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商品名称：数学指南（英文版）格沃斯研究数学专业教材数学工具和词汇数学竞赛书籍世界图书出版公司9787510050688

商品编号：590356617945

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重量：0.000千克

上架时间：2021-11-04 11:13:46

ISBN编号：9787510050688

书名：数学指南,数学指南

产品名称：数学指南

作者：(美)格沃斯

出版社名称：世界图书出版公司

定价：199.00元

开本：16开

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基本信息图书名称：数学指南（英文版）作者：格沃斯定价： 199.00 ISBN号： 9787510050688 出版社： SJ图书出版公司开本： 16 装帧：平装内容介绍《数学指南（英文版）》主要内容包括：Preface、Contributors、Introduction、The Origins of Modern Mathematics、Mathematical Concepts、Theorems and Problems、Mathematicians、The Influence of Mathematics、Final Perspectives等。《数学指南(英文)》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SJ**数学家专门为这本《数学指南(英文)》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 ...

基本信息

图书名称：

数学指南（英文版）

作者：

格沃斯

定价：

199.00

ISBN号：

9787510050688

出版社：

SJ图书出版公司

开本：

装帧：

平装

内容介绍

《数学指南（英文版）》主要内容包括：Preface、Contributors、Introduction、The Origins of Modern Mathematics、Mathematical Concepts、Theorems and Problems、Mathematicians、The Influence of Mathematics、Final Perspectives等。

《数学指南(英文)》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SJ**数学家专门为这本《数学指南(英文)》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**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。

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

精彩书摘

It is worth noting that Euclid himself was probably well aware that the parallel postulate was awkward. It asserts a property of straight lines that seems to have made Greek mathematicians and philosophers uncomfortable， and this may be why its appearance in the Elements is delayed until proposition 29 of Book I. The commentator Proclus （fifth century C.E.），in his extensive discussion of Book I of the Elements， observed that the hyperbola and asymptote get closer and closer as they move outwards， but they never meet. lf a line and a curve can do this， why not two lines? The matter needs further analysis. Unfortunately， not much of the Elements would be left： if mathematicians dropped the parallel postulate and retreated to the consequences of the remaining definitions： a significant body of knowledge depends on it. Most notably， the parallel postulate is needed to prove that the angles in a triangle add up to two right angles-a crucial result in establishing many other theorems about angles in figures， including the Pythagorean theorem.
Whatever claims educators may have made about Euclid's Elements down the ages， a significant number of experts knew that it was an unsatisfactory compromise： a useful and remarkably rigorous theory could be had， but only at the price of accepting the parallel postulate. But the parallel postulate was difficult to accept on trust： it did not have the same intuitively obvious feel of the other axioms and there was no obvious way of verifying it. The higher one's standards， the more painful this compromise was. What， the experts asked， was to be done?
One Greek discussion must suffice here. In Proclus's view， if the truth of the parallel postulate was not obvious， and yet geometry was bare without it， then the only possibility was that it was true because it was a theorem， And so he gave it a proof. He argued as follows. Let two lines m and n cross a third line k at P and Q， respectively， and make angles with it that add up to two right angles. Now draw a line I that crosses m at P and enters the space between the lines m and n. The distance between I and m as one moves away from the point P continually increases， said Proclus， and therefore line I must eventually cross line n.
Proclus's argument is flawed. The flaw is subtle， and sets us up for what is to come. He was correct that the distance between the lines 1 and m increases indefinitely. But his argument assumes that the distance between lines m and n does not also increase indefinitely， and is instead bounded. Now Proclus knew very well that if the parallel postulate is granted， then it can be shown that the lines m and n are parallel and that the distance between them is a constant. But until the parallel postulate is proved， nothing prevents one saying that the lines m and n diverge. Proclus's proof does not therefore work unless one can show that lines that do not meet also do not diverge.
……

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