For those pointing out that the Fibonacci sequence originated in India, yes, I agree! I learned this from Manjul Bhargava, and discussed the matter in some tweets a few years ago:
I’ve spent the morning reading this preprint: arxiv.org/abs/1805.11556. It has a story behind it. A finance person named @MarcosCarreira does math for pleasure, inspired by @CutTheKnotMath. While playing with a classic problem, he finds something weird in a famous paper about it.
It seems that Marcos discovered an error in that famous paper (by Gilbert and Mosteller) which nobody noticed until now. But I’m not an expert in probability, and it would be great if those of you who are would take a look at Marcos’s paper. It strikes as a neat piece of work.
Marcos uncovered the error by running numerical simulations and finding that his results didn’t quite match the predictions of the classic analysis. Puzzled, he redid the analysis very carefully himself, helped by Mathematica, and found a subtle mistake in the earlier work.
I just received this new book, and at a glance, it looks terrific. Very creatively conceived, written, and illustrated. I came to that conclusion after reading two pages at random. Take a look at them below and see what you think:
The teacher in me likes the question in the cloudy enclosure, and the gentle way it’s approached after that. The playful drawings help too. The question itself is really deep, and you can see the author appreciates that.
And now that the right question has been asked, we can learn what geometry and topology are really about, and the key distinction between them. Again, all this is helped by precise yet lighthearted drawings and layout.
I'm teaching a course on asymptotics and perturbation methods, and thought it might be fun to share the lectures on @YouTube. Here's lecture 1, which introduces the idea of asymptotic expansions. (For more about the course, see the rest of this thread.)
Asymptotic methods and perturbation theory are clever techniques for finding approximate analytical solutions to complicated problems by exploiting the presence of a large or small parameter. This course is an introduction to such methods.
The prerequisites are a knowledge of calculus and differential equations at an undergraduate level. The course emphasizes concrete examples, intuition, and applications to science and engineering, rather than theorems, proofs, and rigor. The treatment is friendly yet careful.
In an hour, I'll meet my students in Math Explorations, a course we teach in an inquiry-based format. I LOVE this class! But like all teachers, I'm feeling the usual first-day jitters. To calm myself, I'm re-reading "The art of asking good questions": artofmathematics.org/blogs/vecke/th…
The course materials are available at the website for the wonderful "Discovering the Art of Mathematics" project artofmathematics.org. They offer 11 free books on fascinating topics like math and music, patterns, dance, games and puzzles, knots, infinity, etc. A real feast!
Today was my first day of class, and I zoomed with the 200+ students in my "multivariable calculus for engineers" course. We had an unexpectedly wonderful session, super interactive. As you can see, I'm still on a high from it! And I want to share what worked so well... 1/n
I was really anxious about this first class, and about how dead it would be on Zoom, but somehow by making it warm and fun, the class and I established a rapport. Most of them are freshmen and very apprehensive. This warm welcome to @Cornell seems to have been the right call. 2/n
I got there a half hour early and chatted with the students who were already there. We talked about lots of things (including my dog). Just chillin... 3/n