37 citations · 53 across the 10 of their papers we have counts for
10 papers
Sophie Germain, mathématicienne extraordinaire: A story stranger than fiction
David Pengelley
Sophie Germain (1776-1831) was the first woman we know who did important original research in mathematics, specifically in elasticity theory and number theory. Celebrating her semi…
How did Fermat discover his theorem?
David Pengelley
In 1640 Pierre de Fermat discovered his theorem that if is prime and is not divisible by , then is divisible by ; or, as we write today, $a^{p-1}\equiv1\p…
Towards active processes for teaching and learning
Mai Gehrke, David Pengelley
We discuss parallels between students and teachers in the process of pedagogical reform. Reform aims for students to develop their own process for becoming independent learners, an…
Dances between continuous and discrete: Euler's summation formula
David J. Pengelley
Leonhard Euler likely developed his summation formula in 1732, and soon used it to estimate the sum of the reciprocal squares to 14 digits --- a value mathematicians had been compe…
From lecture to active learning: Rewards for all, and is it really so difficult?
David Pengelley
We describe the evolution of a personal non-lecture active learning pedagogy developed in numerous courses at all university levels. A distinguishing feature is its tight integrati…
Evidence-based teaching: how do we all get there?
David Pengelley, Dev Sinha
There are compelling reasons to shift our pedagogy toward evidence-based active learning methods that substantially improve student success, and now plenty of resources to aid in t…
How efficiently can one untangle a double-twist? Waving is believing!
David Pengelley, Daniel Ramras
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, a…
The odd-primary Kudo-Araki-May algebra of algebraic Steenrod operations and invariant theory
David J Pengelley, Frank Williams
We describe bialgebras of lower-indexed algebraic Steenrod operations over the field with p elements, p an odd prime. These go beyond the operations that can act nontrivially in to…
"Voici ce que j'ai trouve": Sophie Germain's grand plan to prove Fermat's Last Theorem
Reinhard Laubenbacher, David Pengelley
A study of Sophie Germain's extensive manuscripts on Fermat's Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the sing…
Global structure of the mod two symmetric algebra, H^*(BO;F_2), over the Steenrod Algebra
David J. Pengelley, Frank Williams
The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A, and is isomorphic to the mod two cohomology of BO, the cl…