#### PHYS 106(F)Being Human in STEM

This course combines academic inquiry and community engagement to investigate the themes of diversity and social climate within STEM (science, technology, engineering and mathematics) disciplines. Students will examine how diverse identities including but not limited to gender, race, disability, sexuality, national origin, socioeconomic status, religion, and ethnicity shape the STEM experience both at Williams and nationally. We will ground our understanding through critical reading of primary scholarly research on topics such as implicit bias, identity threat, and effects of team diversity on excellence. From there, we will execute small group projects. Students will design, execute, and evaluate interventions that relate to the course goals and that have direct relevance to Williams students, faculty, and staff. For example, a student group could implement a survey of minoritized STEM students, or create a qualitative interview-based assessment of how socioeconomic status impacts students' abilities to participate in STEM fields. Course work includes weekly readings, reflective/opinion writing, in class discussion, and the development and presentation of a group project. [ more ]

Taught by: Phoebe Cohen, Savan Kharel

Catalog details#### PHYS 107Spacetime and Quanta

Last offered Fall 2017

Quantum mechanics and Einstein's relativity both drastically altered our view of the physical world when they were developed in the early twentieth century. In this course we will learn about the central concepts that define relativity and quantum mechanics, along with some of the diverse phenomena the two theories describe. These investigations will prepare us to discuss developments in condensed matter: explaining what makes materials different along with discussing exotic effects like superconductivity and superfluidity. We will also discuss recent developments in cosmology, where observations have produced a surprising picture for the make-up of our universe. This course is intended for students whose primary interests lie outside of the natural sciences and mathematics. The mathematics used will be algebra and trigonometry. [ more ]

Taught by: Swati Singh

Catalog details#### PHYS 108(F)Energy Science and Technology

Energy use has skyrocketed in the United States and elsewhere in the world, causing significant economic and political shifts, as well as concerns for the environment. This course will address the physics and technology of energy generation, consumption, and conservation. It will cover a wide range of energy sources, including fossil fuels, hydropower, solar energy, wind energy, and nuclear energy. We will discuss energy use in transportation, manufacturing, building heating, and building lighting. Students will learn to compare the efficiencies and environmental impacts of various energy sources and uses. [ more ]

Taught by: Kevin Jones

Catalog details#### PHYS 109(F)Sound, Light, and Perception

Light and sound allow us to perceive the world around us, from appreciating music and art to learning the details of atomic structure. Because of their importance in human experience, light and sound have long been the subject of scientific inquiry. How are sound and light related? How do physiology and neural processing allow us to hear and see the world around us? What are the origins of color and musical pitch? This course introduces the science and technology of light and sound to students not majoring in physics. We will start with the origins of sound and light as wave phenomena, and go on to topics including color, the optics of vision, the meaning of musical pitch and tone, and the physical basis of hearing. We will also discuss some recent technological applications of light, such as lasers and optical communications. The class will meet for two 75-minute periods each week for a variable mixture of lecture, discussion, and hands-on, interactive experiments. [ more ]

Taught by: Protik Majumder

Catalog details#### PHYS 131(F)Introduction to Mechanics

We focus first on the Newtonian mechanics of point particles: the relationship between velocity, acceleration, and position; the puzzle of circular motion; forces, Newton's laws, and gravitation; energy and momentum; and the physics of vibrations. Then we turn to the basic properties of waves, such as interference and refraction, as exemplified by sound and light waves. We also study the optics of lenses, mirrors and the human eye. This course is not intended for students who have successfully completed an AP physics course in high school. [ more ]

Taught by: Graham Giovanetti

Catalog details#### PHYS 132(S)Electromagnetism and the Physics of Matter

This course is intended as the second half of a one-year survey of physics with some emphasis on applications to medicine. In the first part of the semester we will focus on electromagnetic phenomena. We will introduce the concept of electric and magnetic fields and study in detail the way in which electrical circuits and circuit elements work. The deep connection between electric and magnetic phenomena is highlighted with a discussion of Faraday's Law of Induction. Following our introduction to electromagnetism we will discuss some of the most central topics in twentieth-century physics, including Einstein's theory of special relativity and some aspects of quantum theory. We will end with a treatment of nuclear physics, radioactivity, and uses of radiation. [ more ]

Taught by: Savan Kharel

Catalog details#### PHYS 141(F)Mechanics and Waves

This is the typical first course for a prospective physics major. It covers the same topics as PHYS 131, but with a higher level of mathematical sophistication. It is intended for students with solid backgrounds in the sciences, either from high school or college, who are comfortable with basic calculus. [ more ]

Taught by: Katharine Jensen

Catalog details#### PHYS 142(S)Foundations of Modern Physics

Newtonian Mechanics, spectacular as it is in describing planetary motion and a wide range of other phenomena, only hints at the richness of behaviors seen in the universe. Special relativity, which extends physics into the realm of high speeds and high energies, requires we rethink our basic notions of space and time. Quantum mechanics successfully describes atoms, molecules, and solids while at the same time calling into question our expectation of what can be predicted by a physical theory. Statistical physics reveals new behaviors that emerge when many particles are present in a system. This course will survey ideas from each of these three arenas, and can serve either as a terminal course for those seeking to complete a year of physics or as the basis for future advanced study of these topics. [ more ]

Taught by: Charlie Doret

Catalog details#### PHYS 151(F)Seminar in Modern Physics

Newtonian Mechanics, spectacular as it is in describing planetary motion and a wide range of other phenomena, only hints at the richness of behaviors seen in the universe. Special relativity has extended physics into the realm of high speeds and high energies and requires us to rethink our basic notions of space and time. Quantum mechanics successfully describes atoms, molecules, and solids while at the same time calling into question our notions of what can be predicted by a physical theory. Statistical physics reveals new behaviors that emerge when many particles are present in a system. This course covers the same basic material as PHYS 142 but in a small seminar format for students with strong prior preparation in physics. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 201(F)Electricity and Magnetism

The classical theory of electricity and magnetism is very rich yet it can be written in a remarkably succinct form using Maxwell's equations. This course is an introduction to electricity and magnetism and their mathematical description, connecting electric and magnetic phenomena via the special theory of relativity. Topics include electrostatics, magnetic fields, electromagnetic induction, DC and AC circuits, and the electromagnetic properties of matter. The laboratory component of the course is an introduction to electronics where students will develop skills in building and debugging electrical circuits. [ more ]

Taught by: David Tucker-Smith

Catalog details#### PHYS 202(S)Vibrations, Waves and Optics

Waves and oscillations characterize many different physical systems, including vibrating strings, springs, water waves, sound waves, electromagnetic waves, and gravitational waves. Quantum mechanics even describes particles with wave functions. Despite these diverse settings waves exhibit several common characteristics, so that the understanding of a few simple systems can provide insight into a wide array of phenomena. In this course we begin with the study of oscillations of simple systems with only a few degrees of freedom. We then move on to study transverse and longitudinal waves in continuous media in order to gain a general description of wave behavior. The rest of the course focuses on electromagnetic waves and in particular on optical examples of wave phenomena. In addition to well known optical effects such as interference and diffraction, we will study a number of modern applications of optics such as short pulse lasers and optical communications. Throughout the course mathematical methods useful for higher-level physics will be introduced. [ more ]

Taught by: Graham Giovanetti

Catalog details#### PHYS 210(S)Mathematical Methods for Scientists

This course covers a variety of mathematical methods used in the sciences, focusing particularly on the solution of ordinary and partial differential equations. In addition to calling attention to certain special equations that arise frequently in the study of waves and diffusion, we develop general techniques such as looking for series solutions and, in the case of nonlinear equations, using phase portraits and linearizing around fixed points. We study some simple numerical techniques for solving differential equations. A series of optional sessions in Mathematica will be offered for students who are not already familiar with this computational tool. [ more ]

Taught by: Daniel Aalberts, David Tucker-Smith

Catalog details#### PHYS 231 TFacts of Life

Last offered Fall 2012

The cancer death rate scales like (age)^{6} so it was thought that a proliferating cancer cell must have acquired 6 mutations. The probability of having had N sexual partners scales like N^{2.4.} Body Mass Index = Mass / Length^{2}. The heart rate is proportional to the organism's mass^{0.75}. The number of policemen scales like population^{1.15}. Power-law relationships often describe emergent phenomena of self-organizing systems.
In this course we will learn how to obtain data and plot it in an informative way, including estimates of the errors of fits. We will learn how to describe phenomena with differential equations and to find analytic and numerical solutions. With those tools we will study the human experience: births, body size, sex, death rates (by cause, by age, by gender), metrics of cities, distributions of common names, population growth rates, per capita use of energy, the spread of disease, etc. Projects will involve applying the methods to new phenomena. [ more ]

#### PHYS 234(S)Introduction to Materials Science

Materials Science is the study of how the microscopic structure of materials--whether steel, carbon fiber, glass, wood, plastic, or mayonnaise--determines their macroscopic mechanical, thermal, electric, and other properties. Topics of this course include classifying materials; material structure; thermodynamics and phase transformations; material properties and testing; how solids bend, flow, and ultimately break; and how to choose the right material for design applications. Materials Science is a highly interdisciplinary field and as a result the course prerequisites are broad but also flexible. Interested students who are unsure about their preparation are strongly encouraged to contact the instructor. [ more ]

Taught by: Katharine Jensen

Catalog details#### PHYS 301(F)Quantum Physics

This course serves as a one-semester introduction to the history, formalism, and phenomenology of quantum mechanics. We begin with a discussion of the historical origins of the quantum theory, and the Schroedinger wave equation. The concepts of matter waves and wave-packets are introduced. Solutions to one-dimensional problems will be treated prior to introducing the system which serves as a hallmark of the success of quantum theory, the three-dimensional hydrogen atom. In the second half of the course, we will develop the important connection between the underlying mathematical formalism and the physical predictions of the quantum theory and introduce the Heisenberg formalism. We then go on to apply this knowledge to several important problems within the realm of atomic and nuclear physics concentrating on applications involving angular momentum and spins. [ more ]

Taught by: Charlie Doret

Catalog details#### PHYS 302(S)Stat Mechanics & Thermodynamics

Macroscopic objects are made up of huge numbers of fundamental particles interacting in simple ways--obeying the Schrõdinger equation, Newton's and Coulomb's Laws--and these objects can be described by macroscopic properties like temperature, pressure, magnetization, heat capacity, conductivity, etc. In this course we will develop the tools of statistical physics, which will allow us to predict the cooperative phenomena that emerge in large ensembles of interacting particles. We will apply those tools to a wide variety of physical questions, including the behavior of gases, polymers, heat engines, biological and astrophysical systems, magnets, and electrons in solids. [ more ]

Taught by: Protik Majumder

Catalog details#### PHYS 308Energy Science and Technology, Advanced Section

Last offered Spring 2013

Energy use has skyrocketed in the United States and elsewhere in the world, causing significant economic and political shifts, as well as concerns for the environment. This course will address the physics and technology of energy generation, consumption, and conservation. It will cover a wide range of energy sources, including fossil fuels, hydropower, solar energy, wind energy, and nuclear energy. We will discuss energy use in transportation, manufacturing, building heating, and building lighting. Students will learn to compare the efficiencies and environmental impacts of various energy sources and uses. PHYS 308 is an advanced section of PHYS 108 "Energy Science and Technology" and is intended for students who have substantial background in college-level physics. It will include all of the material in PHYS 108, supplemented with more advanced readings and more challenging assignments. [ more ]

#### PHYS 312Philosophical Implications of Modern Physics

Last offered Spring 2019

Some of the discoveries made by physicists over the last century seem to show that our common sense views are deeply at odds with our most sophisticated and best confirmed scientific theories. The course will present the essential ideas of relativity theory and quantum theory and explore their implications for philosophy. We will ask, for example, what these theories tell us about the nature of space, time, probability and causality. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 314 T(S)Controlling Quanta

This course will explore modern developments in the control of individual quantum systems. Topics covered will include basic physical theories of atoms coupled to photons, underlying mathematical tools (including Lie algebras and groups), and computational methods to simulate and analyze quantum systems. Applications to quantum computing, teleportation, and experimental metaphysics (Bell's inequality) will also be discussed. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 315 T(S)Computational Biology

This course will provide an overview of Computational Biology, the application of computational, mathematical, statistical, and physical problem-solving techniques to interpret the rapidly expanding amount of biological data. Topics covered will include database searching, DNA sequence alignment, clustering, RNA structure prediction, protein structural alignment, methods of analyzing gene expression, networks, and genome assembly using techniques such as string matching, dynamic programming, hidden Markov models, and expectation-maximization. [ more ]

Taught by: Daniel Aalberts

Catalog details#### PHYS 316Protecting Information: Applications of Abstract Algebra and Quantum Physics

Last offered Spring 2017

Living in the information age, we find ourselves depending more and more on codes that protect messages against either noise or eavesdropping. This course examines some of the most important codes currently being used to protect information, including linear codes, which in addition to being mathematically elegant are the most practical codes for error correction, and the RSA public key cryptographic scheme, popular nowadays for internet applications. We also study the standard AES system as well as an increasingly popular cryptographic strategy based on elliptic curves. Looking ahead by a decade or more, we show how a quantum computer could crack the RSA scheme in short order, and how quantum cryptographic devices will achieve security through the inherent unpredictability of quantum events. [ more ]

Taught by: Susan Loepp

Catalog details#### PHYS 319Integrative Bioinformatics, Genomics, and Proteomics Lab

Last offered Fall 2016

What can computational biology teach us about cancer? In this capstone experience for the Genomics, Proteomics, and Bioinformatics program, computational analysis and wet-lab investigations will inform each other, as students majoring in biology, chemistry, computer science, mathematics/statistics, and physics contribute their own expertise to explore how ever-growing gene and protein data-sets can provide key insights into human disease. In this course, we will take advantage of one well-studied system, the highly conserved Ras-related family of proteins, which play a central role in numerous fundamental processes within the cell. The course will integrate bioinformatics and molecular biology, using database searching, alignments and pattern matching, phylogenetics, and recombinant DNA techniques to reconstruct the evolution of gene families by focusing on the gene duplication events and gene rearrangements that have occurred over the course of eukaryotic speciation. By utilizing high through-put approaches to investigate genes involved in the MAPK signal transduction pathway in human colon cancer cell lines, students will uncover regulatory mechanisms that are aberrantly altered by siRNA knockdown of putative regulatory components. This functional genomic strategy will be coupled with independent projects using phosphorylation-state specific antisera to test our hypotheses. Proteomic analysis will introduce the students to de novo structural prediction and threading algorithms, as well as data-mining approaches and Bayesian modeling of protein network dynamics in single cells. Flow cytometry and mass spectrometry will be used to study networks of interacting proteins in colon tumor cells. [ more ]

Taught by: Lois Banta

Catalog details#### PHYS 321(F)Introduction to Particle Physics

The Standard Model of particle physics incorporates special relativity, quantum mechanics, and almost all that we know about elementary particles and their interactions. This course introduces some of the main ideas and phenomena associated with the Standard Model. After a review of relativistic kinematics, we will learn about symmetries in particle physics, Feynman diagrams, and selected applications of quantum electrodynamics, the weak interactions, and quantum chromodynamics. We will conclude with a discussion of spontaneous symmetry breaking and the Higgs mechanism. [ more ]

Taught by: Savan Kharel

Catalog details#### PHYS 402 TApplications of Quantum Mechanics

Last offered Spring 2019

This course will explore a number of important topics in the application of quantum mechanics to physical systems, including perturbation theory, the variational principle and the semiclassical interaction of atoms and radiation. The course will finish up with three weeks on quantum optics including an experimental project on non-classical interference phenomena. Applications and examples will be taken mostly from atomic physics with some discussion of solid state systems. [ more ]

Taught by: Catherine Kealhofer

Catalog details#### PHYS 404 T(S)Unsolved Problems in Galaxy Evolution

In this tutorial, we will learn about galaxies and their evolution by focusing on some of the key mysteries astronomers are trying to solve. Questions may include: How do galaxies turn their gas supply into stars? Is there a universal initial mass function for star formation? What is the origin of multiple stellar populations in globular clusters? Why do some galaxies cease star formation? Which galaxies reionized the universe? We will discuss the nature of each unsolved problem, debate the theories proposed to answer it, and consider how future progress might be made. [ more ]

Taught by: Anne Jaskot

Catalog details#### PHYS 405 T(F)Electromagnetic Theory

This course builds on the material of Physics 201, and explores the application of Maxwell's Equations to understand a range of topics including electric fields and matter, magnetic materials, light, and radiation. As we explore diverse phenomena, we will learn useful approximation techniques and beautiful mathematical tools. In addition to weekly tutorial meetings, the class will meet once a week as a whole to introduce new material. [ more ]

Taught by: Daniel Aalberts

Catalog details#### PHYS 411 TClassical Mechanics

Last offered Fall 2018

This course will explore advanced topics in classical mechanics including the calculus of variations, the Lagrangian and Hamiltonian formulations of mechanics, phase space, non-linear dynamics and chaos, central-force motion, non-inertial reference frames (including implications for physics on a rotating Earth), and rigid-body rotations. Numerical and perturbative techniques will be developed and used extensively. We will also examine the ways in which classical mechanics informs other fields of physics. In addition to weekly tutorial meetings the class with will meet once a week as a whole to discuss new material. [ more ]

Taught by: Daniel Aalberts

Catalog details#### PHYS 412 T(F)Heliophysics

We study all aspects of the Sun, our nearest star. This semester follows the total solar eclipses of August 21, 2017, whose totality crossed the U.S. from coast to coast, and the July 2, 2019, total solar eclipse that crossed Chile and Argentina. In addition to discussing our observations of these eclipses and what has been learned about the solar atmosphere from eclipse research, we discuss the solar interior (including the Nobel-prize-winning solar neutrino experiment and helioseismology), the photosphere, the chromosphere, the corona, and the solar wind. We discuss the Sun as an example of stars in general. We discuss both theoretical aspects and observational techniques, including work at recent total solar eclipses. We discuss results from current spacecraft, including the Solar and Heliospheric Observatory (SOHO), the Solar Dynamics Observatory, the Sun Watcher (SWAP), and Hinode (Sunrise), and the new GOES/UVSI (Solar Ultraviolet Imager) run by an alumnus as well as additional Total Solar Irradiance measurements from ACRIMSAT and SORCE. We will discuss the role of solar observations in confirming Einstein's General Theory of Relativity with the bending of light at the 1919, 1922, and 2017 total solar eclipses as well as gravitational redshift measurements in solar spectral lines, extending our discussion to the recent "chirp" of gravitational radiation reported from several colliding black holes and neutron stars observed with the Laser Interferometer Gravitational-wave Observatory (LIGO). We hope to observe the transit of Mercury across the face of the Sun on November 11, 2019, during the semester; we also discuss our data analysis of recent transits of Mercury we observed from the ground and from space (most recently in May 2016). We will highlight the 2004 and 2012 transits of Venus across the face of the Sun as observed from Earth, the first such transits of Venus since 1882, as well as our work in observing transits of Venus from Jupiter with the Hubble. [ more ]

Taught by: Jay Pasachoff

Catalog details#### PHYS 418(S)Gravity

This course is an introduction Einstein's theory of general relativity. We begin with a review of special relativity, emphasizing geometrical aspects of Minkowski spacetime. Working from the equivalence principle, we then motivate gravity as spacetime curvature, and study in detail the Schwarzschild geometry around a spherically symmetric mass. After this application, we use tensors to develop Einstein's equation, which describes how energy density curves spacetime. With this equation in hand we study the Friedmann-Robertson-Walker geometries for an expanding universe, and finally, we linearize Einstein's equation to develop the theory of gravitational waves. [ more ]

Taught by: David Tucker-Smith

Catalog details#### PHYS 451Condensed Matter Physics

Last offered Spring 2019

Condensed matter physics is an important area of current research and serves as the basis for modern electronic technology. We plan to explore the physics of metals, insulators, semiconductors, superconductors, and photonic crystals, with particular attention to structure, thermal properties, energy bands, and electronic properties. [ more ]

Taught by: Daniel Aalberts

Catalog details#### PHYS 475Methods in Mathematical Fluid Dynamics

Last offered Spring 2016

The mathematical study of fluids is an exciting field with applications in areas such as engineering, physics and biology. The applied nature of the subject has led to important developments in aerodynamics and hydrodynamics. From ocean currents and exploding supernovae to weather prediction and even traffic flow, several partial differential equations (pde) have been proposed as models to study fluid phenomena. This course is designed to both, introduce students to some of the techniques used in mathematical fluid dynamics and lay down a foundation for future research in this and other related areas. Briefly, we start with the method of characteristics, a useful tool in the study of pde. Symmetry and geometrical arguments, special solutions, energy methods, particle trajectories, and techniques from ordinary differential equations (ode) are also discussed. A special focus will be on models from hydrodynamics. These include the KdV and the Camasss Holm equations (and generalizations thereof), and the Euler equations of ideal fluids. Mainly, we will be concerned with models whose solutions depend on time and one spatial variable, although depending on student interest and time, we may also investigate higher-dimensional models. [ more ]

#### PHYS 493(F)Senior Research: Physics

An original experimental or theoretical investigation is carried out under the direction of a faculty member in Physics, as discussed above under the heading of *The Degree with Honors in Physics*. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 494(S)Senior Research: Physics

An original experimental or theoretical investigation is carried out under the direction of a faculty member in Physics, as discussed above under the heading of *The Degree with Honors in Physics*. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 495(F)Senior Research: Astrophysics

An original experimental or theoretical investigation is carried out under the direction of a faculty member in Astronomy or Physics, as discussed under the heading of the degree with honors in Astrophysics above. [ more ]

Taught by: Jay Pasachoff

Catalog details#### PHYS 496(S)Senior Research: Astrophysics

An original experimental or theoretical investigation is carried out under the direction of a faculty member in Astronomy or Physics, as discussed under the heading of the degree with honors in Astrophysics above. [ more ]

Taught by: Jay Pasachoff

Catalog details#### PHYS 497(F)Independent Study: Physics

Physics independent study. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 498(S)Independent Study: Physics

Physics independent study. [ more ]

Taught by: Frederick Strauch

Catalog details#### PHYS 499(F, S)Physics and Astronomy Colloquium

Physicists and Astronomers from around the country come to explain their research. Students of Physics and Astronomy at any level are welcome. Registration is not necessary to attend. A non-credit course. [ more ]

Taught by: Frederick Strauch

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