| 查看: 127 | 回复: 0 | |||
| 当前主题已经存档。 | |||
[交流]
【转帖】Galois Theory (Graduate Texts in Mathematics)
|
|||
|
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 ] |
回复此楼» 猜你喜欢
寻求一种能扛住强氧化性腐蚀性的容器密封件
已经有7人回复
-
到新单位后，换了新的研究方向，没有团队，持续积累2区以上论文，能申请到面上吗
已经有8人回复
-
申请2026年博士
已经有6人回复
-
请问哪里可以有青B申请的本子可以借鉴一下。
已经有5人回复
-
天津工业大学郑柳春团队欢迎化学化工、高分子化学或有机合成方向的博士生和硕士生加入
已经有5人回复
-
2025冷门绝学什么时候出结果
已经有7人回复
-
请问有评职称，把科研教学业绩算分排序的高校吗
已经有6人回复
-
Bioresource Technology期刊，第一次返修的时候被退回好几次了
已经有7人回复
-
请问下大家为什么这个铃木偶联几乎不反应呢
已经有5人回复
-
康复大学泰山学者周祺惠团队招收博士研究生
已经有6人回复
