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Title: Algebra by Saunders Mac Lane, American Mathematical Society ISBN: 0-8218-1646-2 Publisher: American Mathematical Society Pub. Date: April, 1999 Format: Hardcover Volumes: 1 List Price(USD): $45.00 |
Average Customer Rating: 4.67 (3 reviews)
Rating: 5
Summary: bold and beautiful
Comment: It has several sections not present in most introductory texts -- affine and projective geometry, multilinear algebra, and linear algebra (the latter only seen in Herstein's Topics in Algebra), category theory, and lattice theory. The first few chapters use permutations a lot for examples, later it uses matrix groups. We are talking about the 3rd edition here -- don't get an earlier edition!
Rating: 5
Summary: THE algebra book, period.
Comment: After getting frustated by nearly all the so-called "authoritative" books on abstract algebra (Lang, Hungerford, Jacobson), I really can say that MacLane/Birkhoff is the best die-hard classic on algebra. Now I must stress that this book IS NOT out-of-print: the third edition is actually published by AMS/Chelsea.
There's an interesting thing about the evolution of this book: the first edition has become famous among mathematicians, because it brought for the first time an elementary exposition of categories and universal constructions, directly from the horse's mouth (MacLane founded the theory of categories together with S. Eilenberg; Birkhoff was the creator of the theory of lattices), which is used as a basic tool throughout the book; it also contained unusual topics such as multilinear algebra and affine and projective spaces, but no Galois theory. The second edition has gained a chapter on Galois theory, but has lost the part on affine and projective spaces.
The third edition is the best! It has recovered the part which was lost in the second edition, and had its exposition considerably polished. While most other books expose abstract algebra as a ugly, prawling monster, MacLane/Birkhoff manage to explain quite esoterical topics (many of them created and/or developed by themselves) in a surprisingly natural and tasty way (compare it with the dry, encyclopaedic style of Hungerford and Lang); although quite big, the book supports several ways of reading and teaching its parts without sacrificing clarity. Another great quality: it is INSPIRING, in the sense that it develops a powerful algebraic intuition, which is, in my opinion, the main obstacle one has to face to learn algebra.
Rating: 4
Summary: A readable text using notation similar to Jacobsen.
Comment: This text is a very readable presentation of first year graduate abstract algebra. The material is presented with notations similar to that of Jacobsen in his "Basic Algebra" texts, and is useful as a review text for qualifiers, or for independent study.
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Title: Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted ISBN: 0486428753 Publisher: Dover Pubns Pub. Date: 04 June, 2003 List Price(USD): $14.95 |
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Title: Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach ISBN: 048668735X Publisher: Dover Pubns Pub. Date: 22 September, 1995 List Price(USD): $11.95 |
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Title: Principles of Mathematical Analysis by Walter Rudin ISBN: 007054235X Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1976 List Price(USD): $147.70 |
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Title: Calculus by Michael Spivak ISBN: 0914098896 Publisher: Publish or Perish Pub. Date: December, 1994 List Price(USD): $70.00 |
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Title: Finite Dimensional Vector Spaces by P. R. Halmos ISBN: 0387900934 Publisher: Springer Verlag Pub. Date: November, 1996 List Price(USD): $49.95 |
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