Fields and Galois Theory

ยท Springer Science & Business Media
แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜
226
แƒ’แƒ•แƒ”แƒ แƒ“แƒ˜
แƒ แƒ”แƒ˜แƒขแƒ˜แƒœแƒ’แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜ แƒ“แƒแƒฃแƒ“แƒแƒกแƒขแƒฃแƒ แƒ”แƒ‘แƒ”แƒšแƒ˜แƒ ย แƒจแƒ”แƒ˜แƒขแƒงแƒ•แƒ”แƒ— แƒ›แƒ”แƒขแƒ˜

แƒแƒ› แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

Fieldsaresetsinwhichallfouroftherationaloperations,memorablydescribed by the mathematician Lewis Carroll as โ€œperdition, distraction, ugli?cation and derisionโ€, can be carried out. They are assuredly the most natural of algebraic objects, since most of mathematics takes place in one ?eld or another, usually the rational ?eld Q, or the real ?eld R, or the complex ?eld C. This book sets out to exhibit the ways in which a systematic study of ?elds, while interesting in its own right, also throws light on several aspects of classical mathematics, notably on ancient geometrical problems such as โ€œsquaring the circleโ€, and on the solution of polynomial equations. The treatment is unashamedly unhistorical. When Galois and Abel dem- strated that a solution by radicals of a quintic equation is not possible, they dealt with permutations of roots. From sets of permutations closed under c- position came the idea of a permutation group, and only later the idea of an abstract group. In solving a long-standing problem of classical algebra, they laid the foundations of modern abstract algebra.

แƒจแƒ”แƒแƒคแƒแƒกแƒ”แƒ— แƒ”แƒก แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜

แƒ’แƒ•แƒ˜แƒ—แƒฎแƒแƒ แƒ˜แƒ— แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒแƒ–แƒ แƒ˜.

แƒ˜แƒœแƒคแƒแƒ แƒ›แƒแƒชแƒ˜แƒ แƒฌแƒแƒ™แƒ˜แƒ—แƒฎแƒ•แƒแƒกแƒ—แƒแƒœ แƒ“แƒแƒ™แƒแƒ•แƒจแƒ˜แƒ แƒ”แƒ‘แƒ˜แƒ—

แƒกแƒ›แƒแƒ แƒขแƒคแƒแƒœแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒขแƒแƒ‘แƒšแƒ”แƒขแƒ”แƒ‘แƒ˜
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แƒšแƒ”แƒžแƒขแƒแƒžแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ”แƒ‘แƒ˜
Google Play-แƒจแƒ˜ แƒจแƒ”แƒซแƒ”แƒœแƒ˜แƒšแƒ˜ แƒแƒฃแƒ“แƒ˜แƒแƒฌแƒ˜แƒ’แƒœแƒ”แƒ‘แƒ˜แƒก แƒ›แƒแƒกแƒ›แƒ”แƒœแƒ แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ˜แƒก แƒ•แƒ”แƒ‘-แƒ‘แƒ แƒแƒฃแƒ–แƒ”แƒ แƒ˜แƒก แƒ’แƒแƒ›แƒแƒงแƒ”แƒœแƒ”แƒ‘แƒ˜แƒ— แƒจแƒ”แƒ’แƒ˜แƒซแƒšแƒ˜แƒแƒ—.
แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒกแƒฎแƒ•แƒ แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜
แƒ”แƒšแƒ”แƒฅแƒขแƒ แƒแƒœแƒฃแƒšแƒ˜ แƒ›แƒ”แƒšแƒœแƒ˜แƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ–แƒ” แƒฌแƒแƒกแƒแƒ™แƒ˜แƒ—แƒฎแƒแƒ“, แƒ แƒแƒ’แƒแƒ แƒ˜แƒชแƒแƒ Kobo eReaders, แƒ—แƒฅแƒ•แƒ”แƒœ แƒฃแƒœแƒ“แƒ แƒฉแƒแƒ›แƒแƒขแƒ•แƒ˜แƒ แƒ—แƒแƒ— แƒคแƒแƒ˜แƒšแƒ˜ แƒ“แƒ แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒแƒ— แƒ˜แƒ’แƒ˜ แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒแƒจแƒ˜. แƒ“แƒแƒฎแƒ›แƒแƒ แƒ”แƒ‘แƒ˜แƒก แƒชแƒ”แƒœแƒขแƒ แƒ˜แƒก แƒ“แƒ”แƒขแƒแƒšแƒฃแƒ แƒ˜ แƒ˜แƒœแƒกแƒขแƒ แƒฃแƒฅแƒชแƒ˜แƒ”แƒ‘แƒ˜แƒก แƒ›แƒ˜แƒฎแƒ”แƒ“แƒ•แƒ˜แƒ— แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒ”แƒ— แƒคแƒแƒ˜แƒšแƒ”แƒ‘แƒ˜ แƒ›แƒฎแƒแƒ แƒ“แƒแƒญแƒ”แƒ แƒ˜แƒš แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ–แƒ”.