Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) by Robert B. Ash (PDF)

Description

Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible.The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐At first I wasn’t sure about whether or not to buy this textbook, but I’m really happy that I did. The concepts are explained very well, and it’s very helpful that all the answers to the problems are included in the textbook.

⭐This is a well-organized and well-explained treatment.

⭐Good job.

⭐This is the book version of a series of lecture notes on abstract algebra written by the author and still available on his web page. However, given the price (it’s a Dover book…) it’s worth buying just to avoid that thick pile of sheets lying around. The best thing about this book is that it avoids formalism whenever it can without sacrificing rigor. Many theorems are “proved” by means of an example of a general case. In this way, the reader gets the intuition behind the result without having to deal with the abstract and sometimes artificial constructs of a rigorous proof. In any case, supplying that rigorous proof can be seen as an extra exercise (or you can look it up elsewhere!). In other words, it’s a great book to learn the ideas behind the theorems dealing with groups, rings, modules and fields.The second part of the book deals with commutative algebra, algebraic number theory, algebraic geometry and homological algebra – areas where it’s very hard to find intuitive explanations in the literature, since books on those subjects tend to assume (quite reasonably) the reader has a solid background in abstract algebra. Unfortunately, that means that examples and intuitive explanations are drastically reduced, sometimes to none at all. That makes this book even more attractive.In any event, after you get the intuition, it will be much easier to to tackle the more rigorous approaches of Dummit & Foote or Hungerford (I don’t know Lang’s book but I’m told it’s much dryer than these two).Or you can start your study of algebra with any of these more traditional books and use Ash’s as a supplement. If a theorem or its proof proof seems opaque, look it up on Ash. Chances are his explanation will clarify things.

⭐This textbook is suitable for an introduction to abstract algebra: it covers the traditional materials such as groups, rings, modules and fields, plus a flavor of commutative algebra, non commutative ring theory, category theory, and homological algebra.The treatment is very detailed and down to earth: in fact, the author does avoid, as he himself claims in the preface, to use the commonly found expression “it is easy to see”.I think this textbook can (and will) replace the classical ones by Bifkoff-MacLane and Fraleigh.If you need a bit advanced treatment, Dummit-Foote may be the next step.But by the time you finish Ash, you may want to read textbooks on specific subjects instead, especially the ones that are given a flavor by him.

⭐I am currently taking a graduate Algebra 2 course. This book has served as an excellent supplement to the lectures! Proofs that we would often skip in class were done in this fine book. The author explains concepts in an easy to understand, casual (yet not too casual) manner that I really enjoy. Also, the exercises have solutions outlined in the back which is always nice.

⭐Just learnt that Professor Ash died in a car accident last month. May God bless him.This book really helps me a lot, as a beginner I find this book to be more “friendly” than the text by Artin and Dummit. I believe that most people would find the proof elegant and understandable. And one thing I really like about this book is that the execrises come with solutions. If you want to learn abstract algebra by yourself, this could be your perfect start.

⭐I used this book as a reference resource for an advanced algebra course. At times, wording of key concepts was a little long. This book is a good complementary reference to Joseph Gallian’s Contemporary Algebra book.

⭐Not many textbooks have solutions to ALL problems. Well done Robert Ash!!

Keywords

Free Download Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) in PDF format
Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) PDF Free Download
Download Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) 2006 PDF Free
Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) 2006 PDF Free Download
Download Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) PDF
Free Download Ebook Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics)