Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, USA and a well known popularizer of mathematics (along the lines of another great mathematics teacher Ian Stewart). I loved Strogatz's book Sync (2003) which dealt with the topic of synchronization of complex systems in a very readable manner. His research focuses on chaos and complexity and he is famous for coauthoring a 1998 Nature paper on "small-world" networks.
In his book The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math (2009), Strogatz explores the thirty year correspondence he maintained with his high school math teacher Don Joffray.
Strogatz paints a memorable picture of his teacher: a humble, unpretending man. As Strogatz says: "One thing about him was unlike any other teacher I'd ever had: he worshipped some of his former students. He'd tell stories about them, legends that made them sound like Olympian figures, gods of mathematics. In my own case, he was more of a fan than a teacher, always marveling at what problems I could invent and solve. It felt slightly strange to be so admired by my own teacher. But I can't say I minded it."
While Joffray stayed on in the school Loomis Chaffee well into his sixties, Strogatz went from height to height: BA (summa cum laude) from Princeton, a Marshall Scholar at Trinity College, Cambridge and then a PhD from Harvard. He began his academic career at MIT in 1989, moving on to Cornell in 1994. He became something of a rockstar mathematician after publication of his books Nonlinear Dynamics and Chaos and Sync.
Strogatz stayed in touch with his teacher Joffray after high school sending him interesting math problems that his teacher might enjoy. Joffray would write asking for help with a difficult problem, typically one posed by some student in his class.
As Strogatz happily puts it: "When one of these letter arrived in the mail, I stopped whatever I was doing to see if I could help. For one thing, they posed fascinating little questions, beautiful excursions off the beaten track of calculus. But maybe more importantly, they gave me a chance to explain math to someone who loved learning it, the best student any teacher could have, someone with perfect preparation and an evident sense of delight and gratitude."
The letters spanning over three decades are mostly about math (personal pains are put on the backburner). But they can be read by someone with a twelfth grade education in science and math. For the most part, the letters deal with fundamental problems in trigonometry and calculus.
For instance, they discuss the irrationality of the square root of 2. Strogatz provides not only the conventional algebraic proof of this (by contradiction) but also a charming geometric proof. The ancient Pythagoreans thought that the universe could be explained completely by whole numbers and their ratios (i.e. by rational numbers). So when it was found that the square root of 2 is not rational, it came as a great shock to them. Legend has it that the person who discovered this fact was killed by the members of the Pythagorean cult.
The letters cover a wide gamut of math: Fibonacci series, chase problems, Feynman's technique of differentiating under the integral sign, dimensional analysis, cycloids, Zeno's paradox, Hero's formula etc. All the discussion is such that any student of science or engineering can follow.
While Strogatz was doing groundbreaking research in chaos theory and complex network theory in this period, he does not allow it intrude in his letters. His letters remain at a level that his high school teacher could understand. Joffray would take the lead from the letters and pose the problems to his math classes which resulted in very challenging and exciting discussions.
Some of Strogatz's techniques of solutions are so clever and innovative that they made my head spin and my imagination boggle. The integral formulation of factorials of fractions (the gamma function as it is called) was well presented. It made me think of all the fun I was missing out on (But on second thoughts, chemical engineering - the subject I teach - is not without its delights).
Strogatz concludes on an emotional note:
"While writing this book, I've been thinking a lot about what I learned from Joff. For years I would have said, not much, meaning not much math. That was true even in high school. But I'm starting to realize what it was that he gave me.
"He let me teach him.
"Before I had any students, he was my student.
"Somehow he knew that's what I needed most. And he let me, and encourage me, and helped me. Like all great teachers do."
A fitting tribute from a student to his teacher and a wonderful book to read and cherish for students and teachers alike.
In his book The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math (2009), Strogatz explores the thirty year correspondence he maintained with his high school math teacher Don Joffray.
Strogatz paints a memorable picture of his teacher: a humble, unpretending man. As Strogatz says: "One thing about him was unlike any other teacher I'd ever had: he worshipped some of his former students. He'd tell stories about them, legends that made them sound like Olympian figures, gods of mathematics. In my own case, he was more of a fan than a teacher, always marveling at what problems I could invent and solve. It felt slightly strange to be so admired by my own teacher. But I can't say I minded it."
While Joffray stayed on in the school Loomis Chaffee well into his sixties, Strogatz went from height to height: BA (summa cum laude) from Princeton, a Marshall Scholar at Trinity College, Cambridge and then a PhD from Harvard. He began his academic career at MIT in 1989, moving on to Cornell in 1994. He became something of a rockstar mathematician after publication of his books Nonlinear Dynamics and Chaos and Sync.
Strogatz stayed in touch with his teacher Joffray after high school sending him interesting math problems that his teacher might enjoy. Joffray would write asking for help with a difficult problem, typically one posed by some student in his class.
As Strogatz happily puts it: "When one of these letter arrived in the mail, I stopped whatever I was doing to see if I could help. For one thing, they posed fascinating little questions, beautiful excursions off the beaten track of calculus. But maybe more importantly, they gave me a chance to explain math to someone who loved learning it, the best student any teacher could have, someone with perfect preparation and an evident sense of delight and gratitude."
The letters spanning over three decades are mostly about math (personal pains are put on the backburner). But they can be read by someone with a twelfth grade education in science and math. For the most part, the letters deal with fundamental problems in trigonometry and calculus.
For instance, they discuss the irrationality of the square root of 2. Strogatz provides not only the conventional algebraic proof of this (by contradiction) but also a charming geometric proof. The ancient Pythagoreans thought that the universe could be explained completely by whole numbers and their ratios (i.e. by rational numbers). So when it was found that the square root of 2 is not rational, it came as a great shock to them. Legend has it that the person who discovered this fact was killed by the members of the Pythagorean cult.
The letters cover a wide gamut of math: Fibonacci series, chase problems, Feynman's technique of differentiating under the integral sign, dimensional analysis, cycloids, Zeno's paradox, Hero's formula etc. All the discussion is such that any student of science or engineering can follow.
While Strogatz was doing groundbreaking research in chaos theory and complex network theory in this period, he does not allow it intrude in his letters. His letters remain at a level that his high school teacher could understand. Joffray would take the lead from the letters and pose the problems to his math classes which resulted in very challenging and exciting discussions.
Some of Strogatz's techniques of solutions are so clever and innovative that they made my head spin and my imagination boggle. The integral formulation of factorials of fractions (the gamma function as it is called) was well presented. It made me think of all the fun I was missing out on (But on second thoughts, chemical engineering - the subject I teach - is not without its delights).
Strogatz concludes on an emotional note:
"While writing this book, I've been thinking a lot about what I learned from Joff. For years I would have said, not much, meaning not much math. That was true even in high school. But I'm starting to realize what it was that he gave me.
"He let me teach him.
"Before I had any students, he was my student.
"Somehow he knew that's what I needed most. And he let me, and encourage me, and helped me. Like all great teachers do."
A fitting tribute from a student to his teacher and a wonderful book to read and cherish for students and teachers alike.
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