Blaise Pascal (1623–1662) was born in Clermont-Ferrand in central France. Even as a teenager his father introduced him to meetings for mathematical discussion in Paris run by Marin Mersenne, who...
Historical Projects in Discrete Mathematics and Computer Science (2009)
Janet Barnett, Guram Bezhanishvili, Hing Leung, Jerry Lodder, David Pengelley, Desh Ranjan
A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science...
TEACHING WITH PRIMARY HISTORICAL SOURCES: SHOULD IT GO MAINSTREAM? CAN IT? (2009)
Many are now teaching mathematics directly with primary historical sources, in a variety of courses and levels. How far should this be taken? Should we adapt or redesign standard courses to a...
Did Euclid Need the Euclidean Algorithm to Prove Unique Factorization? (2008)
number is uniquely a product of primes. The heart of this uniqueness is found in Book VII of Euclid’s Elements [3]: Proposition 30 (Euclid’s Lemma). If a prime divides a product, then it divides...
Janet Barnett, Guram Bezhanishvili, Hing Leung, Jerry Lodder, David Pengelley, Inna Pivkina, ...
• Summation of Numerical Powers. The discovery of closed formulas for discrete sums of numerical powers, motivated by application to approximations for solving area and volume problems in calculus,...
A Project in Algorithms based on a Primary Historical Source about Catalan Numbers (2008)
David Pengelley, Desh Ranjan, Karen Villaverde
We discuss a project based on an original source from 1838 by Gabriel Lamé, which was used to teach dynamic programming in an Algorithms and Data Structures course for junior level computer science...
"Voici ce que j'ai trouve": Sophie Germain's grand plan to prove Fermat's Last Theorem (2008)
Laubenbacher, Reinhard, Pengelley, David
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 single theorem for Case...
Lagrange and the Solution of Numerical Equations (2007)
Reinhard Laubenbacher, Gary Mcgrath, David Pengelley
In 1798 J.-L. Lagrange published an extensive book on the solution of numerical equations. Lagrange had developed a general systematic algorithm for detecting, isolating, and approximating all real...
Excerpts on the Euler-Maclaurin summation formula, from (2007)
tion and exercises may be provided at this site at a later time. The only commentary that remains here summarizes some of those portions of Chapters 5 and 6 that were not translated. In excerpts from...
Janet Barnett, Guram Bezhanishvili, Hing Leung, Jerry Lodder, David Pengelley, Inna Pivkina, ...
• Summation of Numerical Powers. The discovery of closed formulas for discrete sums of numerical powers, motivated by application to approximations for solving area and volume problems in calculus,...
Mathematical masterpieces: teaching with original sources (1996)
Reinhard Laubenbacher, David Pengelley
masterpieces from antiquity to the present. Following a common practice in the humanities, for example in Chicago's Great Books program and St. John's College curriculum, we have students...
Mathematical masterpieces: teaching with original sources (1996)
Reinhard Laubenbacher, David Pengelley
masterpieces from antiquity to the present. Following a common practice in the humanities, for example in Chicago’s Great Books program and St. John’s College curriculum, we have students read...