Customer Reviews

Undergraduate Algebra (Undergraduate Texts in Mathematics)

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I didn't enjoy this book at all. The author, as he states in the preface, has tried to strike a balance between rigour and brevity, while trying to set a standard for the American undergraduate algebra curriculum. The intentions are admirable; however, he doesn't quite pull it off. Most of the important topics are presented either in the text or in the problems. For that matter, they're well chosen, too. But quite often the presentation is either too brief, unclear, or devoid of motivation. Some definitions are ambiguous or imprecise, while the notation is sometimes clumsy. The only redeeming feature is the choice of problems. They vary in difficulty from section to section, but on an average are excellent(a factor that adds to their difficulty is that the material in the text is so skimpy). On the whole, I don't know what purpose this book serves. The average student is better off using Fraleigh or Gallian (or any of the host of easier books avalailable), while Herstein still has much to offer to the motivated one. Jacobson and Cohn(which I used a lot while taking my first Algebra course) are always available as outstanding references.

The book provides an introduction to abstract algebra for undergraduate students. It covers basic topics in the theory of groups, rings, fields, polynomials, vectors and modules.

The book is terse and succinct. It provides very few examples to illustrate the various definitions and theorems. The examples are sorely missing since it is probably the first encounter with abstract mathematical formalism for most students using this book.

The author does not provide motivations for most of the topics he presents. Many of the aforementioned topics are of use in physics, linear algebra and applied math, yet the author fails to mention the relevance of abstract algebra to these fields. Considering the fact that not all students using this book are pure math majors, this may leave many students asking "What is it good for?" too often.

The book contains many excellent exercises varying from the trivial to the highly challenging. However, no solutions are provided and no solutions manual is available. This makes the book highly unsuitable for self-study.

The major strength of the book is its rigor. The author covers many topics not covered by other textbooks and progresses very meticulously towards more complicated topics. He thus builds a strong foundation for future classes in abstract mathematics. For pure math students, the book is a valuable snapshot of how advanced pure math textbooks look like.

For other students looking for an introductory textbook on abstract algebra, "Abstract Algebra: An Introduction" by Thomas W. Hungerford is recommended. It provides a clearer presentation of the material and is better suitable for the beginning student.

Like all Lang books on algebra, everything is very clear. The book goes through group, ring, modules, field, vector spaces, Galois theory andsome set theory including the Axiom of Choice. It does take some work and time to get everything, especially if you are getting acquainted with the topics for the first time. However, a motivated reader can certainly work through the book by himself. The only complaint I have is that the book often does not explain the motivation much.

The title is quite misleading. It sounds innocuous but conceals some pretty neat stuff. This book is an introduction into modern algebra that starts with group theory and continues into Galois theory. It is terse at times but contains all the essentials.

This text should be required reading for all Computer Science majors who have an interest in cryptography or cryptanalysis.