Physical Systems and Mathematical Methods

This intermediate-to-advanced program builds upon previous introductory work in calculus and physics, aiming to deepen students' comprehension of nature, its representation through physical models, and the robust connections between mathematics and physical theories. Our focus is on understanding the nature and formal structure of quantitative physical theories, emphasizing the unification of concepts and mathematical structures that organize diverse physical theories into a coherent body of knowledge. We will pose increasingly sophisticated questions about the nature of physical reality, spanning various scales of space, time, matter, and energy, and develop mathematical and experimental tools to address these inquiries. Additionally, we will explore our studies within a broader historical, philosophical, and cultural context.

In fall, we will develop foundational skills in mathematical methods, covering Differential Equations, Linear Algebra, and Multivariable and Vector calculus. Laboratory activities will enhance our experimental skills and provide us experience with computational tools.

In winter and spring, we will focus on advanced physics topics, including Classical Mechanics, Electromagnetism, and Quantum Mechanics, applying the mathematical methods established in the fall quarter. Our laboratory work will extend and complement the theoretical focus.

Given the challenging nature of the material, consistent class participation and a substantial time commitment outside of class will be required. We aim to create a collaborative and inclusive learning environment that fosters mutual support and success through lectures, workshops, and labs. Weekly assignments include reading, writing, and substantial problem sets. There will be regular quizzes and exams.