An introduction to formal analysis and tonal harmony, and a study of pieces in the standard repertory. Regular exercises in harmony. Prerequisites: ability to read standard notation in treble and bass clefs, including key signatures and time signatures, and the ability to name intervals. (A placement test is given before the fall semester for incoming students.) One 50-minute ear training section required per week, in addition to classroom meetings. Enrollment limited to 20.

An introduction to formal analysis and tonal harmony, and a study of pieces in the standard repertory. Regular exercises in harmony. Prerequisites: ability to read standard notation in treble and bass clefs, including key signatures and time signatures, and the ability to name intervals. (A placement test is given before the fall semester for incoming students.) One 50-minute ear training section required per week, in addition to classroom meetings. Enrollment limited to 20.

This course provides a critical survey of rock music, tracing the music’s development from blues and blackface minstrelsy to heavy metal, grunge, and techno. Emphasis throughout is placed upon understanding musical developments in the context of American race and gender relations and the politics of youth cultures in the U.S. Topics to be covered include: Elvis Presley and American race relations; Jimi Hendrix and the blues; girl groups; the rise of arena rock; and the significance of the DJ in hip hop. Enrollment limited to 45.

This class is an introduction to music history that combines a close study of music from the Western classical tradition with research methodology and an orientation to the discipline of musicology. Organized by genres and concepts, the class looks at classical music as both a repertoire and an object of cultural study. In addition to covering a range of works, we will address their production, performance, and reception through a study of their social and political context, and raise questions of power, representation, and patronage.

Colloquia are especially designed for those with no previous background in music. They emphasize class discussion and written work, which consists of either music or critical prose as appropriate to the topic. Open to all students, but particularly recommended for first-year students and sophomores. An introduction to music notation and to principles of musical organization, including scales, keys, rhythm and meter. Limited to beginners and those who did not place into 110. Enrollment limited to 20.

Topology is a kind of geometry in which important properties of a shape are preserved under continuous motions (homeomorphisms)—for instance, properties like whether one object can be transformed into another by stretching and squishing but not tearing. This course gives students an introduction to some of the classical topics in the area: the basic notions of point set topology (including connectedness and compactness) and the definition and use of the fundamental group. Prerequisites: MTH 280 or 281 or permission of the instructor.

Representation theory is used everywhere, from number theory, combinatorics, and topology, to chemistry, physics, coding theory, and computer graphics. The core question of representation theory is: what are the fundamentally different ways to describe symmetries as groups of matrices acting on an underlying vector space? This course will explain each part of that question and key approaches to answering it. Topics may include irreducible representations, Schur’s Lemma, Maschke’s Theorem, character tables, orthogonality of characters, and representations of specific finite groups.

In this course students work in small groups on original research projects. Students are expected to attend a brief presentation of projects at the start of the semester. Recent topics include interactions between algebra and graph theory, plant patterns, knot theory, and mathematical modeling. This course is open to all students interested in gaining research experience in mathematics. Prerequisites vary depending on the project, but normally 153 and 211 are required.

In this class we don’t do math as much as we talk about doing math and the culture of mathematics. The class includes lectures by students, faculty and visitors on a wide variety of topics, and opportunities to talk with mathematicians about their lives. This course is especially helpful for those considering graduate school in the mathematical sciences. Prerequisites: MTH 211, MTH 212 and two additional mathematics courses at the 200-level, or permission of the instructor. May be repeated once for credit. S/U only.

The topological structure of the real line, compactness, connectedness, functions, continuity, uniform continuity, differentiability, sequences and series of functions, uniform convergence, introduction to Lebesgue measure and integration. Prerequisites: MTH 211 and MTH 212, or permission of the instructor. MTH 153 is strongly encouraged.