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《普林斯顿数学指南》是由菲尔兹奖得主T. Gowers 主编、133 位著名数学家共同参与撰写的大型文集. 《普林斯顿数学指南（第一分册）》，由288 篇长篇论文和短篇条目构成, 目的是对20 世纪最后一二十年纯粹数学的发展给出一个概览, 以帮助青年数学家学习和研究其最活跃的部分, 这些论文和条目都可以独立阅读. 原书有八个部分, 除第Ⅰ部分是一个简短的引论、第Ⅷ部分是《普林斯顿数学指南（第一分册）》的“终曲”以外, 《普林斯顿数学指南（第一分册）》分为三大板块, 核心是第Ⅳ部分“数学的各个分支”, 共26 篇长文, 介绍了20 世纪最后一二十年纯粹数学研究中最重要的成果和最活跃的领域, 第Ⅲ部分“数学概念”和第Ⅴ部分“定理与问题”都是为它服务的短条目. 第二个板块是数学的历史, 由第Ⅱ部分“现代数学的起源”(共7 篇长文)和第Ⅵ部分“数学家传记”(96 位数学家的短篇传记)组成. 第三个板块是数学的应用, 即第Ⅶ部分“数学的影响”(14 篇长文章). 作为《普林斯顿数学指南（第一分册）》“终曲”的第Ⅷ部分“结束语：一些看法”则是对青年数学家的建议等7 篇文章.中译本分为三卷，第一卷包括第I-Ⅲ部分，第二卷即第Ⅳ部分，第三卷包括第V～Ⅷ部分。
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
Presents major ideas and branches of pure mathematics in a clear, accessible style
Defines and explains important mathematical concepts, methods, theorems, and open problems
Introduces the language of mathematics and the goals of mathematical research
Covers number theory, algebra, analysis, geometry, logic, probability, and more
Traces the history and development of modern mathematics
Profiles more than ninety-five mathematicians who influenced those working today
Explores the influence of mathematics on other disciplines
Includes bibliographies, cross-references, and a comprehensive index
