The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

Prologue ixContinuity (1974-75) 1
Pursuit (1976) 8
Relativity (1977) 13
Irrationality (1978-79) 23
Shifts (1980-89) 34
Proof on a Place Mat (March 1989) 42
The Monk and the Mountain (1989-90) 71
Randomness (1990-91) 84
Infinity and Limits (1991) 94
Chaos (1992-95) 107
Celebration (1996-99) 115
The Path of Quickest Descent (2000-2003) 118
Bifurcation (2004) 128
Hero's Formula (2005-Present) 140
Acknowledgments 155
Further Reading 157
Bibliography 161
Photography Credits 163
Index of Math Problems 165