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