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Algebra, Volume II

B. L. van der Waerden
Springer Verlag
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Fernando Q. Gouvêa
, on

In the glad to have you back department, I’m delighted that Springer has decided to reprint the two volumes of B. L. van der Waerden’s Algebra. Based on lectures by Emmy Noether and Emil Artin, this is the book that brought “abstract algebra” to the mathematical world. It is not for the faint of heart: van der Waerden is terse and precise: as he says, “knapp (aber lückenlos).” He does not spend much time on easy details.

On the other hand, the book reflects the excitement that accompanied the birth of axiomatic algebra. It was written when the power of the new methods was still news for most mathematicians, and a guide to the new ideas was still needed. This is that guide. It covers all the usual topics and then some. Not, perhaps, a book to give to an undergraduate (though who knows? for some undergraduates, it might just work), but still a book to treasure. I’m glad it’s back. My only hesitation is to wonder whether it would not have been better to bring it back as one fat volume instead of two thin ones.

Fernando Q. Gouvêa is the editor of MAA Reviews.

12. Linear Algebra

13. Algebras

14. Representation Theory of Groups and Algebras

15. General Ideal Theory of Commutative Rings

16. Theory of Polynomial Ideals

17. Integral Algebraic Elements

18. Fields with Valuations

19. Algebraic Functions of One Variable

20. Topological Algebra