
Evaluations: Goals for the Courses
Mathematics
in the Early Italian Renaissance
In a course on the Early Italian Renaissance, this unit investigates
the reappearance, in Europe around 1500, of original mathematics. Main
questions include what was the state of mathematics at this time? Who
was thinking about it, and why? Materials by Leonardo da Vinci, Piero
della Francesca, Luca Pacioli, and the anonymous authors of abacus school
texts are examined.
Angelo Mazzocco, Spanish
and Italian and Mark Peterson,
Mathematics
Linear
Perspective and Western Art
In an introductory art history survey, this is a unit on linear perspective
that focuses on perspective and the new illusionistic art of the fifteenth
century as the consequence of a new culture of mathematical inquiry.
The theorems of the vanishing point and the observation point are applied
to works of art and proven mathematically.
Paul Staiti, Art and Giuliana
Davidoff, Mathematics
Philosophy
of Science: Scientific Theories As Models
A unit in a philosophy course that introduces scientific theories as
mathematical models. Students study examples of increasing mathematical
sophistication and mathematical modeling of physical systems in the
sciences. Students construct models using Stella software and arrive
at an understanding of scientific theories as mathematical models.
Samuel Mitchell, Philosophy
and Donal O'Shea, Mathematics
Ethnomathematics
Adds a mathematics component to an introductory anthropology course
through a comparison of Melanesian and Western mathematics. Students
acquire a new appreciation of mathematics and its significance in their
culture by studying elements of the mathematical system used by Iqwaye
people of Papua New Guinea: their different counting system and different
concepts of number, notation, and infinity. For the Iqwaye, counting
and numbers are associated with their bodies so the link between human
form and mathematical thinking is close and distinctive.
Debbora Battaglia, Anthropology
and Margaret Robinson, Mathematics
Introducing
Diatonic Set Theory into the Music Theory Curriculum
This unit describes mathematicallyoriented properties of the diatonic
system for use in introductory music theory courses. It focuses on recent
scholarship in the area of diatonic set theory. As students study diatonic
music theory, they simultaneously deal with the corresponding mathematical
properties that describe aspects of and relationships within a diatonic
set in a twelvenote universe. By exploring the mathematical principles
behind the unique aspects of the diatonic set, students of music theory
can better understand tonal relationships between the notes of the scale
and the harmonic significance of these relationships.
Timothy A. Johnson, Music
and Alan Durfee, Mathematics
Cunning
Geometry: The Designing of Medieval Churches
This module appears in courses in art history and in an interdisciplinary
humanities course. It explores the geometric schemata that informed
the architectural designs of medieval churches, some of this era's most
complex and imposing structures. Through physical simulation and other
investigations, students discover the ways in which medieval theories
of optimal geometric form shaped the aesthetics of design in general
and the plans of churches in particular.
Michael Davis, Art and Lester
Senechal, Mathematics
Writing and Reckoning: Sign Systems and Argument In Verbal
and Mathematical Communication
In an introductory writing course, this unit compares prose essays and
mathematical writings to identify the differences and similarities in
these modes of communicating ideas and information. The significance
of the essayist's voice, for example, stands out more meaningfully in
contrast to it's minimal presence in mathematical expositions that take
the description of universal patterns in parsimonious form as their
distinctive aim. However numerous the differences, such comparison also
reveals some common features in the construction of arguments across
disciplines.
Carolyn Collette, English
and Giuliana Davidoff, Mathematics
History
and Statistics: Patterns of Family and Community Life in the Nineteenth
Century
A fourweek introduction to exploratory data analysis in a firstyear
course in history. Using census records and other archival materials
from nineteenthcentury France, students confront some of the sources
and problems involved in reconstructing the social history of ordinary
people and rural communities in the past. In moving from the original
records to data sets, from hand tabulations to computerassisted analyses,
they learn to identify and interpret patterns in numerical data and
to present their results in statistical displays and welldocumented
essays.
Robert Schwartz, History
and Harriet Pollatsek, Mathematics
Geometries
Past and Present
This unit is taught in the College's yearlong interdisciplinary humanities
course Pasts and Presences in Western Civilization. It contrasts the
nineteenth and twentiethcentury views of curved space with earlier
conceptions of the Babylonians, Greeks, and medieval Europeans. In the
process, it explores the paradox whereby rigor and axiomatization free
the imagination and allow geometrical insights to be used in a profoundly
speculative way. Penny Gill,
Politics and Donal O'Shea,
Mathematics

