How efficiently can one untangle a double-twist? Waving is believing! (with Dan Ramras), preprint and animations, to appear in The Mathematical Intelligencer in 2017.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 student active learning via reading in advance, writing, and warmup exercises, as alternatives to lecture:
the lecture-textbook trap with active learning and rewards for
all, a condensed piece to appear in the Notices of the
American Mathematical Society in 2017.
From lecture to active learning: Rewards for all, and is it really so difficult?, an extended piece, preprint.
And here are some supplementary materials:
Further philosophy, my evolution, and personal experiences of the classroom dynamics of teaching this way.
An explanation of my grading and daily logistics of handling several units simultaneously with these assignment parts.
Sample homework guidelines for students about how assignments can be designed to foster an active classroom without lecture.
An overview handout for a sophomore discrete mathematics course of how I present this pedagogy to students.
Example assignments for courses in discrete mathematics and calculus, showing reading questions, warmup exercises, and final exercises.
An actual assignment handout for students, showing the different things I expect them to do.
Translations of primary
historical source materials:
the Euler-Maclaurin summation formula, from Institutiones
Calculi Differentialis by
Leonhard Euler (pdf format), or in (dvi format), also at the Euler Archive.
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.
A few preprints::
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 at NMSU.