数学指南（英文版）[格沃斯 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
Ⅲ.43 Jordan NormaI Form
Ⅲ.44 Knot Polynomials
Ⅲ.45 K-Theory
Ⅲ.46 The Leech lattice
Ⅲ.47 L-Functions
Ⅲ.48 Lie Theory
Ⅲ.49 Linear and Nonlinear Waves and Solitons
Ⅲ.50 Linear Operators and Their Properties
Ⅲ.51 Local and Global in Number Theory
Ⅲ.52 The Mandelbrot Set
Ⅲ.53 Manifolds
Ⅲ.54 Matroids
Ⅲ.55 Measures
……
PartⅤ Theorems and Problems
PartⅥ Mathematicians
PartⅦ The Influence of Mathematics
PartⅧ Final Perspectives
Index