Epsilon sandwiches is a great speech, with advice that I wish I could follow—but it pre-supposes students for whom the referenced very easy proofs are indeed very easy conceptually, and the struggle is only to put those concepts into words. I can believe that this is true of students in a UPenn first analysis course, but it is not true at the less prestigious university where I teach students who are encountering proofs for the first time (well before analysis)—and I have long struggled with how to break down this two-step complication into separate manageable steps with students for whom, say, it is still a real challenge to understand (in the context of proving facts about sums and products of even numbers) why 2(x + y) = 2x + 2y is true, but 2(xy) = (2x)(2y) is not. If anyone knows how to adapt Wilf's advice to such students, then I—and they, in my fall class!—will be grateful to hear it!
svat|3 years ago
• Epsilon Sandwiches https://www2.math.upenn.edu/~wilf/website/MAASpeech
In fact everything by Wilf that I've read is lovely: the paper "Recounting the rationals" (https://www2.math.upenn.edu/~wilf/website/recounting.pdf with Neil Calkin), and the book generatingfunctionology https://www2.math.upenn.edu/~wilf/DownldGF.html
JadeNB|3 years ago