作者：爱德华兹(Harold M.Edwards)
页数：152
出版社：世界图书出版公司
出版日期：2010
ISBN：9787510027420
电子书格式：pdf/epub/txt
内容简介
this exposition of galois theory was originally going to be chapter i of the continuation of my book ferrnat’s last theorem, but it soon outgrew any reasonable bounds for an introductory chapter, and i decided to make it a separate book. however, this decision was prompted by more than just the length. following the precepts of my sermon “read the masters!” [e2], imade the reading of galois’ original memoir a major part of my study of galois theory, and i saw that the modern treatments of galois theory lacked much of the simplicity and clarity of the original. therefore i wanted to write about the theory in a way that would not only explain it, but explain it in terms close enough to galois’ own to make his memoir accessible to the reader, in the same way that i tried to make riemann’s memoir on the zeta function and kummer’s papers on fermat’s last theorem accessible in my earlier books, [eli and [e3]. clearly i could not do this within the confines of one expository chapter
本书特色
这本《伽罗瓦理论》由美国的Harold M. Edwards所著，内容是：This exposition of Galois theory was originally going to be Chapter 1 of thecontinuation of my book Fermat’s Last Theorem, but it soon outgrew anyreasonable bounds for an introductory chapter, and I decided to make it aseparate book. However, this decision was prompted by more than just thelength. Following the precepts of my sermon “Read the Masters!” [E2], I made the reading of Galois’ original memoir a major part of my study ofGalois theory, and I saw that the modern treatments of Galois theory lackedmuch of the simplicity and clarity of the original. Therefore I wanted towrite about the theory in a way that would not only explain it, but explain it in terms close enough to Galois’ own to make his memoir accessible to thereader, in the same way that I tried to make Riemann’s memoir on the zetafunction and Kummer’s papers on Fermat’s Last Theorem accessible in myearlier books, [Eli and I-E3].
目录
1. galois 2. influence of lagrange 3. quadratic equations 4.1700 n.c. to a.o. 1500 5. solution of cubic 6. solution of quartic 7.impossibility of quintic 8. newton 9. symmetric polynomials in roots 10. fundamental theorem on symmetric polynomials 11. proof 12.newton’s theorem 13. discriminants
first exercise set
14. solution of cubic 15. lagrange and vandermonde 16. lagrange resolvents 17. solution of quartic again 18. attempt at quintic ~19.lagrange’s rdfiexions
second exercise set
20. cyciotomic equations 21. the cases n = 3, 5 22. n = 7, 11 23.general case 24. two lemmas 25. gauss’s method ~26. p-gons by ruler and compass 27. summary
third exercise set
28. resolvents 29. lagrange’s theorem 30. proof 31. galois resolvents 32. existence of galois resolvents 33. representation of the splitting field as k(t) ~34. simple algebraic extensions 35. euclidean algorithm 36. construction of simple algebraic extensions 37. galois’method
fourth exercise set
节选
《伽罗瓦理论》内容简介：This exposition of Galois theory was originally going to be Chapter 1 of thecontinuation of my book Fermat’s Last Theorem, but it soon outgrew anyreasonable bounds for an introductory chapter, and I decided to make it aseparate book. However, this decision was prompted by more than just thelength. Following the precepts of my sermon “Read the Masters！” [E2], Imade the reading of Galois’ original memoir a major part of my study ofGalois theory, and I saw that the modern treatments of Galois theory lackedmuch of the simplicity and clarity of the original. Therefore I wanted towrite about the theory in a way that would not only explain it, but explain itin terms close enough to Galois’ own to make his memoir accessible to thereader, in the same way that I tried to make Riemann’s memoir on the zetafunction and Kummer’s papers on Fermat’s Last Theorem accessible in myearlier books, [El] and [E3]. Clearly I could not do this within the confinesof one expository chapter.
