This course focuses on connecting music theory concepts to musical experience. Ever wondered why certain harmonies seem to grab you by the ears? How do chord progressions work? This course provides an introduction to diatonic harmony in a range of tonal styles, including classical music and popular music. Students learn to apply technical theory knowledge flexibly and creatively to analysis, composition, and performance. Discussions include harmonic function, voicing and voice leading, dissonance treatment, non-chord tones, texture, cadences, and phrase structure.

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, the course addresses their production, performance and reception through a study of their social and political context, and raises questions of power, representation and patronage.

Topics of MUS 100 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 MUS 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 MTH 281, or equivalent.

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 explains each part of that question and key approaches to answering it. Discussions 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 MTH 153 and MTH 211 are required. Restrictions: MTH 301rs may be repeated once.

In this class students don’t do math as much as they 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 equivalent. 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 equivalent. MTH 153 is strongly encouraged. Enrollment limited to 20.

This course gives an introduction to the theory and applications of ordinary differential equations. The course explores different applications in physics, chemistry, biology, engineering and social sciences. Students learn to predict the behavior of a particular system described by differential equations by finding exact solutions, making numerical approximations, and performing qualitative and geometric analysis.