# Physical Systems and Applied Mathematics

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 work 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, remote and at-home lab activities, 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.

Fall quarter will be devoted to developing foundational mathematical and experimental skills. Mathematical topics will include multivariable and vector calculus, differential equations, and linear algebra. Laboratory activities will center on the understanding of electronics commonly used in physics experiments. Take-home projects building practical electronics knowledge will be supplemented by simulations and instructor-led remote demonstrations. We will also gain familiarity with some classic experiments in modern physics.

In Winter quarter we will study classical mechanics and classical electromagnetic theory. We will extend the ideas of classical physics to include Einstein's special theory of relativity. Classical electrodynamics and relativity merge in the phenomena of electromagnetic waves. Our explorations will combine these threads with study of optics, with an emphasis on polarized light (explored both theoretically and through at-home explorations using a simple kit), in preparation for Spring work on quantum theory. We will also build theoretical skills in the analysis of experimental errors.

In Spring, physics will focus on theories of the microscopic world and connections with the macroscopic world we are more familiar with in daily life. Theoretical topics will be quantum mechanics and statistical mechanics.

In addition, a spring module in combinatorics will be offered for students in the program and for new students. Combinatorics is the mathematical study of arrangements and, especially, counting. Over the course of the quarter, we'll learn basic counting techniques, briefly apply those skills to questions of probability, and then learn about recurrence relations and generating functions, two powerful techniques for solving counting problems.

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. 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.

To successfully complete this program, students should have access to a scientific calculator, reliable internet access, notebooks, and a digital camera (phone cameras OK) or scanner. Students should expect to spend up to 16 hours in synchronous meetings each week using Zoom, Canvas, and web-based apps. Students will have access to alternatives to synchronous participation if students find themselves unable to participate due to technology, caregiving obligations, economic disruption, health risk, or illness.

### Registration

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 & magnetism).

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#### Signature Required

Students will need to demonstrate content knowledge equivalent to material covered in fall quarter. Contact faculty for more information.

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#### Signature Required

New students may join the program for 4 credits to take Combinatorics. Contact faculty via email caraherj@evergreen.edu with information about how you have met the Calculus I, II, and III prerequisite for Combinatorics.

The physics portions of the program are not open to new students in spring.

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### Academic details

physics, mathematics, engineering, and math and science education.

$45 fee in fall for needed electronics components.

Math and physics textbooks at intermediate and advanced levels are generally very expensive, and may be more than $600 total. However, those texts cover the entire year, and students will be required to have access to these texts for successful completion of the program. More information will be available by the beginning of spring quarter 2020 at the program website.

Content will be equivalent to intermediate or advanced work in undergraduate mathematics (e.g. differential equations, linear algebra) or physics (e.g. classical mechanics, electromagnetism, quantum mechanics, statistical mechanics). Students who successfully complete program requirements will earn upper-division science credit in mathematics or physics in those areas.