数学的读写和证明

图书信息数学的读写和证明

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作者： （美）德普，（美）高更著

出 版 社： 清华大学出版社

出版时间： 2009-11-1

开本： 16开

I S B N ： 9787302214854

定价：￥54.00

内容简介本书详细讨论数学的读写和证明，将学习数学的过程在某种意义下程序化，以使学习者培养出极好的学习习惯，以及学会如何应付面对的问题。本书对初学高等数学的读者来说特别有意义。

目录Contents

Preface Xi

1 The How,wnen. and Why of Mathematics

Spotlight: George P61ya

Tips on Doing Homework

2 Logically Speaking

3 Introducing the contrapositivc and Converse

4 Set Notation and opantificrs

Tips on Quantification

5 Proof Techniques

Tips on Definitions

6 Sets

Spotlight:Paradoxs

7 Operations on Sets

8 More on Operations on Sets

9 The Power Set and the Cartesian Product

Tips on Writing Mathematics

10 Relations

Tips on Reading Mathematics

11 Partitions

Tips on Putting It All Together

12 Order in the Reals

Tips:You Solved It Now What?

13 Functions, Domain, and Range

Spotlight:The Definition of Function

14 Functions, One-to-One, and Onto

15 Inverses

16 Images and Inverse Images

Spotlight. Minimum or Infimum

17 Mathematical Induction

……

18 Sequences

19 Convergence of Sequences of Real Numbers

20 Equivalent Sets

21 Finite Sets and an Infinite Set

22 Countable and Uncountable Sets

23 Metric Spaces

24 Getting to Know Open and Closed Sets

25 Modular Arithmetic

26 Fermat's Little Theorem

27 Projects

28 Appendix

References

Index