怎样证明数学题(英文版•第2版)
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图灵原版数学统计学系列

怎样证明数学题(英文版•第2版)

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本书介绍了数学证明的基本要点,内容通俗而不失严谨,可以帮助高中以上程度的学生熟悉数学语言,迈入数学殿堂.新版添加了200多个练习题,附录中给出部分练习的答案或提示.
本书适用于任何对逻辑和证明感兴趣的人,数学、计算机科学、哲学、语言学专业的读者都可以从中获益匪浅.

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出版信息

  • 书  名怎样证明数学题(英文版•第2版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2009-07-10
  • 书  号978-7-115-20968-9
  • 定  价59.00 元
  • 页  数396
  • 开  本16开
  • 出版状态终止销售
  • 原书名How to Prove It: A Structured Approach
  • 原书号0-521-67599-5

同系列书

目录

Preface to the Second Edition page ix
Preface xi
Introduction 1
1 Sentential Logic 8
1.1 Deductive Reasoning and Logical Connectives 8
1.2 Truth Tables 14
1.3 Variables and Sets 26
1.4 Operations on Sets 34
1.5 The Conditional and Biconditional Connectives 43
2 Quantificational Logic 55
2.1 Quantifiers 55
2.2 Equivalences Involving Quantifiers 64
2.3 More Operations on Sets 73
3 Proofs 84
3.1 Proof Strategies 84
3.2 Proofs Involving Negations and Conditionals 95
3.3 Proofs Involving Quantifiers 108
3.4 Proofs Involving Conjunctions and Biconditionals 124
3.5 Proofs Involving Disjunctions 136
3.6 Existence and Uniqueness Proofs 146
3.7 More Examples of Proofs 155
4 Relations 163
4.1 Ordered Pairs and Cartesian Products 163
4.2 Relations 171
4.3 More About Relations 180
10 Contents
4.4 Ordering Relations 189
4.5 Closures 202
4.6 Equivalence Relations 213
5 Functions 226
5.1 Functions 226
5.2 One-to-one and Onto 236
5.3 Inverses of Functions 245
5.4 Images and Inverse Images: A Research Project 255
6 Mathematical Induction 260
6.1 Proof by Mathematical Induction 260
6.2 More Examples 267
6.3 Recursion 279
6.4 Strong Induction 288
6.5 Closures Again 300
7 Infinite Sets 306
7.1 Equinumerous Sets 306
7.2 Countable and Uncountable Sets 315
7.3 The Cantor–Schr¨oder–Bernstein Theorem 322
Appendix 1: Solutions to Selected Exercises 329
Appendix 2: Proof Designer 373
Suggestions for Further Reading 375
Summary of Proof Techniques 376
Index 381
  • 本书第3版将于2019年10月31日出版,见:
    https://www.amazon.com/dp/1108439535
    https://book.douban.com/subject/30481689
    空军  发表于 2019-03-05 12:39:17
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