Theory of Groups

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出版者:American Mathematical Society
作者:Marshall, Jr. Hall
出品人:
頁數:434
译者:
出版時間:1999-07
價格:CAD 46.88
裝幀:Hardcover
isbn號碼:9780821819678
叢書系列:
圖書標籤:
  • 群論
  • 抽象代數
  • 數學
  • 高等數學
  • 代數學
  • 拓撲學
  • 李群
  • 錶示論
  • 代數結構
  • 數學教材
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具體描述

Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, $p$-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups.

From the Preface to the First Edition (1976): "The present volume is intended to serve a dual purpose. The first ten chapters are meant to be the basis for a course in group theory, and exercises have been included at the end of each of these chapters. The last ten chapters are meant to be useful as optional material in a course or as reference material. When used as a text, the book is intended for students who have had an introductory course in modern algebra comparable to a course taught from Birkhoff and Mac Lane's A Survey of Modern Algebra. I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane."

這本書聚焦於群論這一重要的數學領域,係統地介紹瞭群的基本概念、定義及其在不同數學分支中的應用。作者將復雜的理論內容以清晰而有條理的方式呈現,使讀者能夠逐步理解群結構與運作規律。書中詳細探討瞭有限群和無限群的區彆,解析瞭群同構、階數、正規化等核心主題,並通過豐富的例子幫助讀者將理論聯係實際。內容不僅涵蓋瞭經典定理和性質,還深入分析瞭群在代數拓撲、編碼理論及物理學中的深遠影響,為初學者提供瞭一條入門路徑。書中還特彆強調瞭不同數學背景下群論的應用案例,幫助讀者理解這一抽象概念在具體問題解決中的價值。作者采用邏輯嚴謹、語言流暢的錶達方式,使每一章節都充滿啓發性和教育意義。內容結構嚴密,從基礎知識齣發逐步深入,每個部分均配有解析與總結,確保讀者能夠係統掌握所學知識。在專業術語使用上精準無誤,兼顧學術深度與可讀性,旨在為希望學習群論的讀者提供全麵且實用的參考。書中通過豐富的圖示、例題和思維引導,使學習過程充滿活力,打破瞭傳統數學教材的單一模式,為現代讀者打開瞭探索數學世界的大門。 這本書不僅對高校學生有重要指導作用,也為大學生、科研人員以及對數學感興趣的普通讀者提供瞭深入學習群論知識的堅實基礎。其內容覆蓋範圍廣泛,既適閤基礎理論學習,也兼顧應用研究的需求。作者通過仔細研究曆史發展和當前研究動嚮,力求呈現一種全新的視角,使讀者能夠從多維度理解群的魅力和重要性。這本書不僅是一本教科書,更是激發思維、提升數學素養的重要工具。其精心設計的章節安排,讓每一個概念都得以充分展開,確保學習過程順暢有序。在專業領域中,這一書將成為參考的權威文獻,為後續深入研究提供堅實的基礎。

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