Schedule of Talks for the 2010-2011 Academic Year
Date: Wednesday, October 13, 2010
Speaker: Prof. George P. H. Styan
Department of Mathematics and Statistics
McGill University
Email: styan at math dot mcgill dot ca
Title: Some comments on old magic squares illustrated with postage stamps
Abstract: Our interest focuses on old magic squares for which the Moore-Penrose inverse matrix is also magic. Special attention is given to magic squares from India. In particular we study a 4 x 4 most-perfect pandiagonal magic square which the sixth-century Indian astronomer, mathematician, and astrologer Daivajna Varahamihira (505-587 AD) apparently devised for making several different varieties of perfume. We also study some magic squares given by the Jain polymath Thakkura Pheru (fl. 1291-1323) and some given by the Kerala mathematician Narayana Pandita (1340-1400), as well some discovered in temples in Dudhai (Jhansi district), in Gwalior, and in Khajuraho. We also comment on the magic square depicted in the 1514 engraving entitled Melencolia I by the German painter and printmaker Albrecht Dürer (1471-1528) and explore a connection between Albrecht Dürer and the Italian mathematician and "Father of Accounting" Fra Luca Bartolomeo de Pacioli (c. 1446-1517).

This colloquium is based on joint research with Ka Lok Chu, S. W. Drury and Götz Trenkler and supported, in part, by the Natural Sciences and Engineering Research Council of Canada.

Date: Wednesday, November 3, 2010
Speaker: Prof. Joseph Malkevitch
Department of Mathematics
York College/Graduate Center - CUNY
Email: jmalkevitch at york dot cuny dot edu
Title: A Brief History of the Mathematics of Convex Polyhedra
Abstract: Physical examples of polyhedra exist from thousands of years ago, and mathematicians who have studied them include Euclid, Archimedes, Pappus, da Vinci, Descartes, Euler, Cauchy, Steinitz, Coxeter, and Grünbaum. This talk will emphasize the evolution of regularity concepts for polyhedra and the change from viewing convex polyhedra as metrical structures to combinatorial objects.
Date: Wednesday, December 1, 2010
Speaker: Prof. Karen Parshall
Departments of Mathematics and History
University of Virginia
Email: khp3k at virginia dot edu
Title: Algebra: Creating New Mathematical Entities in Victorian Britain
Abstract: Analytic geometry and mathematical physics may have interested a majority of mathematicians in Victorian Britain, but algebra also served to focus their mathematical attention. In the century's first half, algebraic work centered on the development of the so-called "symbolical algebra" and the creation of new algebras, while in its second, the theory of invariants dominated and the abstract theory of groups witnessed key developments. Underlying much of this research was the philosophical question of how free mathematicians were to create new mathematical entities. The Victorian British response was ultimately, "quite."
Date: Wednesday, February 2, 2011
[Postponed due to inclement weather]
Date: Wednesday, March 2, 2011
Speaker: Prof. Craig Fraser
Institute for the History and Philosophy of Science and Technology
University of Toronto
Email: cfraser at chass dot utoronto dot ca
Title: Abraham de Moivre and de Moivre's Identity
Date: Wednesday, April 6, 2011
Speaker: Prof. Rob Bradley
Department of Mathematics and Computer Science
Adelphi University
Email: bradley at adelphi dot edu
Title: The Binomial Theorem from Newton to Cauchy
Abstract: Newton discovered the General Binomial Theorem in the 1660s. Although he could demonstrate that it was true in many special cases, he did not initially have a general proof. Taylor's theorem provides a satisfactory proof that is within the grasp of a modern undergraduate, but an elementary proof (one not requiring the differential calculus) was considered desirable. Such a proof was finally given by Euler in 1775. It became widely known in a somewhat more polished form thanks to Cauchy's Cours d'analyse (1821).

We investigate the historical and pedagogical reasons for preferring elementary proofs over calculus-based ones and present the details of the Euler-Cauchy proof.

Date: Wednesday, May 4, 2011
Speaker: Prof. Fred Rickey
Department of Mathematics
United Sates Military Academy, West Point
Email: Frederick dot Rickey at usma dot edu
Title: Logic in Warsaw, 1915-1939
Abstract: Stanislaw Lesniewski (1886-1939) and Jan Lukasiewicz (1878-1956) joined the University of Warsaw faculty soon after it was converted from a Russian language university to Polish. They were good teachers and were doing interesting research so a school started to form around them. A few years later they were joined by Alfred Tarski (1901-1983), who was Lesniewski's only Ph.D. student. Since Tarski immigrated to the US, his later work is well known, but the early work of the three is not so well known. After setting the scene, we will describe some of the work of Lukasiewicz on Aristotle's syllogistic and many-valued logics as well as the foundational system of Protothetic, Ontology, and Mereology, that Lesniewski developed from his own analysis of the Russell antinomy.