代数:地下笔记(剑桥数学教材系列） 英文原版 Algebra : Notes from the Underground Paolo Aluffi

基本信息

Format Paperback | 488 pages

Dimensions 171 x 244 x 27mm | 840g

Publication date 31 Jul 2021

Publisher Cambridge University Press

Language English

ISBN10 1108958230

ISBN13 9781108958233

页面参数仅供参考，具体以实物为准

书籍简介

从环到模块到群到场，这本抽象代数的本科生入门书籍遵循了一条非常规的路径。该书强调了对这一主题的现代观点，温和地提到了各种结构所依据的统一的分类原则和普遍属性的作用。一个主要特点是对模块的处理，包括对欧几里得域上有限生成模块的分类定理的证明。还介绍了Noetherian模块和一些jing确复合体的语言。此外，标准课题——如中国余数定理、高斯定理、西洛定理、交替群的简单性、场扩展的标准结果和伽罗瓦理论的基本定理--都得到了详细的处理。学生会喜欢这本书的对话风格，400多道练习题，附录中包含了大约150个主要文本问题的完整解决方案，以及附录中的基本逻辑和朴素集合论的一般背景。

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naive set theory.

作者简介

保罗·阿鲁菲是佛罗里达州立大学的数学教授。阿鲁菲在威廉·富尔顿的指导下，以一篇关于平面三次曲线的计数几何的论文获得了布朗大学的博士学位。他的研究兴趣是代数几何，尤其是交集理论及其在奇点理论中的应用以及与理论物理的联系。他撰写了约70份研究出版物，并在15个国家就其工作进行了演讲。除了地下笔记之外，他还出版了一本研究生水平的代数教科书(代数:第0章，AMS)和一本面向公众的意大利语数学书(Fare matematica，Aracne Editrice)。

Paolo Aluffi is Professor of Mathematics at Florida State University. Aluffi earned a Ph.D. from Brown University with a dissertation on the enumerative geometry of plane cubic curves, under the supervision of William Fulton. His research interests are in algebraic geometry, particularly intersection theory and its application to the theory of singularities and connections with theoretical physics. He has authored about 70 research publications and given lectures on his work in 15 countries. Beside Notes from the Underground, he has published a graduate-level textbook in algebra (Algebra: Chapter 0, AMS) and a mathematics book for the general public, in Italian (Fare matematica, Aracne Editrice).