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. Class sections limited to 20.

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.

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.

Calderwood Seminar.Combinatorial ideas permeate biology at all scales, from the combinatorial properties of the sequences of letters (nucleotides) representing DNA and RNA, to the symmetries often observed in cell divisions, to the graphs that can be used to represent evolutionary trees.  We will focus on key combinatorial ideas that arise on multiple scales in biology, including molecular, cellular, and organism, especially: counting and classification, symmetries, and combinatorial graphs.  The class will interview mathematicians and biologists about their current research, and wil

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. This course is graded satisfactory/unsatisfactory 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.

This course gives an introduction to the theory and applications of ordinary differential equations. We explore different applications in physics, chemistry, biology, engineering and social sciences. We 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.

An introduction to probability, including combinatorial probability, random variables, discrete and continuous distributions. Prerequisites: MTH 153 and MTH 212 (may be taken concurrently), or permission of the instructor.

An introduction to probability, including combinatorial probability, random variables, discrete and continuous distributions. Prerequisites: MTH 153 and MTH 212 (may be taken concurrently), or permission of the instructor.