数学指南英文 [格沃斯(CowersT·) 著] 2013年版

数学指南(英文版) 作者:格沃斯(CowersT·) 著 出版时间:2013年版 内容简介 《数学指南》编著者Timothy Gowers、JuneBarrow-Green、Imre Leader 。本书是一部所有对数学感兴趣的人员的参考书籍。书中包括了由世界著名数学家专门为本书编写近200多词条,这些词条介绍了基本的数学工具和词汇,追溯现代数学起源,解释了关键性术语和概念,重申了数学重要领域的核心思想,描述了著名数学家的贡献和成就,深层次挖掘了数学在生物、金融和音乐等领域的重要影响。本书以如此广的覆盖面具有无与伦比的深度,包括了纯数学领域最活跃和最令人兴奋的分支,提供了这个领域最关键的专业化知识背景和广阔前景,用易于接受和理解的方式承载了大量的信息,这些对于数学专业的本科生、研究生、科研人员和学者了解专业之外的知识是必不可少的。目次:导引;现代数学起源;数学概念;数学分支;定理和问题;数学家;数学的影响;最后展望。读者对象:所有对数学感兴趣的学生和科研人员。 目录 Pre face Contributors Part I Introduction I.1 What Is Mathematics About? I.2 The Language and Grammar of Mathematics I.3 Some Fundamental Mathematical Definitions I.4 The General Goals of Mathematical Research Part II The Origins of Modern Mathematics II.1 From Numbers to Number Systems II.2 Geometry II.3 The Development of Abstract Algebra II.4 Algorithms II.5 The Development of Rigor in Mathematical Analysis II.6 The Development of the Idea of Proof II.7 The Crisis in the Foundations of Mathematics Part III Mathematical Concepts III.1 The Axiom of Choice III.2 The Axiom of Determinacy III.3 Bayesian Analysis III.4 Braid Groups III.5 Buildings III.6 Calabi-Yau Manifolds III.7 Cardinals III.8 Categories III.9 Compactness and Compactification III.10 ComputationaI Complexity Classes III.11 Countable and Uncountable Sets III.12 C*.Algebras III.13 Curvature III.14 Designs III.15 Determinants III.16 Differential Forms and lntegration III.17 Dimension III.18 Distributions III.19 Duality III.20 Dynamical Systems and Chaos III.21 Elliptic Curves III.22 The Euclidean Algorithm and Continued Fractions III.23 The Euler and Navier-Stokes Equations III.24 Expanders III.25 The Exponential and Logarithmic Functions III.26 The Fast Fourier Transform III.27 The Fourier Transform III.28 Fuchsian Groups III.29 Function Spaces III.30 Galois Groups III.31 The Gamma Function III.32 Generating Functions III.33 Genus III.34 Graphs III.35 Hamiltonians III.36 The Heat Equation III.37 Hilbert Spaces III.38 Homology and Cohomology III.39 Homotopy Groups III.40 The Ideal Class Group III.41 Irrational and Transcendental Numbers III.42 The Ising Model