The thirty-first meeting was held on October 25-26, 2013, at Xavier University. We continued the thread begun at the last meeting by reading from the work of Karl Weierstrass (1815-1897). Along with Cauchy, Weierstrass has long been regarded as one of the central figures in the rigorization of analysis in the nineteenth century. We read two pieces "by" Weierstrass (given that the first was actually written by his student, H. A. Schwarz):
- Differentialrechnung, Ausarbeitung der Vorlesung an dem Königlichen Gewerbeinstitut zu Berlin im Sommersemester 1861 von H. A. Schwarz (Differential calculus, an elaboration of lecture notes at the Royal Technical Institute in Berlin in the summer semester of 1861 by H. A. Schwarz), as excerpted in Eléments d'analyse de Karl Weierstrass, by Paul Dugac, Archive for Hist. Exact Sci., vol. 10, No. 1/2 (28.VI.1973), 118-125;
- Über continuirliche functionen eines reellen arguments,
die für keinen werth des letzteren einen bestimmten, differentialquotienten
besitzen (On continuous functions of a real argument which possess
derivatives at not a single of their values), Königl. Akad. Wiss. (1872),
Mathematische Werke II, 71-74.
This task was made far more challenging by the fact that neither of these pieces are available in their entirety in English translation and facility with German is weak among the members of the seminar. So Wiebke Diestelkamp (U Dayton, and current President of the MAA Ohio Section) agreed to produce a rough translation for us of both pieces. For this we acknowledge her kind assistance.