Rating: 
Summary: OK intro for students who lack proper mathematical maturity.
Review: I took my first abstract algebra class at a university with a strong math program (thru a college release program my high school was offering). We used Gallian's text. The text offers a decent intro to this beautiful subject, but its strong applied flavor may be disagreeable to many mathematicians. Also, the treatment of algebra in this text can hardly be considered rigorous. The text does not suit my tastes, it should be used for mathematical physics classes (or some other field where applied abstract algebra is needed).I recommend two textbooks I checked out from the library to supplement my class (for a fuller, more rigorous treatment of algebra). These are 'Algebra' by Michael Artin, and 'Topics in Algebra' by I.N. Herstein.
Rating: 
Summary: Despite lack of rigor, best undergrad text available.
Review: I took the regular Abstract Algebra course at Purdue as a sophomore, and this book made me decide to switch majors from Physics into Mathematics. Gallian's treatment of algebra is NOT the most thorough. On the other hand, this book is a relatively gentle introduction to the topic, with plenty of good examples included. This would be a good book to base a 'gifted' Algebra course on. I would strongly suggest that very strong students supplement this with Thomas Hungerford's _Algebra_; similarly I recommend that first year graduate students get this book as a 'softer' perspective for when (not if ;)) they get lost. Profs should pick up this book as an example of how to write a palatible math book in the unfortunate academic climate we have today (although I wouldn't sacrifice rigor); teaching assistants should use this for anecdotal material to throw at students. I especially enjoyed the biographies of famous mathematicians and the background that Gallian provides on topics in Algebra (such as his description of the Twenty Five Years' War), which made this book quite pleasant even in the grueling moments.
Rating:
Summary: The most lucid text on Abstract Algebra that I have seen.
Review: I used this book as the textbook for an undergraduate course in Abstract Algebra. It is very concise, clear and informative. The coverage of topics is very comprehensive, covering all that is needed at this level. The book makes the material fascinating, compelling and easily understandable. The exercises at the end of each chapter are at the right level of difficulty and help to elucidate the subject matter. This book is the ideal starting point for anyone with an interest in Abstract Algebra. Highly reccommended.
Rating:
Summary: Excellent undergraduate abstract algebra textbook
Review: I used this book for my Abstract Algebra course at Whitman College. It is genuinely fun and interesting to read. It has many interesting quotes and biographical sketches. The problems are just the right difficultly to be challenging but not frustratingly hard. One interesting thing is that the problem sets include computer application questions. Our class did not use these sections, but some of the problems looked interesting. I found the text to be well organized and understandable. Numerous examples are included which help for understanding abstract concepts. Neither my friends nor I have noticed any typographical errors. Theorems and corollaries are shaded in a blue background for ease of reference. Every time new notation is introduced, possible ambiguities are discussed. Also, possible confusions about new concepts and common mixups are addressed. I have only taken one semester of algebra at the current time, so have only used the first half of this book. I feel that it is one of the best textbooks I have used for a mathematics class.
Rating:
Summary: Great Book!
Review: I'm in a 4th year group theory class and have found this book to be highly useful in learning my course material. It gives lots of proofs, lots of excercises with lots of theory and good explanations. I have no complaints!
Rating:
Summary: Assessment
Review: This book has been explicitly designed for the use of mentor and students at graduate and undergraduate level. This book presents comprehensive coverage starting from the fundamentals of mathematics to advanced algebra. The theories are explained with abundant examples and exercises which makes the concepts more clear and understandable. The author has exclusively ended the book by providing physical approach of algebra in physical sciences.
Rating:
Summary: Assessment
Review: This book has been explicitly designed for the use of mentor and students at graduate and undergraduate level. This book presents comprehensive coverage starting from the fundamentals of mathematics to advanced algebra. The theories are explained with abundant examples and exercises which makes the concepts more clear and understandable. The author has exclusively ended the book by providing physical approach of algebra in physical sciences.
Rating:
Summary: A pleasure for all who see the world in terms of math
Review: This book is more than a find --- it's a treasure chest. Gallian does more for the reader than just throwing a bunch of theory at them and laughing as the reader struggles to understand proofs and apply them himself; he provides a multitude of examples. And by a multitude, I don't mean three or four comprehensive examples per chapter: I mean three or four *per proof*. And often Gallian steps back a moment to discuss the proof or theorem he just outlaid in more conceptual terms, sometimes just as good as an example. The book is a delight, and absolutely perfect for the independent learner. Gallian gives a good background on integers, modular arithmetic, induction and the like in his chapter 0, and then eases his way into group theory in the next two chapters. He goes on to then concentrate on the most important forms of group the student will use, taking him through subgroups, cyclic groups, and permutation groups. Then he outlines some of the most important tools the reader will use when he's trying to deduce the properties and structure of a groups, like isomorphisms, cosets and Lagrange's Theorem, external and internal direct products, normal subgroups and factors groups, and homomorphisms. In the third part of the book, Gallian teaches rings. This section is set up much like the first section; he goes over the structure of rings themselves and then elaborates on tools which will help the mathematician to deduce structure and properties of rings more easily. Part four of the book, on fields, is set up much the same way. Part five of the book is on special topics: sylow theorems, simple groups, symmetry groups, crystollagraphics groups, galois theory, etc.. The most important feature of the book overall is its plethora of exercises and answers. Gallian averages about 45 exercises *per chapter,* and every four chapters or so there is another set of supplementary exercises covering the previous material. And there is a wonderful appendix in the back of the book which has the answers (some more detailed than others) to every other problem. In conclusion, this book is perfect for the independent learner, and a dream for a professor who seeks a textbook of ultimate clarity. This is the best textbook on advanced mathematics I have ever come across, accessible to a (bright) freshman in college.
Rating:
Summary: A pleasure for all who see the world in terms of math
Review: This book is more than a find --- it's a treasure chest. Gallian does more for the reader than just throwing a bunch of theory at them and laughing as the reader struggles to understand proofs and apply them himself; he provides a multitude of examples. And by a multitude, I don't mean three or four comprehensive examples per chapter: I mean three or four *per proof*. And often Gallian steps back a moment to discuss the proof or theorem he just outlaid in more conceptual terms, sometimes just as good as an example. The book is a delight, and absolutely perfect for the independent learner. Gallian gives a good background on integers, modular arithmetic, induction and the like in his chapter 0, and then eases his way into group theory in the next two chapters. He goes on to then concentrate on the most important forms of group the student will use, taking him through subgroups, cyclic groups, and permutation groups. Then he outlines some of the most important tools the reader will use when he's trying to deduce the properties and structure of a groups, like isomorphisms, cosets and Lagrange's Theorem, external and internal direct products, normal subgroups and factors groups, and homomorphisms. In the third part of the book, Gallian teaches rings. This section is set up much like the first section; he goes over the structure of rings themselves and then elaborates on tools which will help the mathematician to deduce structure and properties of rings more easily. Part four of the book, on fields, is set up much the same way. Part five of the book is on special topics: sylow theorems, simple groups, symmetry groups, crystollagraphics groups, galois theory, etc.. The most important feature of the book overall is its plethora of exercises and answers. Gallian averages about 45 exercises *per chapter,* and every four chapters or so there is another set of supplementary exercises covering the previous material. And there is a wonderful appendix in the back of the book which has the answers (some more detailed than others) to every other problem. In conclusion, this book is perfect for the independent learner, and a dream for a professor who seeks a textbook of ultimate clarity. This is the best textbook on advanced mathematics I have ever come across, accessible to a (bright) freshman in college.
Rating:
Summary: Wonderful Abstract Text
Review: This is possibly the most addictive Abstract Algebra book ever. Filled with a wonderful selection of problems, Gallian discusses many aspects of groups and rings in a way that is enjoyable to study. The love of mathematics that is shown in this book is reflected by how Gallian eloquently weaves principles of group and ring theory with beautifully selected INTRUIGING problems. I enjoyed this book more than any other math text I have had.
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