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 mathematically-oriented 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 twelve-note 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 four-week introduction to exploratory data analysis in a first-year course in history. Using census records and other archival materials from nineteenth-century 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 computer-assisted analyses, they learn to identify and interpret patterns in numerical data and to present their results in statistical displays and well-documented essays.
Robert Schwartz, History and Harriet Pollatsek, Mathematics

Geometries Past and Present
This unit is taught in the College's year-long interdisciplinary humanities course Pasts and Presences in Western Civilization. It contrasts the nineteenth and twentieth-century 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