Spring 2026 Course Search

This course covers the breadth of university calculus: differentiation, integration, infinite series, and ordinary differential equations. It focuses on concepts and interconnections. In order to cover this much material, computational techniques are de-emphasized. The approach is historically based and classical, following original texts where possible.

Multivariable calculus is one of the core parts of an undergraduate mathematics curriculum. Introductory calculus mostly concentrates on situations where there is one input and one output variable; multivariable extends differentiation, integration, and differential equations to cases where there are multiple input and output variables. In this way, multivariable calculus combines calculus and linear algebra; the subject can also be called vector and matrix calculus.

Everything is geometry! This class is about two things: first, about how mathematicians have extended the concept of "geometry" beyond triangles and circles, into higher-dimensional spaces, curved spaces, spaces of functions, discrete spaces, and more. Second, about how this extension of "geometry" can allow us to apply our powerful geometric intuition to a wide range of problems that might not initially seem geometric, both within mathematics, and in physics, computer science, and elsewhere.

In this course, we will focus on developing the statistical skills needed to answer questions by collecting data, designing experimental studies, and analyzing large publicly available datasets. The skills learned will also help students to be critical consumers of statistical results. We will use a variety of datasets to develop skills in data management, analysis, and effective presentation of results.

Discrete mathematics studies problems that can be broken up into distinct pieces. Some examples of these sorts of systems are letters or numbers in a password, pixels on a computer screen, the connections between friends on Facebook, and driving directions (along established roads) between two cities. In this course we will develop the tools needed to solve relevant, real-world problems. Topics will include: combinatorics (clever ways of counting things), number theory and graph theory. Possible applications include probability, social networks, optimization, and cryptography.

Throughout history, people have played games — games of chance and games of skill. Many of us grew up playing all kinds of different games, and most of those are infused with the core tenets of statistical reasoning and understanding: probability, risk assessment, expected value, and game theory. This course will look at statistics and probability through this lens. We will consider dice, cards, and several ‘classic’ board games. We will consider situations with both complete and hidden information and how to analyze those.

Composers throughout the ages have cut their teeth on the study of counterpoint – the intricate practice of writing melodies for several voices sounding at once. In this course, we’ll look mainly at 16th-century composers of counterpoint, and sing through pieces from Palestrina to Weelkes, while learning to compose in a variety of practices such as canons, the motet, and familiar style. We’ll gradually work our way from two-voice to four-voice counterpoint, and set texts in a variety of harmonic styles.

In this course, students will develop skills in aural perception, learning to visualize, sing, and notate music through melodic, harmonic, and rhythmic exercises. Students will learn to identify key signatures, intervals, 7th chords, triads, key relationships, common cadences and phrase structures, larger forms, tempo markings, and more.