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
……

5 Functions
6 Relations
7 Cardinahty
8 The Real Numbers
9 Probability and Randomness
10 Algebra and Symmetry
11 Projects

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