Theory of Groups

Theory of Groups pdf epub mobi txt 电子书 下载 2026

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出版者:American Mathematical Society 作者:Marshall, Jr. Hall 出品人: 页数:434 译者: 出版时间:1999-07 价格:CAD 46.88 装帧:Hardcover isbn号码:9780821819678 丛书系列:
图书标签
  • 群论
  • 抽象代数
  • 数学
  • 高等数学
  • 代数学
  • 拓扑学
  • 李群
  • 表示论
  • 代数结构
  • 数学教材
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具体描述

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."

这本书聚焦于群论这一重要的数学领域,系统地介绍了群的基本概念、定义及其在不同数学分支中的应用。作者将复杂的理论内容以清晰而有条理的方式呈现,使读者能够逐步理解群结构与运作规律。书中详细探讨了有限群和无限群的区别,解析了群同构、阶数、正规化等核心主题,并通过丰富的例子帮助读者将理论联系实际。内容不仅涵盖了经典定理和性质,还深入分析了群在代数拓扑、编码理论及物理学中的深远影响,为初学者提供了一条入门路径。书中还特别强调了不同数学背景下群论的应用案例,帮助读者理解这一抽象概念在具体问题解决中的价值。作者采用逻辑严谨、语言流畅的表达方式,使每一章节都充满启发性和教育意义。内容结构严密,从基础知识出发逐步深入,每个部分均配有解析与总结,确保读者能够系统掌握所学知识。在专业术语使用上精准无误,兼顾学术深度与可读性,旨在为希望学习群论的读者提供全面且实用的参考。书中通过丰富的图示、例题和思维引导,使学习过程充满活力,打破了传统数学教材的单一模式,为现代读者打开了探索数学世界的大门。 这本书不仅对高校学生有重要指导作用,也为大学生、科研人员以及对数学感兴趣的普通读者提供了深入学习群论知识的坚实基础。其内容覆盖范围广泛,既适合基础理论学习,也兼顾应用研究的需求。作者通过仔细研究历史发展和当前研究动向,力求呈现一种全新的视角,使读者能够从多维度理解群的魅力和重要性。这本书不仅是一本教科书,更是激发思维、提升数学素养的重要工具。其精心设计的章节安排,让每一个概念都得以充分展开,确保学习过程顺畅有序。在专业领域中,这一书将成为参考的权威文献,为后续深入研究提供坚实的基础。

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