By Steven H. Strogatz

**Publish yr note:** First released July fifth 2009

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*The Calculus of Friendship* is the tale of a unprecedented connection among a instructor and a scholar, as chronicled via greater than thirty years of letters among them. What makes their courting detailed is that it's dependent virtually fullyyt on a shared love of calculus. For them, calculus is greater than a department of arithmetic; it's a video game they love taking part in jointly, a relentless whilst all else is in flux. the trainer is going from the leading of his profession to retirement, competes in whitewater kayaking on the foreign point, and loses a son. the coed matures from highschool math whiz to Ivy League professor, suffers the surprising dying of a father or mother, and errors right into a marriage destined to fail. but via all of it they take shelter within the haven of calculus--until an afternoon comes whilst calculus is not any longer enough.

Like calculus itself, *The Calculus of Friendship* is an exploration of swap. It's concerning the transformation that happens in a student's middle, as he and his instructor opposite roles, as they age, as they're buffeted by way of existence itself. Written via a popular instructor and communicator of arithmetic, *The Calculus of Friendship* is hot, intimate, and deeply relocating. the main inspiring principles of calculus, differential equations, and chaos idea are defined via metaphors, photos, and anecdotes in a fashion that every one readers will locate appealing, or even poignant. Math lovers, from highschool scholars to pros, will get pleasure from the offbeat difficulties and lucid reasons within the letters.

For an individual whose lifestyles has been replaced through a mentor, *The Calculus of Friendship* might be an unforgettable trip.

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**Example text**

Following Ed’s lead, it was the first time I ever treated Mr. Joffray as a kind of friend, approachable on almost equal terms. Ed certainly acted that way toward him, so why shouldn’t I? Joff cooked hamburgers for all of us and seemed so pleased to see us both, delighted that we’d made the drive down from Boston. We spent a few happy hours playing with his programmable calculator, showing him how to explore chaos, which was then the hottest subject in science. Looking at the graying Xerox copy of that third item in the folder—a news clipping about some research I’d done— I’m confused about the chronology.

For one thing, it looks weird to be taking the sine function of whole numbers like 1, 2, 3. Normally, we take sine functions of angles, and those are typically simple fractions of p (or 1808), like p=2 or p=4. Sine of 1 or 2, without any p’s in them, looks bizarre. The more serious twist, though, is that the sine function oscillates. It can be positive or negative. It’s a wave, bobbling up and down. This means that some of the terms in the series will be positive (like sin1 1 and sin2 2Þ; while others will be negative (like sin4 4 and sin5 5).

You’re taught various rules to determine if a given series converges or diverges, and it’s easy to lose sight of how amazing all this is, how mind-boggling. Proof on a Place Mat (March 1989) 45 You’re being asked to think about an infinite number of numbers added together. Infinity, right there on the page in front of you. But with calculus, you can handle it nevertheless. There was a twist, however, in this particular question. The sin k is unusual. You never see that in a first course in calculus.