- 作 者：PamelaGorkin等编著
- 出 版 社：北京：清华大学出版社
- 出版年份：2009
- ISBN：9787302214854
- 标注页数：398 页
- PDF页数：417 页
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The How,When,and Why of Mathematics 1
Spotlight:George Pólya 10
Tips on Doing Homework 14
2 Logically Speaking 17
3 Introducing the Contrapositive and Converse 31
4 Set Notation and Quantifiers 39
Tips on Quantification 51
5 Proof Techniques 53
Tips on Definitions 61
6 Sets 63
Spotlight:Paradoxes 72
7 Operations on Sets 79
8 More on Operations on Sets 89
9 The Power Set and the Cartesian Product 97
Tips on Writing Mathematics 106
10 Relations 109
Tips on Reading Mathematics 115
11 Partitions 119
Tips on Putting It All Together 127
12 Order in the Reals 129
Tips:You Solved It.Now What? 144
13 Functions,Domain,and Range 147
Spotlight:The Definition of Function 157
14 Functions,One-to-One,and Onto 163
15 Inverses 175
16 Images and Inverse Images 191
Spotlight:Minimum or Infimum 199
17 Mathematical Induction 207
18 Sequences 223
19 Convergence of Sequences of Real Numbers 237
20 Equivalent Sets 251
21 Finite Sets and an Infinite Set 261
22 Countable and Uncountable Sets 271
23 Metric Spaces 283
24 Getting to Know Open and Closed Sets 297
25 Modular Arithmetic 313
26 Fermat's Little Theorem 331
Spotlight:Public and Secret Research 337
27 Projects 343
Tips on Talking about Mathematics 343
27.1 Picture Proofs 346
27.2 The Best Number of All 348
27.3 Set Constructions 350
27.4 Rational and Irrational Numbers 353
27.5 Irrationality of e and π 355
27.6 When Does f-1=1/f? 358
27.7 Pascal's Triangle 360
27.8 The Cantor Set 362
27.9 The Cauchy-Bunyakovsky-Schwarz Inequality 366
27.10 Algebraic Numbers 368
27.11 The RSA Code 371
Spotlight:Hilbert's Seventh Problem 374
28 Appendix 379
28.1 Algebraic Properties of R 379
28.2 Order Properties of R 380
28.3 Pólya's List 382
References 383
Index 389