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 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.

The mathematics of how you can stream videos while your mom is using the same cable to call on the phone. Hilbert spaces, Fourier series, Fourier transform, discrete Fourier transforms, wavelets, multiresolution analysis, applications. Prerequisite: MTH 280 or MTH 281.

The course will cover topics from different parts of mathematics, with the common theme that they play some role in the design of neural networks. We will also look at some neural networks’ applications and at how mathematics is integrated. Topics will include: What is a neural network, examples and applications; Universal approximation theorems (Cybenko and others); Examples of loss functions; Gradient Descent and Stochastic Gradient descent; Generalization gap, training vs testing data; Quick review of game theory, Nash equilibrium; Generative Adversarial Networks (GAN); Unrolled GANs.

This course provides an introduction to category theory through the language of universal algebra and module theory. Topics include: semigroups, monoids, quasigroups, modules, hom sets, categories, functors, representable functors. Additional topics may be covered if time permits: varieties, Birkhoff's Theorem, congruences, adjunctions. Course consists of lectures, weekly student presentations, one midterm exam and a final presentation. Prerequisites: MTH 233 or equivalent. (E)

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.

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.

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 equivalent.