数学指南

图书信息

分类：科学技术,自然科学,数学

作者简介

作者简介 暂缺《数学指南》作者简介

内容简介

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

图书目录
Pre faceContributorsPart Ⅰ IntroductionⅠ.1 What Is Mathematics About?Ⅰ.2 The Language and Grammar of MathematicsⅠ.3 Some Fundamental Mathematical DefinitionsⅠ.4 The General Goals of Mathematical ResearchPart Ⅱ The Origins of Modern MathematicsⅡ.1 From Numbers to Number SystemsⅡ.2 GeometryⅡ.3 The Development of Abstract AlgebraⅡ.4 AlgorithmsⅡ.5 The Development of Rigor in Mathematical AnalysisⅡ.6 The Development of the Idea of ProofⅡ.7 The Crisis in the Foundations of MathematicsPart Ⅲ Mathematical ConceptsⅢ.1 The Axiom of ChoiceⅢ.2 The Axiom of DeterminacyⅢ.3 Bayesian AnalysisⅢ.4 Braid GroupsⅢ.5 BuildingsⅢ.6 Calabi-Yau ManifoldsⅢ.7 CardinalsⅢ.8 CategoriesⅢ.9 Compactness and CompactificationⅢ.10 ComputationaI Complexity ClassesⅢ.11 Countable and Uncountable SetsⅢ.12 C*.AlgebrasⅢ.13 CurvatureⅢ.14 DesignsⅢ.15 DeterminantsⅢ.16 Differential Forms and lntegrationⅢ.17 DimensionⅢ.18 DistributionsⅢ.19 DualityⅢ.20 Dynamical Systems and ChaosⅢ.21 Elliptic CurvesⅢ.22 The Euclidean Algorithm and Continued FractionsⅢ.23 The Euler and Navier-Stokes EquationsⅢ.24 ExpandersⅢ.25 The Exponential and Logarithmic FunctionsⅢ.26 The Fast Fourier TransformⅢ.27 The Fourier TransformⅢ.28 Fuchsian GroupsⅢ.29 Function SpacesⅢ.30 Galois GroupsⅢ.31 The Gamma FunctionⅢ.32 Generating FunctionsⅢ.33 GenusⅢ.34 GraphsⅢ.35 HamiltoniansⅢ.36 The Heat EquationⅢ.37 Hilbert SpacesⅢ.38 Homology and CohomologyⅢ.39 Homotopy GroupsⅢ.40 The Ideal Class GroupⅢ.41 Irrational and Transcendental NumbersⅢ.42 The Ising ModelⅢ.43 Jordan NormaI FormⅢ.44 Knot PolynomialsⅢ.45 K-TheoryⅢ.46 The Leech latticeⅢ.47 L-FunctionsⅢ.48 Lie TheoryⅢ.49 Linear and Nonlinear Waves and SolitonsⅢ.50 Linear Operators and Their PropertiesⅢ.51 Local and Global in Number TheoryⅢ.52 The Mandelbrot SetⅢ.53 ManifoldsⅢ.54 MatroidsⅢ.55 Measures……PartⅤ Theorems and ProblemsPartⅥ MathematiciansPartⅦ The Influence of MathematicsPartⅧ Final PerspectivesIndex