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.

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.

How does influence travel from one thing to another? In Newton’s mechanics of particles and forces, influences travel instantaneously across arbitrarily far distances. Newton himself felt this to be incorrect, but he did not suggest a solution to this problem of “action at a distance.” To solve this problem, we need a richer ontology: The world is made not only of particles, but also of fields. As examples of the field concept, we study the theory and applications of the electric field and the magnetic field.

Students will observe using the telescopes at Stickney Observatory for a series of astronomical observing projects. After a range of initial assigned projects designed to acquaint students with the capabilities of the observing equipment and astrophysically interesting observations, students will propose and carry out their own observing projects looking at astrophysical phenomena of interest to them. As this is a projects class, it is expected that students will be able to devote significant time (mostly at night) observing on their own or in small teams.