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Preface

1 Let's Play£¡
1£®1 A Direct Approach
1£®2 Fibonacci Numbers and the Golden Ratio
1£®3 Inductive Reasoning
1£®4 Natural Numbers and Divisibility
1£®5 The Primes
1£®6 The Integers
1£®7 The Rationals£¬ the Reals£¬ and the Square Root of 2
1£®8 End-of-Chapter Exercises

2 Discovering and Presenting Mathematics
2£®1 Truth£¬ Tabulated
2£®2 Valid Arguments and Direct Proofs
2£®3 Proofs by Contradiction
2£®4 Converse and Contrapositive
2£®5 Quantifiers
2£®6 Induction
2£®7 Ubiquitous Terminology
2£®8 The Process of Doing Mathematics
2£®9 Writing Up Your Mathematics
2£®10 End-of-Chapter Exercises

3 Sets
3£®1 Set Builder Notation
3£®2 Sizes and Subsets
3£®3 Union£¬ Intersection£¬ Difference£¬ and Complement
3£®4 Many Laws and a Few Proofs
3£®5 Indexing
3£®6 Cartesian Product
3£®7 Power
3£®8 Counting Subsets
3£®9 A Curious Set
3£®10 End-of-Chapter Exercises

4 The Integers and the Fundamental Theorem of Arithmetic
4£®1 The Well-Ordering Principle and Criminals
4£®2 Integer Combinations and Relatively Prime Integers
4£®3 The Fundamental Theorem of Arithmetic
4£®4 LCM and GCD
4£®5 Numbers and Closure
4£®6 End-of-Chapter Exercises
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5 Functions
6 Relations
7 Cardinahty
8 The Real Numbers
9 Probability and Randomness
10 Algebra and Symmetry
11 Projects

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