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泰勒斯的遗产 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

泰勒斯的遗产 英文
  • W.S.Anglin，J.Lambek编著 著
  • 出版社： 北京：清华大学出版社
  • ISBN：9787302214830
  • 出版时间：2009
  • 标注页数：331页
  • 文件大小：9MB
  • 文件页数：346页
  • 主题词：数学史－高等学校－教材－英文；数学哲学－高等学校－教材－英文

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图书目录

0 Introduction1

PART Ⅰ：History and Philosophy of Mathematics5

1 Egyptian Mathematics7

2 Scales of Notation11

3 Prime Numbers15

4 Sumerian-Babylonian Mathematics21

5 More about Mesopotamian Mathematics25

6 The Dawn of Greek Mathematics29

7 Pythagoras and His School33

8 Perfect Numbers37

9 Regular Polyhedra41

10 The Crisis of Incommensurables47

11 From Heraclitus to Democritus53

12 Mathematics in Athens59

13 Plato and Aristotle on Mathematics67

14 Constructions with Ruler and Compass71

15 The Impossibility of Solving the Classical Problems79

16 Euclid83

17 Non-Euclidean Geometry and Hilbert's Axioms89

18 Alexandria from 300 BC to 200 BC93

19 Archimedes97

20 Alexandria from 200 BC to 500 AD103

21 Mathematics in China and India111

22 Mathematics in Islamic Countries117

23 New Beginnings in Europe121

24 Mathematics in the Renaissance125

25 The Cubic and Quartic Equations133

26 Renaissance Mathematics Continued139

27 The Seventeenth Century in France145

28 The Seventeenth Century Continued153

29 Leibniz159

30 The Eighteenth Century163

31 The Law of Quadratic Reciprocity169

PART Ⅱ：Foundations of Mathematics173

1 The Number System175

2 Natural Numbers(Peano's Approach)179

3 The Integers183

4 The Rationals187

5 The Real Numbers191

6 Complex Numbers195

7 The Fundamental Theorem of Algebra199

8 Quaternions203

9 Quaternions Applied to Number Theory207

10 Quaternions Applied to Physics211

11 Quaternions in Quantum Mechanics215

12 Cardinal Numbers219

13 Cardinal Arithmetic223

14 Continued Fractions227

15 The Fundamental Theorem of Arithmetic231

16 Linear Diophantine Equations233

17 Quadratic Surds237

18 Pythagorean Triangles and Fermat's Last Theorem241

19 What Is a Calculation?245

20 Recursive and Recursively Enumerable Sets251

21 Hilbert's Tenth Problem255

22 Lambda Calculus259

23 Logic from Aristotle to Russell265

24 Intuitionistic Propositional Calculus271

25 How to Interpret Intuitionistic Logic277

26 Intuitionistic Predicate Calculus281

27 Intuitionistic Type Theory285

28 G？del's Theorems289

29 Proof of G？del's Incompleteness Theorem291

30 More about G？del's Theorems293

31 Concrete Categories295

32 Graphs and Categories297

33 Functors299

34 Natural Transformations303

35 A Natural Transformation between Vector Spaces307

References311

Index321

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