內容簡介
本書詳細討論數學的讀寫和證明，將學習數學的過程在某種意義下程式化，以使學習者培養出極好的學習習慣，以及學會如何應付面對的問題。本書對初學高等數學的讀者來說特別有意義。
目錄
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
