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Title: Galois Theory (Graduate Texts in Mathematics 101) by Harold M. Edwards ISBN: 0-387-90980-X Publisher: Springer Verlag Pub. Date: November, 1997 Format: Hardcover Volumes: 1 List Price(USD): $56.95 |
Average Customer Rating: 4 (2 reviews)
Rating: 5
Summary: Best treatment for the "mechanics" of Galois Theory
Comment: This is the only book I have seen that "mechanically dissects" galois theory. Other books would give a succession of "theorem-proofs" that eventually proved the Galois solvability theorem but when I was finished, I still could not intuitively understand how the solvability of Galois groups to corresponds to solvability by radicals.
Instead of plodding thru theorem-proof without insight or motivation, this book actually works thru the relation between the algebra of polynomial solutions and the structure of their groups. Ultimately it shows the structure that an equation must have to be solvable (equivalently to have a solvable Galois group).
Unlike the other reader who did not get alot out of Galois' original writing, it opened a window of understanding for me.
Make no mistake, understanding the material here took considerable effort to work out the math on paper to follow the examples and the proofs. Perhaps the book could be improved by adding more detail in places, but then, this is a graduate-level text.
This is the second book I have read from Harold Edwards. I found I learn an awful lot of the low-level details of a subject that I can't find anywhere else. I believe he is one of the best authors in mathematics today. I would happily collect all his works.
Rating: 3
Summary: Too historical, anecdotal
Comment: I found this book kind of hard to read. The author tried to give topics motivation by putting them in their historical context, but I found that this muddied the treatment so that the reader is left wishing that the author would chose between a history book and a math book. I disagree with the author that the original text of Galois is the best way to learn the theory, I found it considerably less readable than Artin's book, and it placed Galois theory too much in its historical context of solution by radicals. This obscured its manifold modern uses...
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Title: Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards ISBN: 0387950028 Publisher: Springer Verlag Pub. Date: January, 2000 List Price(USD): $49.95 |
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Title: Complex Analysis (4th Ed) (Graduate Texts in Mathematics, 103) by Serge Lang ISBN: 0387985921 Publisher: Springer Verlag Pub. Date: 15 January, 1999 List Price(USD): $69.95 |
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Title: Fourier Analysis on Finite Groups and Applications by Audrey Terras ISBN: 0521457181 Publisher: Cambridge Univ Pr (Trd) Pub. Date: 01 May, 1999 List Price(USD): $22.95 |
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Title: Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) by Joseph H. Silverman, J. Tate ISBN: 0387978259 Publisher: Springer Verlag Pub. Date: April, 1996 List Price(USD): $39.95 |
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Title: Undergraduate Commutative Algebra by Miles Reid ISBN: 0521458897 Publisher: Cambridge University Press Pub. Date: 30 November, 1995 List Price(USD): $22.00 |
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