Modern Algebra

Rating:
Summary: After Calc math
Review: After finishing up the math at a local college, I was somewhat at a loss as to what I should study next. Fishing around I found that everyone would recommend algebra, but couldn't begin to point me to a book. If this is you, this is your book.

Rating:
Summary: Attractive & rigorous but probably best as a supplement.
Review: Hard reading at times but worth the money. Get Durbin's "Modern Algebra" if you can afford it. Despite what some other reviewers are saying the exercises alone validate buying the book. CONTENTS: ALGEBRAIC STRUCTURES (sets,isomorphism in general, groups, an embedding theorem), NEW STRUCTURES FROM OLD (equivalence relations, quotient structures, some isomorphism theorems), THE NATURAL NUMBERS, RINGS AND FIELDS, VECTOR SPACES, POLYNOMIALS, REAL AND COMPLEX NUMBERS (constructions), ALGEBRAIC EXTENSIONS OF FIELDS (Galois Theory), LINEAR OPERATORS, INNER PRODUCT SPACES (Spectral Theorem), AXIOM OF CHOICE.

Rating:
Summary: somewhat clear presentation...inappropriate exercises
Review: The text itself is reasonably good...i.e. what's presented is clear. However, there are two major problems.

1) The book goes for breadth and sacrifices depth. 2) Most of the exercises are inappropriate.

For example, one little section studies cyclic groups briefly, but the meat of it is presented in the exercises, such as the exercises requiring you to prove Sylow's theorems. How can a reader who's barely grasped the material from a few scant pages tackle such a complicated assignment.

this makes the book quite useless for self study, but it's kind of nice as a reference.

Rating:
Summary: teach yourself algebra
Review: This book has received much undue criticism from other reviewers. Yes, the book is too thick (should be two volumes) and a bit old. But consider this:

I've self-taught myself most of this book in the past year, while attending school full-time as a materials science major (a whole field known to shy away from mathematics).

This book is unbelievably affordable and covers most of the main topics of modern algebra (good enough for those of us who just want to learn basics).

The book is entirely self-contained, which helps a lot if you don't have the most extensive mathematics background.

If your discipline isn't math but you're tired of "learning," ie. skirting around mathematical topics, in your classes, check out this book.

Rating:
Summary: teach yourself algebra
Review: This is a reprint of the 1965 edition. This book was originally a two volume set. It's now a large 818-page, unwieldy paperback in the narrow format of Dover reprints. (Don't get me wrong I love Dover reprints, this one is just too thick for the format). The second half from page 512 on is all that is worth while anyway. This book is very pendantic in the worse "New Math" sense (circa 1960). Meaning it emphasizes arbitrary abstract axioms, lacks historic perspective, concrete examples and real world applications; and, much is left to the reader as exercises. This is a shame since Modern Algebra is rich in history and application. The pedantic pretensions don't stop there. The book uses the number theorem approach to proofs without mentioning their common names (Since history is completely absent, this isn't a surprise). This is NOT a standard reference today, if it ever was in the past. Memorizing the theorem numbers will do you no good in your coffee shop conversations. The book only gets interesting in it's latter half, it's too bad you have to lug the first 500 pages along for the ride. Adding insult to pedantry, the really interesting parts are left as exercises! That's ok if you're paying big bucks for a professor and a TA to help you along, but as a self-study book, it's down right annoying. If you're looking for an introduction, I'd recommend Herstein's Topics in Algebra or Birkoff & MacLane's Survey over this one. If you're looking for more advanced treatment, I'd recommend Van der Waerden's Modern Algebra or Jacobson's Lectures in Abstract Algebra. These come in multi-volume sets that making reading easier. I'm sure there are better current books on the subject, but I'm not familiar enough to make a recommendation. I can only dissuade you from purchasing this one as your only reference or an intro.

Rating:
Summary: Marginally worth while
Review: This is a reprint of the 1965 edition. This book was originally a two volume set. It's now a large 818-page, unwieldy paperback in the narrow format of Dover reprints. (Don't get me wrong I love Dover reprints, this one is just too thick for the format). The second half from page 512 on is all that is worth while anyway. This book is very pendantic in the worse "New Math" sense (circa 1960). Meaning it emphasizes arbitrary abstract axioms, lacks historic perspective, concrete examples and real world applications; and, much is left to the reader as exercises. This is a shame since Modern Algebra is rich in history and application. The pedantic pretensions don't stop there. The book uses the number theorem approach to proofs without mentioning their common names (Since history is completely absent, this isn't a surprise). This is NOT a standard reference today, if it ever was in the past. Memorizing the theorem numbers will do you no good in your coffee shop conversations. The book only gets interesting in it's latter half, it's too bad you have to lug the first 500 pages along for the ride. Adding insult to pedantry, the really interesting parts are left as exercises! That's ok if you're paying big bucks for a professor and a TA to help you along, but as a self-study book, it's down right annoying. If you're looking for an introduction, I'd recommend Herstein's Topics in Algebra or Birkoff & MacLane's Survey over this one. If you're looking for more advanced treatment, I'd recommend Van der Waerden's Modern Algebra or Jacobson's Lectures in Abstract Algebra. These come in multi-volume sets that making reading easier. I'm sure there are better current books on the subject, but I'm not familiar enough to make a recommendation. I can only dissuade you from purchasing this one as your only reference or an intro.

Rating:
Summary: Attractive & rigorous but probably best as a supplement.
Review: This is a summary that embraces most of the basic topics of the modern algebra. But we don't demand too much to a book that tries to make so much. In general, the book is a very good introduction to the lineal algebra if we take into account the relating chapters to the Vectorial Spaces, the Lineal Operators and The Spaces with Interior Product. The relating chapters to the Algebraic Structures, Rings and Fields constitute the basic introduction to the rest of the book and they are been in a very meticulous way, where each term is introduced in a very orderly and coherent form. The relating chapters to the natural Numbers and the Real Numbers and Complexes complete the work, with a very special care where they are presented each one of the numeric sets in such a form that leave satisfied to who wants a good introduction to these topics. Each one of these chapters requires of the content of the chapters of basic introduction that before mentioned. The chapter of the Polynomials is delicious, simple, and gives pleasure to read it. In the chapter Algebraic Extensions of Fields explains in a very pleasant way the theory of Galois. In this book many concepts watered along many volumes of books that not treat other diverse topics dedicated exclusively to the Modern algebra were gathered. The whole book this full with exercises (more than 1300 along the whole work) in that the concepts are applied introduced in each chapter, and also, many of those exercises not include concepts presented in the theory, and that they enrich more the work. This book is, in definitive, a well written, very orderly work, rich in content, and with abundant exercises that help us to the understanding of this topic. If you want a good book of Modern Algebra for Undergraduates, this the one of them.