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【转帖】Galois Theory (Graduate Texts in Mathematics)
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Galois Theory (Graduate Texts in Mathematics) Publisher: Springer Number Of Pages: 172 Publication Date: 1997-11-26 Sales Rank: 502465 ISBN / ASIN: 038790980X EAN: 9780387909806 Binding: Hardcover Manufacturer: Springer Studio: Springer Average Rating: 4.5 This book is an introduction to Galois theory along the lines of Galois' "Memoir on the Conditions for Solvability of Equations by Radicals". Some antecedents of Galois theory in the works of Gauss, Lagrange, Vandemonde, Newton, and even the ancient Babylonians, are explained in order to put Galois' main ideas in their historical setting. The modern formulation of the theory is also explained. The book contains many exercises - with answers - and an English translation of Galois' memoir. Review: Breath the air of Galois This is not an excellent exposition of Galois theory. It is, however, a book well worth reading for the single reason that it sticks to Galois, including a full translation of Galois' 1831 memoir (13 pages). The immediate goal for Galois was to understand solvability by radicals, in particular of the general n:th degree equation. But to understand Galois we must first study what was done before him (§§1-27). Lagrange is the most important predecessor. He presented a unified approach to the solvable cases (n<5) in terms of "resolvents", which he hoped would point forward to the n>4 cases. This resolvent business is historical ballast, we would say today, but it is from this tradition that Galois departs. In particular, he arrives at the "Galois group" in terms of resolvents. With the Galois group in place, things flow more smoothly. Essentially as in the modern theory, Galois shows that if an equation is solvable by radicals then its Galois group is "solvable". All this is §§28-48. Edwards the constructivist now inserts a bunch of Kronecker material on the existence of roots (§§49-61). Then it's back to Galois (§§62-71) to see how he puts his theory to use. Galois doesn't even bother to spell out that the unsolvability of the general equation of degree n>4 follows since its Galois group S_n is not solvable; instead he finds a curious criterion for solvability which is involves no group theory (even Edwards calls this result "rather strange"  .Password: gigapedia.orgType: PDF Size: 22.14 MB MD5: 775aec19f55770ee4e58b7f5816e4517 http://rapidshare.com/files/41655443/038790980X.zip.html http://mihd.net/hg1z0l [ Last edited by laizuliang on 2007-12-18 at 20:10 ] |
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