数论
数论
Number Theory: An approach through history from Hammurapi to Legendre Douban
[法]André Weil translator: 胥鸣伟 / 王元(校) publishing house: 高等教育出版社 2010 - 4
《数论:从汉穆拉比到勒让德的历史导引》内容简介:数论——或者一些人称之为的算术,是最古老、最纯粹、最有活力、最初等却也是最深奥的数学领域。这门学科具有“数学皇后”的名声绝非偶然。一些最为复杂的传统的数学思想便是由对数论的基本问题的研究发展起来的。 对数论有杰出贡献的韦伊,写成了诠释数论历史的这《数论:从汉穆拉比到勒让德的历史导引》;他的研究内容涵盖了大约三十六个世纪的算术工作——从一块可追溯到汉穆拉比王朝的古巴比伦的泥板到勒让德的《论数论》(1798)。韦伊一直希望向有较好教育背景的读者讲述他的研究领域,这促使他在问题的分析、数论方法的演变以及它们在数学中的意义方面使用了历史性的解读方法。在他的论述过程中,韦伊和读者一起来到现代数论的四位主要作者(费马、欧拉、拉格朗日、勒让德)的工作室,并在那里进行了一场仔细的、带有批判眼光的查验。《数论:从汉穆拉比到勒让德的历史导引》富含知识史的广博内容,对了解我们的文化遗产有很重要的贡献。
Read Oct. 22, 2019
看了几十页就跳过数学看人物了,睡前和别人说:以前以为数论难好歹陈述能看懂。
对丢番图方程不感兴趣,倒是角谷猜想黎曼假设这些对我很有趣。其实这本书没讲的高斯时代正好接Klein的《数学在19世纪的发展》,这些书我就都姑且定性为专家找灵感吧。
数论 数学史
代数数论简史
Douban
冯克勤 publishing house: 湖南教育出版社 2002 - 1
《代数数论简史(精装)》试图简要介绍代数数论二百年的发展途径,并沿着历史的线索讲述了代数数论的主要思想、方法、成就和一些重大事件。
Read Jan. 15, 2020
内容是接着weil那本 太硬了,到头来感觉日本人那本数论讲这些东西更好。方程,局限地说PDE,是分析的主动力,数论就是代数的对应物了,它还要从自己外的一切数学吸取养分。代数学(群环域等等)还是诺特时代从数论划分的,数还会一直生长出更多好的,深刻的数学。
数论 数学史
The Shaping of Arithmetic - After C.F. Gauß's Disquisitiones Arithmeticae
Douban
Goldstein, Catherine (EDT)/ Schappacher, Norbert (EDT)/ Schwermer, Joachim (EDT) publishing house: Springer 2006 - 3
The cultural historian Theodore Merz called it the great book with seven seals, the mathematician Leopold Kronecker, the book of all books : already one century after their publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) had acquired an almost mythical reputation. They had served throughout the XIX th century as an ideal of exposition in matters of notation, problems and methods; as a model of organisation of the material and theory building; and last but not least as a source of mathematical inspiration. Various readings of the Disquisitiones Arithmeticae have left their marks on developments as different as Galois' theory of algebraic equations, Lucas' primalitytests, and Dedekind's theory of ideals.The present volume revisits successive periods in the reception of Gauss's book: it studies which parts were taken up when, which themes were further explored. It also focusses on how specific mathematicians reacted to the Disquisitiones Arithmeticae: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev. An astounding variety of research programmes in the theory of numbers can be traced back toGauss's book. The 18 authors - mathematicians, historians, philosophers - who have collaborated for this volume, contribute in-depth studies on the various aspects of the bicentennary voyage of this mathematical text through history, and the way that the number theory we know today came into being and diversified.