12 of 14 people found the following review helpful:
5.0 out of 5 stars
a classic, for better and for worse, March 23, 2006
A Kid's Review
mathematically, this book is first rate. I turn to it when stuck on a passage in hungerford. However, this book shows its age in certain respects - e.g. category theory is completely snubbed - hence the index doesn't square well with a lot of the current standard terminology.
Still, the fact that this book is in its seventh english printing says something about its value. It's like reading Dirac's principles of QM: sure, Griffiths is much easier, and exactly covers the standard undergrad subject matter -- but Dirac does it all in a third of the space, and with such brilliant clarity...
Bottom line: don't buy this as your first algebra book, because it's old-fashioned. The point of reading a textbook is to get you far enough out there that you can read the current literature and be done with textbooks. But, if you already own Dummit and Foote (for undergrad material, lots of hand-holding in tough parts) and Lang or Hungerford (or even Herstein) for the standard first-year grad course perspective, this will round out your algebra library nicely.
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4 of 4 people found the following review helpful:
5.0 out of 5 stars
The "Bible" of Abstract Algebra, August 25, 2009
There are millions of Christian books to explain God's Words, but the best book is still The Bible.
Isomorphically, this book is the "Bible" for Abstract Algebra, being the first textbook in the world (@1930) on axiomatic algebra, originated from the theory's "inventors" E. Artin and E. Noether's lectures, and compiled by their grand-master student Van der Waerden.
It was quite a long journey for me to find this book. I first ordered from Amazon.com's used book "Moderne Algebra", but realised it was in German upon receipt. Then I asked a friend from Beijing to search and he took 3 months to get the English Translation for me (Volume 1 and 2, 7th Edition @1966).
Agree this is not the first entry-level book for students with no prior knowledge. Although the book is very thin (I like holding a book curled in my palm while reading), most of the original definitions and confusions not explained in many other algebra textbooks are clarified here by the grand master.
For examples:
1. Why Normal Subgroup (he called Normal divisor) is also named Invariant Subgroup or Self-conjugate subgroup.
2. Ideal: Principal, Maximal, Prime.
and who still says Abstract Algebra is 'abstract' after reading his analogies below on Automorphism and Symmetric Group:
3. Automorphism of a set is an expression of its SYMMETRY, using geometry figures undergoing transformation (rotation, reflextion), a mapping upon itself, with certain properties (distance, angles) preserved.
4. Why called Sn the 'Symmetric' Group ? because the functions of x1, x2,...,xn, which remain invariant under all permutations of the group, are the 'Symmetric Functions'.
etc...
The 'jewel' insights were found in a single sentence or notes. But they gave me an 'AH-HA' pleasure because they clarified all my past 30 years of confusion. The joy of discovering these 'truths' is very overwhelming, for someone who had been confused by other "derivative" books.
As Abel advised: "Read directly from the Masters". This is THE BOOK!
Suggestion to the Publisher Springer: To gather a team of experts to re-write the new 2010 8th edition, expand on the contents with more exercises (and solutions, please), update all the Math terminologies with modern ones (eg. Normal divisor, Euclidean ring, etc) and modern symbols.
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