David J. Pengelley
Professor Emeritus
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003, USA
David Pengelley

Here's my detailed vita, which lists all my publications.

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:

Beating 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:

Excerpts on 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::

  • The bridge between the continuous and the discrete via original sources
  • A graduate course on the role of history in teaching mathematics
  • Dances between continuous and discrete: Euler's summation formula (pdf) or (dvi)
  • Arthur Cayley and the first paper on group theory (appeared in "Using recent history of mathematics in teaching mathematics", ed. Amy Shell et al, MAA Notes Series, Mathematical Association of America)
  • Did Euclid need the Euclidean algorithm to prove unique factorization? (appeared in the American Mathematical Monthly)
  • "Voici ce que j'ai trouv�": Sophie Germain's grand plan to prove Fermat's Last Theorem (January 2010 revision), in Historia Mathematica (2010).
  • Sophie'�s Diary, by Dora Musielak, (book review in the Mathematical Intelligencer, 2010)
  • Teaching With Primary Historical Sources: Should it Go Mainstream? Can it?,  opening keynote address at HPM 2008, the quadrennial international meeting of the International Study Group on Relations Between History and Pedagogy of Mathematics, Mexico City, 2008.

  • 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.

    Page maintained by David Pengelley, davidp@nmsu.edu
    Last revised on July 27, 2017.