圖書信息
出版社: 清華大學出版社; 第1版 (2009年
外文書名: The Heritage of Thales
叢書名: Springer 大學數學圖書
平裝: 327頁
正文語種: 英語
開本: 16
ISBN: 9787302214830
條形碼: 9787302214830
尺寸: 24.4 x 17.2 x 1.6 cm
重量: 558 g
作者簡介
作者：(美國)安格林(W.S.Anglin) (美國)蘭貝克(J.Lambek)
內容簡介
《泰勒斯的遺產》以專題方式講述數學的歷史和數學的哲學（非史論型著作），每個專題相對獨立。《泰勒斯的遺產》以數學歷史為線索，以數學為內容主體，以數學哲學為引申，易讀、易懂，是本科生學習數學過程中非常好的課外讀物。
目錄
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
