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Conceptual and problem solving skills in preparation for PHYS 211: --analysis and mathematical descriptions of physical situations --understanding the meaning of the solutions Prerequisite: Credit or concurrent registration in MATH 220 or MATH 221.

[IAI Code: P1900L] Newton's Laws, work and energy, rotational motion, fluids, thermodynamics, and waves. A noncalculus-based approach for majors in the life sciences, preprofessional health programs, agriculture, and veterinary medicine. Credit is not given toward graduation for: Credit is not given for both PHYS 101 and either PHYS 211 or PHYS 213. Prerequisite: Trigonometry.

Electric forces and fields, electric potential, electric circuits, magnetic forces and fields, geometrical optics, relativity, and modern physics. A noncalculus-based approach for majors in the life sciences, preprofessional health programs, agriculture, and veterinary medicine. Credit is not given for both PHYS 102 and either PHYS 212 or PHYS 214. Prerequisite: PHYS 101.

Exploration of careers founded on physics undergraduate training. Introduction to the Physics Department, faculty, research and curricula. Outside speaker presentations. Approved for S/U grading only.

Approved for letter and S/U grading. May be repeated.

[IAI Code: P2900L and PHY911] Newton's Laws, work and energy, static properties and fluids, oscillations, transverse waves, systems of particles, and rotations. A calculus-based approach for majors in engineering, mathematics, physics and chemistry. Credit is not given toward graduation for: Credit is not given for both PHYS 211 and PHYS 101. Prerequisite: Credit or concurrent registration in MATH 231.

[IAI Code: PHY912] Coulomb's Law, electric fields, Gauss' Law, electric potential, capacitance, circuits, magnetic forces and fields, Ampere's law, induction, electromagnetic waves, polarization, and geometrical optics. A calculus-based approach for majors in engineering, mathematics, physics, and chemistry. Credit is not given toward graduation for: Credit is not given for both PHYS 212 and PHYS 102. Prerequisite: PHYS 211; credit or concurrent registration in MATH 241.

First and second laws of thermodynamics including kinetic theory of gases, heat capacity, heat engines, introduction to entropy and statistical mechanics, and introduction to application of free energy and Boltzmann factor. A calculus-based approach for majors in engineering, mathematics, physics and chemistry. Credit is not given for both PHYS 213 and PHYS 101. Prerequisite: PHYS 211; credit or concurrent registration in MATH 241.

Interference and diffraction, photons and matter waves, the Bohr atom, uncertainty principle, and wave mechanics. A calculus-based course for majors in engineering, mathematics, physics, and chemistry. Credit is not given for both PHYS 214 and PHYS 102. Prerequisite: PHYS 212.

Supplement to PHYS 212 with a collaborative group learning approach to improving conceptual understanding and problem solving in introductory calculus-based electricity & magnetism. Prerequisite: PHYS 100; concurrent registration in PHYS 212.

Theory of Special Relativity, with applications to kinematics and dynamics. Key mathematical methods as they apply to aspects of electromagnetic theory and classical mechanics, including vector analysis, series expansions, matrices, Fourier analysis, partial differentiation, three-dimensional calculus, and simple differential equations. Prerequisite: Credit or concurrent registration in PHYS 212.

Project-based course that explores computational algorithms to solve a selection of physics problems. Algorithmic methods include Monte Carlo, numerical integration, machine learning, and simulation of dynamical systems. Topics will be selected from application areas that include chaos, orbital motion, particle physics, quantum computation, climate and fluid dynamics. No prior programming experience is required. Approved for both Letter and S/U grading. Prerequisite: Concurrent enrollment in PHYS 225.

Kinematics and dynamics of classical systems, including a review of Newtonian kinematics and dynamics. Three dimensional motion, variable mass, and conservation laws; damped and periodically driven oscillations; gravitational potential of extended objects and motion in rotating frames of reference; Lagrangian and Hamiltonian mechanics. Prerequisite: PHYS 225; credit or concurrent registration in MATH 285 or MATH 286.

Continuation of PHYS 325. Central force motion, collisions and scattering, rotational motion, coupled oscillations, continuous media, and fluid dynamics. Prerequisite: PHYS 325.

Same as ATMS 302. See ATMS 302.

A basic introduction to probability and data analysis from a physics perspective. The methods of extracting meaningful information from data using probability theory and statistical analyses will be presented. Additionally, students will gain familiarity with the concepts through programming exercises using Python notebooks. Topics to be covered include basics of statistics and probability theory, probability distributions, estimators, uncertainties, confidence intervals and hypothesis testing, Fourier, and Monte Carlo methods. Prerequisite: PHYS 211, PHYS 212, and PHYS 213.

Introduction to quantum information and computing for sophomores, juniors and seniors from any major. Self-contained description of quantum states and qubits, operators, measurements, tensor products, density matrices, quantum gates and circuits, and quantum computing/simulation algorithms. One of the key points of departure from classical physics, quantum entanglement, is threaded throughout all these topics including a dedicated discussion of Bell's theorem. Students will apply these basic aspects of quantum mechanics to program online quantum computers (e.g., IBM cloud) to gain insight into canonical algorithms such as Deutsch-Jozsa, Shor, and/or Grover as well as standard protocols such as teleportation and entanglement swapping. Prerequisite: PHYS 214.

Designed to support Learning Assistants (LAs) who are working as instructional aids in lab or discussion sections of the introductory physics courses. Students will study pedagogical strategies for instructor-student interaction and philosophies guiding lab design and/or discussion problem creation. Prerequisite: Instructor Approval Required. Lab LAs must have successfully completed PHYS 101, PHYS 102, PHYS 211, or PHYS 212. Discussion LAs must have successfully completed PHYS 100 and PHYS 211.

Designed for students who have been Learning Assistants (LAs) in the lab sections of the introductory physics courses or in discussion sections of PHYS 100 and who have successfully completed PHYS 394. The goal of the course is to provide students the opportunity to pursue their interest in the Learning Assistant program by continuing working as assistants in the lab or discussions sections of the introductory physics courses and at the same time conduct a study on the program. At the end of the semester students present their work at the Expert LA symposium. May be repeated if topics vary, to a maximum of 2 credit hours. Prerequisite: PHYS 394.

Experiments and techniques in classical mechanics and electromagnetism, emphasizing hands-on, skills-based learning. Dynamics of electrical and mechanical oscillators in both time and frequency domains. Measurements of electrostatic fields, transmission lines, EM waves, and radiation. Electromagnetic phenomena in dielectrics, conductors, and magnetic materials. Development of practical skills in experimental design, data acquisition, uncertainty quantification, numerical modeling, and scientific communication. 4 undergraduate hours. 4 graduate hours. Prerequisite: PHYS 325. Credit or concurrent enrollment in PHYS 435 or ECE 329.

Wave kinematics; geometrical optics: basic concepts, ray-tracing and matrix formalism, Gaussian imaging by thick lenses, stops, apertures, and intensity relations; interference; interference spectroscopy and coherence; diffraction: Fresnel-Kirchhoff formulation, Fraunhofer case, Fresnel case, and holography; polarized light. 4 undergraduate hours. 3 or 4 graduate hours. (3 hours without lab). Prerequisite: PHYS 214 and PHYS 435 or ECE 329.

Techniques and experiments in the physics of atoms, atomic nuclei, molecules, the solid state, and other areas of modern physical research. 5 undergraduate hours. 4 graduate hours. Prerequisite: Credit or concurrent registration in PHYS 485 or PHYS 486.

Physics of semiconductor devices; theory and application of discrete and integrated devices in linear circuits; use of operational amplifiers and feedback; regulation, oscillators, and modulation; emphasizes practical experience. 5 undergraduate hours. 4 graduate hours. Prerequisite: PHYS 325.

For advanced undergraduate and graduate students in Physics interested in the connection between biology and physics (no prior biology experience needed). This course explores Nobel Prize-winning experiments in biological physics and quantitative biology. Students will learn important techniques, including: optical imaging beyond the diffraction limit; optical trapping of microorganisms and subcellular structures; optical detection using nitrogen vacancy centers; molecular biology and statistical analyses for testing evolutionary models; and computational prediction of protein folding. 4 undergraduate hours. 4 graduate hours. The course requires intermediate background in statistics and basic coding skills in Python or Matlab. Prerequisite: PHYS 213, PHYS 214, and PHYS 325 or equivalent; CS 101 or CS 124 or equivalent. This course is meant for undergraduate students of junior or senior standing, or graduate students in physics.

Equilibrium thermodynamics, statistical mechanics, and kinetic theory of gases. A unified treatment is used in that the principles of heat and thermodynamics are discussed along with statistical postulates and the microscopic approach of introductory quantum mechanics. 4 undergraduate hours. 4 graduate hours. Credit is not given for both PHYS 427 and any of ME 404, CHEM 444, MSE 500. Prerequisite: PHYS 213; PHYS 214; PHYS 435 or ECE 329.

Static electric and magnetic fields, their interactions with electric charge and current, and their transformation properties; the effect of special relativity is incorporated. Macroscopic fields in material media are described. Register for the lecture and one of the discussion sections. 3 undergraduate hours. 3 graduate hours. Prerequisite: MATH 285 and PHYS 325. Credit or concurrent enrollment in MATH 257 or MATH 416.

Time-dependent fields. Electromagnetic induction, Maxwell's equations, electromagnetic wave propagation in various media and structures, and electromagnetic radiation from charge and current distributions. Relativistic covariance of Maxwell's equations. undergraduate hours. 3 graduate hours. Prerequisite: PHYS 435.

This is an immersive advanced computational physics course. The goals in this class are to program from scratch, simulate, and understand the physics within a series of multi-week projects spanning areas such as quantum computing, statistical mechanics, the renormalization group, machine learning, and topological insulators. The course approach (lectures, one-on-one interaction in class, etc.) is centered around giving you the information and skills you need to succeed in carrying out these projects. 3 undergraduate hours. No graduate credit. Prerequisite: PHYS 246.

Same as CSE 485 and MSE 485. See MSE 485.

Basic concepts of quantum theory which underlie modern theories of the properties of materials; elements of atomic and nuclear theory; kinetic theory and statistical mechanics; quantum theory and simple applications; atomic spectra and atomic structure; molecular structure and chemical binding. 3 undergraduate hours. 3 graduate hours. Credit is not given for both PHYS 485 and CHEM 442. Prerequisite: PHYS 325. Credit or concurrent registration in PHYS 435.

Atomic phenomena integrated with an introduction to quantum theory; evidence for the atomic nature of matter and the properties of the Schrodinger equation, single particle solutions in one dimension, the hydrogen atom, perturbation theory, external fields, and atomic spectroscopy of outer electrons. 4 undergraduate hours. 4 graduate hours. Prerequisite: PHYS 214 and PHYS 435 or ECE 329.

Continuation of PHYS 486. Identical particles, spectral hyperfine structure, magnetic properties of matter, atomic spectroscopy of inner electrons, high-energy photon effects, molecular binding and spectra, emission and absorption of light, and symmetry principles. 4 undergraduate hours. 4 graduate hours. Prerequisite: PHYS 486.

Examination of current research topics through extensive reading, writing, and oral-presentation activities. 3 undergraduate hours. No graduate credit.

Individual study at an advanced level in a subject not covered by course offerings. 1 to 4 undergraduate hours. 1 to 4 graduate hours. May be repeated. Prerequisite: Consent of instructor.

Designed to give students a solid foundation in machine learning applications to physics, positioning itself at the intersection of machine learning and data-intensive science. This course will introduce students to the fundamentals of analysis and interpretation of scientific data, and applications of machine learning to problems common in laboratory science such as classification and regression. There will be two 75-minute classes each week, split into discussions of core principles and hands-on exercises involving coding and data. There will be a few projects throughout semester that will build on the course material and utilize open source software and open data in physics and related fields. The list of topics will evolve, according to the interests of the class and instructors. Material will be clustered into units of varying duration, as indicated below. The lists of suggested readings and references are advisory; a large amount of material of excellent quality is now available on the worldwide web, particularly on the sites of university courses addressing the topics of each unit. A distinguishing feature of this course is its sharp focus on endeavors in the data-rich physical sciences as the arenas in which modern machine learning techniques are taught. The course uses open scientific data, open source software from data science and physics-related fields, and publicly-available information as enabling elements. Research-inspired projects are an important part of the course and students will not only execute them but will play an active role in helping define and shape them. Example projects might include machine learning approaches to searches for new particles or interactions at high-energy colliders; methods of particle tracking and reconstruction; identification, classification and measurement of astrophysical phenomena; novel approaches to medical imaging and simulation using techniques from physics and machine learning; machine learning in quantum information science. Through these projects and the course material, students will learn how large datasets in physics are generated, curated, and analyzed, using machine learning as a tool to generate key insights in both experimental and theoretical science. Prerequisite: Familiarity with a high-level computing language such as C++, Python, or Java; mathematical competence typical of graduates (either as majors or minors) from undergraduate programs in Physics and Astronomy. Primarily for students in the Engineering: Instrumentation and Applied Physics, MEng program. Other students may enroll with permission of the M.Eng. program director.

Review of Maxwell's equations; relativistic formulation of the electromagnetic field and the motion of charged particles; plane and guided waves; retarded potentials; radiation from simple antennas; radiation from accelerated charged particles; scattering and further topics. Prerequisite: PHYS 436.

Core techniques of mathematical physics widely used in the physical sciences. Calculus of variations and its applications; partial differential equations of mathematical physics (including classification and boundary conditions); separation of variables, series solutions of ordinary differential equations and Sturm-Liouville eigenproblems; Legendre polynomials, spherical harmonics, Bessel functions and their applications; normal mode eigenproblems (including the wave and diffusion equations); inhomogeneous ordinary differential equations (including variation of parameters); inhomogeneous partial differential equations and Green functions; potential theory; integral equations (including Fredholm theory). Prerequisite: MATH 285.

Experimental and theoretical fundamentals of quantum information, using nonclassical features of quantum physics (wave-particle duality, superposition, and entanglement) to surpass the information-processing capabilities of classical systems. Underlying fundamental quantum phenomena, including tests of nonlocality, quantum erasers, the quantum Zeno effect, squeezed light, multi-particle interference, state transformations of the Bloch sphere, and decoherence; quantum cryptography and teleportation; quantum information theory; quantum computation algorithms and techniques for error correction; experimental "qubit" systems. Prerequisite: PHYS 486 is recommended.

Systematic introduction to Einstein's theory, with emphasis on modern coordinate-free methods of computation. Review of special relativity, modern differential geometry, foundations of general relativity, laws of physics in the presence of a gravitational field, linearized theory, and experimental tests of gravitation theories. Same as ASTR 515. Prerequisite: PHYS 436.

Students will engage in the collaborative design and execution of a year-long Instrumentation and measurement-intensive technical project. Required activities will include a written project proposal of work to be undertaken, informal group-generated oral presentations on technical issues, periodic formal written progress reports, a final project oral presentation, and a final project paper. The set of projects might include investigations suggested by industry partners. 4 graduate hours. No professional credit. May be repeated in consecutive terms to a total of 8 hours. Prerequisite: Primarily for students in the Engineering: Instrumentation and Applied Physics, MEng program. Other students may enroll with permission of the M.Eng. program director.

The goal of the course is to familiarize students with some of the techniques available to them when defining and proposing a technical project in an unfamiliar domain. There will be two 50-minute classes each week, split into a discussion of basic principles and a simple hands-on laboratory exercise. The list of topics will evolve, according to the interests of the class and instructors. 2 graduate hours. No professional credit. Prerequisite: Concurrent registration in PHYS 523 required. Primarily for students in the Engineering: Instrumentation and Applied Physics, MEng program. Other students may enroll with permission of the MEng program director.

Covers the theoretical foundation of machine learning using ideas from functional analysis, spectral graph theory, stochastic processes and other branches of physics. The emphasis is on modern physics-inspired mathematical, statistical and Monte Carlo methods for analyzing scientific data. Topics to be covered include review of linear algebra and Hilbert space, spectral graph theory, clustering methods, dimensional reduction techniques, Reproducing Kernel Hilbert Space, kernel embedding, Grassmannian manifolds, matrix and tensor decompositions, stochastic sampling methods, numerical optimization, cross entropy method, Markov Chain Monte Carlo, and Gaussian Process. Prerequisite: Strong background in linear algebra, analysis, statistical mechanics, classical mechanics, and quantum mechanics.

Hartree-Fock theory and electron-electron interactions; electron-phonon interactions; electron dynamics and transport; BCS theory of superconductivity; elastic properties; thermal properties due to anharmonicity; defects in solids. Prerequisite: PHYS 560 and PHYS 581.

Same as ECE 535. See ECE 535.

Basic calculations in elementary particle theory. Quantum electrodynamics, quantum chromodynamics, and the Glashow-Weinberg-Salam theory of weak and electromagnetic interactions as applied to the phenomenology of particle decays and high energy reactions. Prerequisite: Recommended: credit or concurrent registration in PHYS 582.

Second course in quantum mechanics. Operators, state vectors, and the formal structure of quantum theory; operator treatments of simple systems; angular momentum and vector addition coefficients; stationary state perturbation theory; introduction to scattering theory for particles without spin, partial wave analysis, and Born approximation; examples taken from atomic, nuclear, and elementary particle physics. Prerequisite: PHYS 485 or PHYS 487.

Standard techniques of field theory as used by experimenters and theorists; relativistic quantum mechanics of a single particle; Lagrangian field theories, perturbation theory, and calculation of lowest-order processes; introduction to Feynman diagrams and higher order processes; examples taken from quantum electrodynamics, solid-state and elementary particle physics, and many-body theory. Prerequisite: PHYS 581.

Introduction to research in the Department of Physics. Advice on choosing a field of research and finding a research advisor. Faculty-presented overviews of the major areas of research available in the Physics Department. General discussions on instructional topics as well as ethics in teaching and sciences.

Individual study in a subject not covered in course offerings may be arranged for credit by registration under this number. May be repeated. 2 to 16 hours for full term; 1 to 8 hours for half-term. Prerequisite: Consent of instructor.

Subject offerings of new and developing areas of knowledge in physics intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. May be repeated in the same or separate terms if topics vary.

Approved for S/U grading only. May be repeated in the same term or in separate terms.