伽羅瓦理論（第2版）（英文版） [Galois Theory 2nd ed] 下載 mobi epub pdf 電子書 2024

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內容簡介

　　《伽羅瓦理論(第2版)(英文版)》是第二版，較一版有很大的改進。證明更加清晰、詳盡。由於多變形對稱群和多項式的Galois群的相似性，書中以平麵上的多邊形對稱群為開始。這種相似性可以幫助讀者理解書中的有關理論知識。書中也包含瞭一些新的定理，例如：不可約情形。書中用完整的證明和大量練習清晰、有效地講述瞭Galois理論。包括：立方、四次方公式的Galois理論的基本理論；五次Galois大定理的不可解性；立方和四次方Galois群的計算。補充瞭群論、尺規結構和Galois的早期曆史。《伽羅瓦理論(第2版)(英文版)》是一本Galois理論簡明教程，很適閤研究生一年級作為教材學習；也是一本很理想的課外學習書。目次：對稱；環；同態和理想；商環；域上的多項式環；素理想和大理想；不可約多項式；經典多項式；分裂域；Galois群；單位根；根式可解性；特徵的獨立性；Galois擴張；Galois理論的基本定理；應用；Galois大定理；判彆式；二次、三次、四次多項式的Galois群；結尾。

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目錄

Preface to the Second Edition
Preface to the First Edition
To the Reader
Symmetry
Rings
Domains and Fields
Homomorphisms and Ideals
Quotient Rings
Polynomial Rings over Fields
Prime Ideals and Maximal Ideals
Irreducible Polynomials
Classical Formulas
Splitting Fields
The Galois Group
Roots of Unity
Solvability by Radicals
Independence of Characters
Galois Extensions
The Fundamental Theorem of Galois Theory

前言/序言

　　There are too many errors in the first edition， and so a "corrected nth printing" would have been appropriate. However， given the opportunity to makechanges， I felt that a second edition would give me the flexibility to changeany portion of the text that I felt I could improve. The first edition aimedto give a geodesic path to the Fundamental Theorem of Galois Theory，and I still think its brevity is valuable. Alas， the book is now a bit longer，but I feel that the changes are worthwhile. I began by rewriting almost allthe text， trying to make proofs clearer， and often giving more details thanbefore. Since many students find the road to the Fundamental Theoreman intricate one， the book now begins with a short section on symmetrygroups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guideby helping readers organize the various definitions and constructions. Theexposition has been reorganized so that the discussion of solvability byradicals now appears later; this makes the proof of the Abel-Ruffini theorem easier to digest. I have also included several theorems not in the firstedition. For example， the Casus Irreducibilis is now proved， in keepingwith a historical interest lurking in these pages.
　　I am indebted to Gareth Jones at the University of Southampton who，after having taught a course with the first edition as text， sent me a detailed list of errata along with perspicacious comments and suggestions. Ialso thank Evan Houston， Adam Lewenberg， and Jack Shamash who madevaluable comments as well. This new edition owes much to the generosityof these readers， and I am grateful to them.

伽羅瓦理論（第2版）（英文版） [Galois Theory 2nd ed] 下載 mobi epub pdf txt 電子書 格式

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還行的教材，瞎看吧。

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比較薄，放在床頭，沒事的時候看看，也算是迴顧大學時光，伽羅華理論的中文與英文書籍都較多。

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全新正版，很好

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比較深的一本書，慢慢研讀。

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伽羅華理論中的經典之一

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買來學習一下，雖然興趣不全在此，看看這書。

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gssjfldlsk

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經過兩個多世紀，一些著名的數學傢，如歐拉、旺德濛德、拉格朗日、魯菲尼等，都做瞭很多工作，但都未取得重大的進展。19世紀上半葉，阿貝爾受高斯處理二項方程 (p為素數)的方法的啓示，研究五次以上代數方程的求解問題，終於證明瞭五次以上的方程不能用根式求解。他還發現一類能用根式求解的特殊方程。這類方程現在稱為阿貝爾方程。阿貝爾還試圖研究齣能用根式求解的方程的特性，由於他的早逝而未能完成這項工作。伽羅瓦理論還特彆對尺規作圖問題給齣完全的刻畫。人們已經證明：這種作圖問題可歸結為解有理數域上的某些代數方程。這樣一來，一個用直尺和圓規作圖的問題是否可解，就轉化為研究相應方程的伽羅瓦群的性質。

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伽羅瓦理論是我買Rotman的第三本書瞭，內容講得通俗易懂。內容分布閤理，給人一種輕鬆的感覺。

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