The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Collomb on Sep 22, I have been looking for a book to review some algebra I studied over 20 years ago, and after comparing hundreds of books yes literally! I am glad I finally discovered this one. Why is this book so great? It covers abstract algebra from basics to Galois theory including solvability by radicals, so you should not need any other book to cover the basics before Masters level 2. The book does not assume any prerequisite and is easy to follow even if you did not touch abstract Algebra for a while 3.
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The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Customer Book Reviews Perfect, no The book contains 33 chapters, of which the first roughly 22 make up the core of a two semester undergraduate algebra course covering groups, rings, and fields.
Gallian is great at providing examples, and gives definitions and theorems with very clear and concise language. For the most part, he tends to try to use standard terminology and provides plenty of examples and diagrams to aid students with the learning. The material presented in these chapters demonstrate the true beauty of abstract algebra, and while it is very unlikely that a traditional course could ever include all of these chapters as part of the core material, these chapters provide great opportunities for student projects, promoting student interest in research, or even a "third" semester of special topics in abstract algebra for motivated undergraduates.
The book has some very nice exercises, including some which are more or less standard, and some which present material at a much more advanced level. There is no shortage of exercises either.
Each chapter provides anywhere from or so exercises representing all levels, as well as additional "supplemental" exercises every few chapters. Hints and selected solutions are provided at the end of the textbook for odd numbered exercises, which I would strongly advise not turning to until you believe that you fully understand the material at hand and simply want to check your work.
However, solutions and hints are a very excellent key to ensuring that you understand the material. Gallian tends to give very brief hints which can motivate a complete proof for students making a serious attempt to know the information, but still requires the student to develop a complete proof without being completely coddled.
Of course, for even-numbered exercises, sometimes which are "paired" with the preceding exercises, there are no solutions or hints, but the flow follows along naturally. Some serious mathematicians are put off by the inclusion of history discussions in the text, along with the sprinkling of various pop-culture quotes at different places, and while some textbooks do get a little silly over these things, none of this tends to distract from the ability to learn the material.
One unfortunate aspect about this book is that the popularity of it has turned it in to one of those books where the publisher keeps cranking out new editions of the book at a pace that is completely unnecessary. It is great when a new edition is published and contains significant and substantial updates, but the updates to this book have really not been necessary for the past few editions.
But with that being said, most of the more recent older editions of the book are sufficient for the material, you just have to be careful with the numbering of exercises. This book is one of the standards for an upper-level undergraduate abstract algebra course and hopefully it will remain that way until somebody comes up with something a little bit better.
In the current era, though, it provides an excellent and readable text for students which is capable of further motivating interest in the pardon the pun field of abstract algebra.
By Kippy on May 26, This is a good book. It starts with a clear example of a group and develops a wonderul theory of groups and rings. There are exercises that are easy enough to where you get a good understanding of the material and others hard enough to present a nice challenge.
The book presents the material well. It also gives us a nice history of major figures in abstract algebra. Good, but not great By Daniel Miller on Aug 03, Abstract algebra is an inherently abstract, formal, non-intuitive subject, and while it can be made less difficult, it cannot be made easy.
The book shies away from precise definitions, formal proofs, and that elusive thing known as "mathematical maturity. It is really well organized, easy to follow along, but still taught in pretty good depth. I recommend it! Excellent: very easy to read By M. This book is very easy to read and covers a one year undergraduate course in algebra.
If you want to learn the basics about groups, rings and fields, this book will teach you all you need to know as an undergraduate. What this book is not: maths for grad students. It comes with lots of exercises do them!
Clear exposition of the material By A on Dec 15, Good book. Easy to understand, gentle enough as a first text but advanced enough to make you work. This text was required for an introductory abstract algebra course I took. Another user complained about the difficulty of the book and the fact that some of the proofs are not self contained. In particular he mentioned caleys theorem as an example. I had no problem competing the extra steps required not listed in the theorem when I read it.
Also, he mentioned that the exercises were difficult. And most surprisingly, he claims that professors ask too much from students generally. If anything most schools practically hand out undergraduate math degrees. Only slightly different cover, other than that it is By Sbana69 on Aug 10, Only slightly different cover, other than that it is the same exazct book as I had at the bookstore for less than half the price. Perfect for newbies like me! This is the most interesting introductory book for beginners like me.
Thank you for the Abstract Algebra baby food. Yum Yum. OK book to go with a good instructor By Allison S. I felt that this book worked OK because of the quality of my professor, but I do not feel it is a good book if you want to teach yourself and are new to the concepts in it. There are many places where the proof will say "clearly" or another similar phrase when it is most definitely not clear to any one but the author. All in all I am not selling back my book because I feel that it has some good concepts in it, but I am also hanging onto my notes from class in order to interpret the book at a later date if need be.
By Charles Saunders on Oct 29, If you are looking for a rigorous step in abstract algebra this is probably not the book you want. If you are taking a fairly elementary one semester undergrad course and will never see this subject again, it is great. The proofs are weak compare to Hungerford - the intro NOT the grad text - or Dummit and Foote - which, admittedly is more advanced, but not that much. This subject like topology and real analysis tends to depend on where you are and what you want.
Great textbook By M. Ortiz on Sep 27, I am a math major in my junior year, and this is the first textbook I have actually enjoyed reading. It is full of useful examples and it is clearly written and structured so that it is very easy to follow.
The best algebra book ever! I attempted this course three semesters ago and it was my first proofing course. I could follow in class but I could not do the proofs and I dropped the course. I took the course again three semesters later after a course on how to read and write proofs and after about five other proof based courses and I loved it!
What a difference a little math maturity makes! I have one more semester before I graduate and this is going down as my favorite text and course.
If you have some proof experience under your belt, you will do fine in this course with this text. Gallian does expect the reader to fill in some of the details on their own.
First of all, this book is thankfully small. Actually, quite a bit smaller than most mathematics textbooks I have been carrying around these years. There are chapters and there are sections, like elements latter in sets former ; each section outlining some key concepts or theorems.
The problems for each section do correlate closely to the course concepts. The author begins with a review of the foundations of mathematics and some property of sets and then begins with an introduction to groups before moving to a more detailed look. One thing you will not easily learn from the book, however, is that algebraic proofs rely more on a bag of clever, annoying tricks than some fundamental comprehension of the subject matter.
Overall, the book construction is fairly study, the material inside is comprehensive and fairly digestible, particularly with the subject matter broken down and explained as Gallian does. And, there you have it. Good introductory book. By David Copeland on Jan 03, I bought this book as a required text for a upper level undergraduate course in Abstract Algebra.
I found the book to be a very good source for examples and problems. Many of the problems have solutions in the back which is a good feature. The book is thourough, rigorous, and at the same time easy to read. The ideas and concepts are presented so naturally that you almost forget you are reading a mathematics text. Five Stars By Terence R. Shore on Sep 10, I bought the book to learn more about finite fields that are used in cryptography.
Hardly any concrete examples and is just so scattered brained. Also, every chapter has tons of exercises that the book gives no clear insight on how to solve. Well done. I found Gallian to be the most helpful. Gallian offers a readable text with clearly written proofs and proof methodologies that were useful since abstract algebra requires skill in proof writing.
This particular edition is in a Hardcover format. It was published by Brooks Cole and has a total of pages in the book. To buy this book at the lowest price, Click Here. Similar Books.
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