Review of Abstract Algebra: An Introduction by Thomas W. Hungerford
Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It is a fascinating and challenging subject that has many applications in cryptography, coding theory, number theory, geometry, and physics. However, learning abstract algebra can also be daunting for students who are not familiar with its concepts and methods.
One of the books that aims to introduce abstract algebra to undergraduate students is Abstract Algebra: An Introduction by Thomas W. Hungerford. This book was first published in 1990 and has been revised several times since then. The latest edition, the third one, was published in 2014 by Cengage Learning. It contains 16 chapters and covers topics such as integers, polynomials, rings, fields, groups, factorization, Galois theory, Sylow theorems, and applications.
What sets this book apart from other textbooks on abstract algebra is its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. The book also offers a groups first option that allows instructors to cover groups before rings if they prefer.
Abstract Algebra An Introduction 3rd Edition 2014 PDFAbstract Algebra An Introduction 3rd 39
The book is written in a clear and engaging style that makes abstract algebra accessible and interesting to students. The author provides many examples, exercises, and historical notes throughout the book to illustrate and reinforce the concepts and results. The exercises range from routine computations to challenging problems that require creativity and insight. The book also includes appendices that review some prerequisite topics such as logic, set theory, functions, matrices, and complex numbers.
In conclusion, Abstract Algebra: An Introduction by Thomas W. Hungerford is a well-written and well-organized textbook that introduces abstract algebra to undergraduate students in a thematic and pedagogical way. It covers the core topics of abstract algebra as well as some advanced topics and applications. It is suitable for a one- or two-semester course on abstract algebra and can be used as a reference for further study or research.