泰勒斯的遗产(影印版)(Springer大学数学图书)(The Heritage of Thales)
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品牌: 安格林(W.S.Anglin)
基本信息·出版社：清华大学出版社
·页码：327 页
·出版日期：2009年11月
·ISBN：9787302214830
·条形码：9787302214830
·版本：第1版
·装帧：平装
·开本：16
·正文语种：英语
·丛书名：Springer大学数学图书
·外文书名：The Heritage of Thales
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内容简介《泰勒斯的遗产》以专题方式讲述数学的历史和数学的哲学（非史论型著作），每个专题相对独立。《泰勒斯的遗产》以数学历史为线索，以数学为内容主体，以数学哲学为引申，易读、易懂，是本科生学习数学过程中非常好的课外读物。
编辑推荐《泰勒斯的遗产》：Springer大学数学图书:影印版
目录
Preface
0 Introduction
PART Ⅰ: History and Philosophy of Mathematics
1 Egyptian Mathematics
2 Scales of Notation
3 Prime Numbers
4 Sumerian-Babylonian Mathematics
5 More about Mesopotamian Mathematics
6 The Dawn of Greek Mathematics
7 Pythagoras and His School
8 Perfect Numbers
9 Regular Polyhedra
10 The Crisis of Incommensurables
11 From Heraclitus to Democritus
12 Mathematics in Athens
13 Plato and Aristotle on Mathematics
14 Constructions with Ruler and Compass
15 The Impossibility of Solving the Classical Problems
16 Euclid
17 Non-Euclidean Geometry and Hilbert's Axioms
18 Alexandria from 300 BC to 200 BC
19 Archimedes
20 Alexandria from 200 BC to 500 AD
21 Mathematics in China and India
22 Mathematics in Islamic Countries
23 New Beginnings in Europe
24 Mathematics in the Renaissance
25 The Cubic and Quartic Equations
26 Renaissance Mathematics Continued
27 The Seventeenth Century in France
28 The Seventeenth Century Continued
29 Leibniz
30 The Eighteenth Century
31 The Law of Quadratic Reciprocity
PART Ⅱ: Foundations of Mathematics
1 The Number System
2 Natural Numbers (Peano's Approach)
3 The Integers
4 The Rationals
5 The Real Numbers
6 Complex Numbers
7 The Fundamental Theorem of Algebra
8 Quaternions
9 Quaternions Applied to Number Theory
10 Quaternions Applied to Physics
11 Quaternions in Quantum Mechanics
12 Cardinal Numbers
13 Cardinal Arithmetic
14 Continued Fractions
15 The Fundamental Theorem of Arithmetic
16 Linear Diophantine Equations
17 Quadratic Surds
18 Pythagorean Triangles and Fermat's Last Theorem
19 What Is a Calculation?
20 Recursive and Recursively Enumerable Sets
21 Hilbert's Tenth Problem
22 Lambda Calculus
23 Logic from Aristotle to Russell
24 Intuitionistic Propositional Calculus
25 How to Interpret Intuitionistic Logic
26 Intuitionistic Predicate Calculus
27 Intuitionistic Type Theory
28 Godel's Theorems
29 Proof of GSdel's Incompleteness Theorem
30 More about Godel's Theorems
31 Concrete Categories
32 Graphs and Categories
33 Functors
34 Natural Transformations
35 A Natural Transformation between Vector Spaces
References
Index
……[看更多目录]
序言在学校教书多年，当学生（特别是本科生）问有什么好的参考书时，我们所能推荐的似乎除了教材还是教材，而且不同教材之间的差别并不明显、特色也不鲜明。所以多年前我们就开始酝酿，希望为本科学生引进一些好的参考书，为此清华大学数学科学系的许多教授与清华大学出版社共同付出了很多心血。
这里首批推出的十余本图书，是从Springer出版社的多个系列丛书中精心挑选出来的。在丛书的筹划过程中，我们挑选图书最重要的标准并不是完美，而是有特色并包容各个学派（有些书甚至有争议，比如从数学上看也许不够严格），其出发点是希望我们的学生能够吸纳百家之长；同时，在价格方面，我们也做了很多工作，以使得本系列丛书的价格能让更多学校和学生接受，使得更多学生能够从中受益。
本系列图书按其定位，大体有如下四种类型（一本书可以属于多类，但这里限于篇幅不能一一介绍）。
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Pythagoras and His School
Pythagoras （570-500 BC） was born in Samoa, a Greek island off the coast of what is now Turkey. According to ancient sources （Iamblichus, Porphyry and Diogenes Liberties）, he traveled and studied in the Persian empire, which extended then from northern Greece to the Indus Valley and included ancient Mesopotamia. We know （Plimpton 322） that the Babyloni- ans understood what is now called the 'theorem of Pythagoras', although the latter may have given the first proof. Pythagoras may have learned the theory of 'Pythagorean triangles' from the Babylonians. According to the above mentioned sources, Pythagoras also studied under the Zoroastrian priests, the so-called 'Magi'. However, judging from his belief in reincarnation and his vegetarianism, it is more likely that he was influenced by Hindu tradition. Even his mathematics has an Indian flavour. About 525 BC, Pythagoras emigrated to Croton （modern Crotone） in southern Italy, where he founded a society, half-way between a political party and a religious cult, which came to be known as the 'Pythagorean Brotherhood.' Some members of this society were admitted to an inner circle consisting of the so-called 'mathematicians'. The word 'mathematics' was in fact introduced by Pythagoras. The first part of this word is an old Indo-European root, related to the English word 'mind'. The modern meaning of 'mathematics' is due to Aristotle.
