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.

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 to lecture:
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 historical source materials:

Excerpts on the Euler-Maclaurin summation formula, from Institutiones Calculi Differentialis by
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:

  • 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 trouvé": 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 March 11, 2016.