Elements of Modern Algebra

This is definitely one of my best math books. The main feature of this book is that the readers feel very easy to follow the provided concepts and understand what is important. I really don't know any other book as good as this one. Probably only David C. Lay's "Linear Algebra and Its Applications" can compete with this one. I truly recommend anyone who studies modern algebra to take a look at this. Good luck!

It is surely one of the books I most enjoyed!! But its pricey, thats why a lot of colleges (or professors) try to avoid it. The book has eight chapters: 1) Fundamentals 2) The integers 3) Groups 4) More on Groups 5) Rings, Integral domains, and fields 6) More on rings 7) Real and Complex Numbers 8) Ploynomials. Definitions and Theorems stand out in Boxes, then later comes the examples!! (Plz Mathematicians who write books, just take a look here, see how nicely a book can be written, then go for the challenge). one of the good things in this book, is that it does not assume you took a class in number theory before, so it introduces in the first two chapters everything (from a typical number theory class) that you would need in modern algebra class. (that might be a drawback for a student who took number theory class, and his professor is determined to start from the first chapter in this book). other than the definitions and theorems stand out clearly, The author give examples on how that theorem can be used!! and The examples sometimes are really good!! What's best in this book, are the problems after each chapter, they rank from direct applications to theorems, to CHallenging problems! (at least challenging for me). But note that some of the problems depend on each other! so if ur stuck on one problem, that means you might need to use a result from an earlier problem in the same chapter. its a drawback that the author does not say "use problem ... to solve this one", I think they assume that anyone solving the problems, is solving all of them in sequence, which what students SHOULD do. There is no way you can get a good grasp on the material in this book, unless you are a genius, or you solve ALL the problems after each chapter (at least a very good amount of them). I found best thing to do is try solving them in sequence, if you dont have time to solve all of them, then skip the ones that you REALLY think you can solve, and this way you can use the result later on. I would recommend this book to anyone interested in modern (abstract) algebra! But I think a pre-requisite to self-study in this book is exposition to how to write proofs rigorously. (well sure thats the pre-requisite for any math course, but usually this subject is one of the first subjects studied in upper level math courses, and you better take another course that exposes you to how to write proofs, if your buying this book for self-study).

I thoroughly enjoyed my modern algebra class, with an excellent professor and this excellent book. The book is very clearly written, and the concepts of sets, groups, rings, fields, and number systems are explained with detail. This is especially important since my summer research in number theory requires an understanding of these algebraic structures.

I found the ideas in this book to be very accesible to the student with little mathematics experience (as I have). It is very straight foward, contains illuminating example problems, and even has an application section at the end of each chapter. Many abstract algebra books assume that you can prove anything. However, Gilbert's book focuses on the techniques of learning how to prove.