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This program explores mathematical structures underlying the physical world. While nature appears complex, it often follows elegant, consistent rules that can be expressed through mathematics. Our goal is to uncover and articulate this order by studying foundational physical theories and systematically developing the mathematical tools required to model them.

In the fall quarter, we begin with a study of classical mechanics, the mathematical framework of Newton's deterministic universe. Emphasis will be placed on linear systems, where analytical solutions are feasible. Key mathematical techniques will include differential equations, vector calculus, and linear algebra.

In the winter quarter, we shift to nonlinear systems, exploring chaos theory and its challenge to classical determinism. We move into relativity, extending classical mechanics into regimes of high velocity and mass through Einstein’s theories of special and general relativity. This portion also introduces other topics in mathematical analysis, such as calculus of variations, integral transforms, and an introduction to differential geometry.

The program integrates lectures, tutorials, collaborative workshops, student-led presentations, and computational labs, along with seminars in the philosophy and history of mathematics and physics, encouraging students to connect theory with broader scientific and intellectual contexts.

Anticipated Credit Equivalencies:

Fall Quarter

4* - Classical Mechanics
4* - Differential Equations
4* - Multivariable Calculus
4* - Linear Algebra

Winter Quarter

5* - Relativity
5* - Non-Linear Dynamics
4* - Mathematical Methods 
2* - Projects