How efficiently can one untangle a double-twist? Waving is believing! (with Dan Ramras), preprint and animations.I have extensive web material on Teaching with Original Historical Sources in Mathematics, which includes versions of quite a number of my joint publications in this area.
Classroom teaching methods for
active student work in class via
advance reading, writing, and warmup exercises, as alternatives
Here are thoughts about the classroom dynamics of teaching this way. Here is an explanation of my grading and daily logistics of handling several units simultaneously with these assignment parts. Here are sample homework guidelines for students about how assignments can be designed to foster an active classroom without lecture. Here is an overview handout for a sophomore discrete mathematics course of how I present this pedagogy to students. Here are example assignments for courses in discrete mathematics and calculus, showing reading questions, warmup exercises, and final exercises. Here is an actual assignment handout for students, showing the different things I expect them to do.
Translations of primary
the Euler-Maclaurin summation formula, from Institutiones
Leonhard Euler (pdf format), or in (dvi format).
Excerpt from a letter of Monsieur Lame to Monsieur Liouville on the question: Given a convex polygon, in how many ways can one partition it into triangles by mean of diagonals?: Lame's elegant geometric solution to finding the one step recursion relation solving Euler's decomposition problem, leading to the factorial formula for Catalan numbers.
Some more papers:
OK, here's a photo taken at the 1999 Boulder conference on homotopy theory. On the left is Italian algebraic topologist Luciano Lomonaco, on the right is me.
You might find another photo of me playing badminton