Future Talks by Fred Rickey
"The Mathematics that George Washington Studied,"
Joint meeting of the New Jersey and Metro New York sections of the MAA,
Saint Peter's University, Jersey City, NJ, November 1, 2014.
As a teenager, George Washington
compiled two notebooks (179 pages) about the mathematics he studied:
decimal arithmetic, geometry, logarithms and trigonometry, and
surveying. We will examine an example of each of these, pointing out
(when we can) where the explanations and problems came from, as well as
a few errors in the manuscript.
These notebooks have had a hard life.
For half of the nineteenth century they were on loan to biographers who
treated them casually and dispersed some pages. We shall describe some
of our success in locating these missing pages. Once they were sold to
the government they were disbound and the pages reordered. This
troublesome issue will also be described.
"The Infinitesimal Calculus using Nonstandard Analysis," TARS Seminar, USMA, November 5 and 12.
In 1960 the logician Abraham Robinson
found a way to give a mathematically consistent theory of
infinitesimals, thus justifying their use by Leibniz, Euler, and many
others. We shall construct a model of the hyperreals that contains
infinitesimals and infinite real numbers. Then we shall give
definitions of the basic calculus notions, continuity,
differentiability, and the integral. An abundance of easy examples and
proofs will be provided to show that this approach is nicer than the
standard epsilon-delta approach. This talk will be self contained and
accessible to all.
"The Mathematics that George Washington Studied," Providence College, November 19, 2014.
"Great Logicians of the Twentieth Century: Russell, Hilbert, Tarsli, Gödel, Cohen, and Robinson,"West Point, November 25, 2014.
This is a presentation for
students in a Foundations of Mathematics class, but everyone else is
interested. We will present short biographies, descriptions of famous
results, and ideas about further reading, devoting just six minutes to
each of these individuals. We will paint the history of logic in the
twentieth century in broad strokes.
"The Life and Logic of Stanisław Leśniewski,"AMS
Special Session on Mathematics in Poland: Interbellum, World War II,
and Immediate Post-War Developments, Joint Mathematics Meetings, San
Antonio, TX, January 12, 2015.
Leśniewski (1886-1939) received his
Ph.D. in Lwów under the direction of Kazimierz Twardowski in
1912. After spending World War I in Russia, he was appointed, in 1919,
professor of the philosophy of mathematics, at the newly reopened
University of Warsaw. Starting in 1916 he began developing mereology, a
theory of parts and wholes. This was followed by his ontology, a theory
of names and it was underpinned by protothetic, a very general theory
of deduction with quantifiers over all types of variables.
We shall not describe these theories in
any detail, but will concentrate on discussing three of his important
contributions: his analysis of Russell's antinomy, his views on
definitions, and his precision in describing the rules of procedure for
his logical systems.
Information about some talks that I have given since retirement and also in the past.
Updated October 2014.