現代数学の系譜11 ガロア理論を読む13 [転載禁止]©2ch.net

[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む13 [転載禁止]©2ch.net (654ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除ﾚｽ栞

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索歴削→次ｽﾚ栞削→次ｽﾚ過去ﾛｸﾞﾒﾆｭｰ

413: 現代数学の系譜11 ガロア理論を読む [] 2015/05/16(土) 12:43:42.37 ID:3tqJtzYJ

>>410 補足

「Galois for 21st-Century Readers Harold M. Edwards」より

In this paper, I have tried to explain the First Memoir to modern readers, going through it proposition by proposition.
The most important proposition, and the one I most emphasize, is Proposition 2, the one about which Galois wrote in the margin,
“There is something to be completed in this proof. I do not have the time”
(the sections “Proposition 2” and “Proposed Revision of Proposition 2” below).
My interpretation suggests how Galois might have stated and proved it given a little more time.
This revised Proposition 2, combined with Proposition 1 (which I also revise, but only to make the statement Galois surely intended),
contains the equivalent of what is now called the fundamental theorem of Galois theory.
I do not assume that the reader has ready access to the First Memoir and have tried to make the explanations stand on their own,
but serious readers would be foolish to be satisfied with my rewarmed version of Galois’s theory.
The original, however flawed and incomplete itmay be, is indisputably one of the most valuable and insightful documents in the history of mathematics.

http://wc2014.5ch.net/test/read.cgi/math/1428205549/413

418: 現代数学の系譜11 ガロア理論を読む [] 2015/05/16(土) 15:17:13.88 ID:3tqJtzYJ

>>413 つづき

「Galois for 21st-Century Readers Harold M. Edwards」より

Again, Study the Masters
The introduction to my 1974 book Riemann’s Zeta Function was an exhortation to “Read the classics!”
A few years later I discovered Niels Henrik Abel’s remark that “It appears to me that if one wants to make progress in mathematics one should study the masters and not the pupils,” which then became my constant refrain.
Abel’s contrast of “masters” to “pupils” is an important addition to the message.
“Read the classics” doesn’t just mean read good texts; it means read the texts that gave birth to the subjects or gave them their most vivid statements?those written by the “masters”?not the ones written by later “pupils”,
who themselves learned the ideas from the masters and are trying to make presentations that are more accessible or that conform to newer styles.
I have tried to show here that the ideas expressed by what is now called the fundamental theorem of Galois theory are all contained, in a very effective but terse form, in the first few pages of Galois’s First Memoir.
In the course of the writing,I have been forcefully reminded of the extent to which Galois is the master and I the pupil.
Once again, I advise students to Study the masters!
Thanks to Peter Neumann’s meticulous reexamination of all of Galois’s works?not just of the First Memoir?many more students will now be able to do so.

http://wc2014.5ch.net/test/read.cgi/math/1428205549/418

上下前次1-新書関写板覧索設栞歴

ｽﾚ情報赤ﾚｽ抽出画像ﾚｽ抽出歴の未読ｽﾚ AAｻﾑﾈｲﾙ

ぬこの手ぬこTOP 0.039s