دانلود کتاب Introduction to Mathematical Thinking

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Contents......Page 4
Preface......Page 6
What this book is about......Page 8
1.1 More than arithmetic......Page 14
1.2 Mathematical notation......Page 17
1.3 Modern college-level mathematics......Page 19
1.4 Why do you have to learn this stuff?......Page 23
2 Getting precise about language......Page 26
2.1 Mathematical statements......Page 27
2.2 The logical combinators and, or, and not......Page 33
2.3 Implication......Page 42
2.4 Quantifiers......Page 59
3.1 What is a proof?......Page 78
3.2 Proof by contradiction......Page 81
3.3 Proving conditionals......Page 84
3.4 Proving quantified statements......Page 87
3.5 Induction proofs......Page 90
4.1 The integers......Page 99
4.2 The real numbers......Page 110
4.3 Completeness......Page 113
4.4 Sequences......Page 118
Appendix: Set theory......Page 123
Index......Page 130