The presentation includes various features to support and extend the material, such as exercises, multiple-term course options, motivating questions, and a collection of projects in Chapter 23. Abstract algebra is a deep subject that has the power to transform not only one's perspective on mathematics but also one's way of thinking. This book serves as a manual to a new way of thinking, aiming to instill a desire to understand the material, encourage further exploration, and develop a genuine appreciation for the subject.

Weight: 716g
Dimension: 239 x 243 x 31 (mm)
ISBN-13: 9780367748616