David J. Pengelley
Professor
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003, USA
505-646-2723, 505-646-1064 (FAX)
davidp@nmsu.edu
David Pengelley

My home pages are under development.  Here's my detailed vita, which lists all my publications.

At the Hopf Topology Archive you will find preprints of some of my papers in algebraic topology:

  • Stabilizing the lower operations for mod 2 cohomology (with T. Bisson and F. Williams)
  • Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology (with F. Williams)
  • A global structure theorem for the mod 2 Dickson algebras, and unstable cyclic modules over the Steenrod and Kudo-Araki-May algebras (with F. Peterson and F. Williams)
  • The global structure of odd-primary Dickson algebras as algebras over the Steenrod algebra (with F. Williams)
    • and more.

    And here is a preprint of  The odd-primary Kudo-Araki-May algebra of algebraic Steenrod operations, and invariant theory

    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.

    Classrom teaching methods for active student work in class via advance reading, writing, and warmup exercises, as alternatives to lecture:
    Here are some thoughts about the classroom dynamics of teaching. And here are sample 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, final exercises, and explaining how I grade these assignment parts, and showing how I handle the daily logistics of several units simultaneously. And here is an actual assignment handout for students, showing the different things I expect them to do.

    Original 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.

    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?
  • "Voici ce que j'ai trouvé": Sophie Germain's grand plan to prove Fermat's Last Theorem (November 2009 revision), to appear in Historia Mathematica.
  • 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 November 17, 2009.