Physical Systems and Applied Mathematics

Fall 2016, Winter 2017, and Spring 2017 quarters

Taught by

Vauhn Foster-Grahler
mathematics, education, anthropological mathematics
  • UG


Proficiency in one year of introductory calculus (including both differential and integral calculus, including multiple integrals) and one year of calculus-based physics (including introductory mechanics and electricity and magnetism).

This intermediate-to-advanced program builds on previous introductory work in calculus and calculus-based physics to deepen students’ understanding of nature, how it can be represented via physical models, and the powerful connections between mathematics and physical theories. We will integrate topics in physics (from classical mechanics, electromagnetism, and quantum mechanics) with topics in applied mathematics (from differential equations, multivariable and vector calculus, and linear algebra). We will also devote time to looking at our studies in a broader historical, philosophical, and cultural context.

We will integrate theory and experiment in a collaborative environment that mirrors practices of contemporary scientists. By studying classical and cutting-edge problems, we aim to ask increasingly sophisticated questions about the nature of physical reality and develop tools for answering those questions. Through readings, lectures, workshops, labs, and seminars we will examine the principal models by which we describe and understand the physical world, expanding from the realms of our immediate senses out to many orders of magnitude of scale of distance, time, matter, and energy. We will emphasize understanding the nature and formal structure of quantitative physical theories, unifying the concepts and mathematical structures that organize different physical theories into a coherent body of knowledge. Mathematical skills will be developed as needed in the context of their use in the physical sciences. Quantitative problem solving will be emphasized, with computational tools used to gain insight into physical processes. The theoretical focus will be complemented with laboratory work.

Our theoretical and experimental investigations will integrate mathematically sophisticated and conceptually challenging subject areas, and will require, for well-prepared students, a significant time commitment of at least 50 hours per week, including mastery of prerequisite material, willingness to work in a learning community, practiced time-management skills, and experience balancing intensive work over extended periods of time. The result should be beautiful and mind-boggling insights into our breathtaking universe. Our goal is to provide students the opportunity to develop the conceptual knowledge and mathematical ability required to pursue further advanced work in physics and related disciplines.

Program Details

Fields of Study

mathematics philosophy of science physics

Preparatory For

physics, mathematics, engineering, and math and science education



Fall Signature Winter Signature Spring Closed

Location and Schedule

Campus Location


Time Offered


Advertised Schedule

First spring class meeting: Monday, April 3 at 9am (Lab 2 1223A)

Online Learning

Enhanced Online Learning

Special Expenses

Math and physics textbooks at intermediate and advanced levels are generally very expensive, and may be more than $600 total for new texts in the fall. However, those texts cover the entire year, and students will be required to have access to these texts for successful completion of the program. Students will also need to own or have easy access to computers with appropriate software. More information will be available by the beginning of spring quarter 2016 at the program website.

May be offered again in

This program or its equivalent will be offered again in 2018-2019.


2016-09-19Fee removed ($50 per quarter).