Preface to Instructors
What Kind of Book Is This?
How Can One Teach from This Book?
Preface to Students
Who Is This Book Written For?
How Can One Learn from This Book?
Acknowledgments
Contents
Part I What's Mathematics?
1 Let's Play a Game!
Problems
2 What's the Name of the Game?
Problems
3 How to Make a Statement
Problems
4 What's True in Mathematics?
Problems
A Ten Famous Conjectures
Problems and Assignments
B Ten Famous Theorems
Problems and Assignments
Part II The Foundations of Mathematics
5 Let's Be Logical!
Problems
6 Setting Examples
Problems
7 Quantifier Mechanics
Problems
8 Let's Be Functional!
Problems
C The Foundations of Set Theory
Problems and Assignments
Part III How to Prove It
9 Universal Proofs
Problems
10 The Domino Effect
Problems
11 More Domino Games
Problems
12 Existential Proofs
Problems
D Ten Famous Problems
Problem 1: Nobody Knows Nothing!
Problem 2: Mathematical Survivor
Problem 3: From the White House
Problem 4: The Towers of Hanoi
Problem 5: Checkerboard Tilings and Primino Numbers
Problem 6: Watching Your Weights
Problem 7: Some Are Sums
Problem 8: A Really ``Mean'' Problem
Problem 9: Waring's Problem with Negativity
Problem 10: Coloring Lines, Planes, and Space
Part IV Advanced Math for Beginners
13 Mathematical Structures
Problems
14 Working in the Fields (and Other Structures)
Problems
15 Group Work
Problems
16 Good Relations
Problems
17 Order, Please!
Problems
18 Now That's the Limit!
Problems
19 Sizing It Up
Problems
20 Infinite Delights
Problems
21 Number Systems Systematically
Problems
22 Games Are Valuable!
Problems
E Graphic Content
Problems and Assignments
F All Games Considered
Problems and Assignments
G A Top Forty List of Math Theorems
Index