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书名 泰勒斯的遗产(Springer大学数学图书影印版)
分类 科学技术-自然科学-数学
作者 (美)安格林//兰贝克
出版社 清华大学出版社
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简介
编辑推荐

该书的基本内容是数学的历史和数学的哲学。数学历史是该书的线索,数学是内容的主体,引申到的是数学哲学。它不是一本史论型的著作,而是采用专题式编写方式,每个专题相对独立,所以比较易读、易懂,是本科生学习数学过程中非常好的课外读物。

内容推荐

本书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。

本书以数学历史为线索,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。

目录

Preface ix

 0 Introduction 1

PART I: History and Philosophy of Mathematics 5

 1 Egyptian Mathematics 7

 2 Scales of Notation 11

 3 Prime Numbers 15

 4 Sumerian-Babylonian Mathematics 21

 5 More about Mesopotamian Mathematics 25

 6 The Dawn of Greek Mathematics 29

 7 PVthagoras and His School 33

 8 Perfect Numbers 37

 9 Regular Polyhedra 41

 10 The Crisis of incommensurables 47

 11 Whom Heraclitus to Democritus 53

 12 Mathematics in Athens 59

 13 Plato and Aristotle on Mathematics 67

 14 Constructions with Ruler and Compass 71

 15 The Impossibility of Solving the Classical Problems 79

 16 Euclid 83

 17 Non-Euclidean Geometry and Hilbert's Axioms 89

 18 Alexandria from 3o0 BC to 20O BC 93

 19 Archimedes 97

 ZO Alexandria from 200 BC to 500 AD 103

 21 Mathematics in China and india 111

 22 Mathematics in Islamic Countries 117

 23 New Beginnings in Europe 121

 24 Mathematics in the Renaissance 125

 25 The Cubic and Quartic Equations 133

 26 Renaissance Mathematics Continued 139

 27 The Seventeenth Century in dance 145

 28 The Seventeenth Century Continued 153

 29 Leibniz 159

 30 The Eighteenth Century 163

 31 The Law of Quadratic Reciprocity 169

PART II: FOundations of Mathematics 173

 1 The Number System 175

 2 Natural Numbers (Peano's Approach) 179

 3 The integers 183

 4 The auctionals 187

 5 The Real Numbers 191

 6 Complex Numbers 195

 7 The Fundamental Theorem of Algebra 199

 8 Quaternions 2O3

 9 Quaternions Applied to Number Theory 207

 10 Quaternions Applied to Physics 211

 11 Quaternions in Quantum Mechanics 215

 12 Cardinal Numbers 219

 13 Cardinal Arithmetic 223

 14 Continued "actions 227

 15 The Fundamental Theorem of Arithmetic 231

 16 Linear Diophantine Equations 233

 17 Quadratic Surds 237

 18 Pythagorean triangles and Fermat's Last Theorem 241

 19 What is a Calculation? 245

 20 Recursive and Recursively Enumerable Sets 251

 21 Hilbert's Tenth Problem 255

 22 Lambda Calculus 259

 23 Logic from Aristotle to Russell 265

 24 Intuitionistic Propositional Calculus 271

 25 How to interpret intuitionistic Logic 277

 26 Intuitionistic Predicate Calculus 281

 27 Intuitionistic Type Theory 285

 28 Godel's Theorems 289

 29 Proof of G5del's incompleteness Theorem 291

 30 More about G5del's Theorems 293

 31 Concrete Categories 295

 32 Graphs and Categories 297

 33 Functors 299

 34 Natural transformations 303

 35 A Natural transformation between Vector Spaces 307

References 311

Index 321

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