代數 pdf epub mobi txt 電子書下載 2024

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SERGE LANG

世界圖書齣版公司

2004-11

914

126.00元

簡裝本

Graduate Texts in Mathematics

9787506271844

圖書標籤: 數學代數 Algebra 經典 Lang math 數學(高級) 傳說

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发表于2024-05-10

代數 epub 下載 mobi 下載 pdf 下載 txt 電子書下載 2024

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圖書描述

《代數》(第3版)：As I see it, the graduate course in algebra must primarily prepare studentsto handle the algebra which they will meet in all of mathematics: topology,partial differential equations, differential geometry, algebraic geometry, analysis,and representation theory, not to speak of algebra itself and algebraic numbertheory with all its ramifications. Hence I have inserted throughout references topapers and books which have appeared during the last decades, to indicate someof the directions in which the algebraic foundations provided by this book areused; I have accompanied these references with some motivating comments, toexplain how the topics of the present book fit into the mathematics that is tocome subsequently in various fields; and I have also mentioned some unsolvedproblems of mathematics in algebra and number theory. The abc conjecture isperhaps the most spectacular of these.

代數下載 mobi epub pdf txt 電子書

著者簡介

Serge Lang (May 19, 1927–September 12, 2005) was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.

He was born in Paris in 1927, and moved with his family to California as a teenager. He graduated from CalTech in 1946, and received a doctorate from Princeton University in 1951. He had positions at the University of Chicago and Columbia University (from 1955, leaving 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University.

(From wikipedia.org)

圖書目錄

代數 pdf epub mobi txt 電子書下載

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用戶評價

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包羅萬象，比較經典。

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就為瞭appendix那個精彩到high的Bourbaki theorem就已經算名著瞭。

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900多頁書僅僅介紹瞭一個結構：模（錶示是其同義詞，群環域嚮量空間是其特例），一個結構定理模的分解為單模（錶示分解為不可約錶示），分解可以理解為非交換傅裏葉變換（級數）；一個對偶Frobenius–Schur （伽瓦羅理論作為其特例）理解為傅裏葉逆變換。連續和離散之間的類比關係是數學學科之間最大聯係。希爾伯特基定理源自主理想環上模的定理和自同態分解jordan形式和有限生成交換群的結構定理等價。抽象代數的本質就是多項式，類比於調和分析本質把所有問題化歸為瞭調和問題一樣，抽象代數把所有的對象翻譯為多項式，然後在多項式範疇裏進行具體的思考。群錶示就是非交換的傅裏葉變換，龐特裏亞金對偶的是局部緊群中的關鍵定理數學有時候初始學習的特例不好理解，例如伽瓦羅定理和傅裏葉分析，但是把他們放在更加抽象的框架

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讀後感

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有幸David S. Dummit的儿子（Evan）给我上过algebra的补习班，他立荐的自然是他爸的书。就易读程度而言，Dummit, Foote可说是代数教程里数一数二的。内容涵盖了基本的代数所必用的知识，而且深入浅出，多有例举，即便是初学也可以读个八九不离十。但这篇是评Lang的。Lang的书...

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代數 pdf epub mobi txt 電子書下載 2024