PHSX - Physics

PHSX 103IN The Physics of How Things Work: 3 Credits (3 Lec)

PREREQUISITE: High School Algebra. (Sp) A practical approach to a broad array of fundamental topics in physics for non-science majors taught by analyzing things that are used and observed in everyday life. Classroom demonstrations will provide the opportunity for in-class analysis, discussions, and hands-on activities. Physics principals will be used to scrutinize issues such as energy and recycling from economic and environmental perspectives. The latest technology in transportation, electronics, and energy production will be analyzed. The connection between basic research in physics and modern technology will be examined. Students will not receive credit if they have passed PHSX 205, PHSX 220, or PHSX 240

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Upon completion of this course, students should be able to: distinguish between a hypothesis, data, analysis, and conclusions in a scientific experiment or observation.
ask scientifically oriented questions
give priority to evidence in responding to questions
formulate explanations from evidence
connect explanations to scientific knowledge
communicate and justify explanations
demonstrate conceptual knowledge of scientific concepts.
conduct an ongoing investigation of physical phenomena in order to obtain data for use in the classroom.

PHSX 111CS The World of Quantum Physics: 3 Credits (3 Lec)

PREREQUISITE: M 121Q or Math Level 400 or higher. (F, Sp) Students will be introduced to quantum physics by exploring its intellectual development, philosophical implications, and impact on society. Important quantum physics experiments will be executed in the classroom and analyzed with instructor guidance. A term paper will require independent research of an historical figure in quantum physics

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Describe the scientific method.
Identify the differences between classical and quantum phenomena.
Describe the philosophical implications of quantum physics for science.
Convey an appreciation of experiments in quantum physics.
Recognize some key scientists of quantum physics and explain their contributions.
Identify examples of the use of quantum physics in modern technology, including quantum computation.
Solve numerical problems associated with quantum physics.

PHSX 200 Research Programs in Physics: 1 Credits (1 Lec)

COREQUISITE: PHSX 224. (Sp) An introduction to the ideas, developments, problems, and experiments of contemporary physics, as they are being explored within the Department of Physics at MSU. Intended as an opportunity for students to identify a potential research area and mentor for their Undergraduate Research course (PHSX 490R)

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Discuss current research topics within the Department of Physics.
Identify a possible undergraduate research project and advisor.

PHSX 201IN Physics by Inquiry: 3 Credits (3 Lab)

(F, Sp) An in-depth exploration of basic physics principles. Scientific model building and proportional reasoning skills will be developed in the context of properties of matter, observational astronomy, and DC electric circuits. For pre-service elementary teachers.

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write and use scientific operational definitions to build a self-consistent scaffolding of the scientific content.
create and interpret representations in the context of linear kinematics (motion graphs, strobe diagrams, etc.)
draw correct free-body diagrams for increasing complex physical situations and use the diagrams to predict the resulting acceleration.
make observations of the moon over an extended period of time and develop a model to explain their observations.

PHSX 205 College Physics I: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: High school trigonometry or M 121Q or (Math Level 4 or Higher). (F, Sp) First semester of sequence. Topics include kinematics and dynamics of linear and rotational motion; work and energy; impulse and momentum; and fluids. Students will not receive credit if they have passed PHSX 220 or PHSX 240. Common exams

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By the end of the course students should be familiar with solving problems of various types including problems involving one or more of the following topics: • Units and Vectors • Kinematics in 1-D and 2-D, including projectile motion • Newton’s three laws of motion • Friction • Energy, Work, Potential Energy, conservative Forces, non-conservative forces • Momentum and Impulse • Center-of-Mass • Rotational Kinematics and Dynamics • Pressure, Density, and Buoyancy • Gravitation

PHSX 207 College Physics II: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: PHSX 205 or PHSX 220 or PHSX 240. (F, Sp, Su) Second semester of sequence. Topics include simple harmonic motion; electric forces and fields; dc electric circuits; magnetic forces and fields; and magnetic induction and motors. Students will not receive credit if they have passed PHSX 222 or PHSX 242. Common exams

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Simple Harmonic Motion and Conservation of Energy
Transverse and Longitudinal Traveling Waves
Transverse and Longitudinal Standing Waves
Electric Charge and Electric Force
Electric Fields and Electric Voltage
Circuit Analysis, Single and Multi-loop Circuits
Equivalent Resistance of Series and Parallel Networks
Kirchhoff’s Rules
Magnetic Fields, Magnetic Force, and Magnetic Flux
Faraday’s Law and Lenz’s Law
Magnetic Induction and Self Induction

PHSX 220 Physics I with Calculus: 4 Credits (3 Lec, 1 Lab)

COREQUISITE: M 171Q or M 181Q. (F, Sp, Su) First semester of a three-semester sequence primarily for engineering and physical science students. Covers topics in mechanics (such as motion, Newton's laws, conservation laws, work, energy, systems of particles, and rotational motion) and in mechanical waves (such as oscillations, wave motion, sound, and superposition). Common exams

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Units and Vectors
Kinematics in 1-D and 2-D
Newton’s three laws of motion
Friction
Energy, Work, Potential Energy, conservative Forces, non-conservative forces
Momentum and Impulse
Center-of-Mass
Rotational motion (Energy, Momentum, Moment of Inertia)
Pressure and Density
Gravitation
Simple Harmonic Motion
Oscillatory Motion
Wave Motion

PHSX 222 Physics II with Calculus: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: PHSX 220 or PHSX 240; M 171Q or M 181Q
COREQUISITE: M 172 or M 182. (F, Sp, Su) Covers topics in electricity and magnetism (such as Coulomb's law, Gauss' law, electric fields, electric potential, dc circuits, magnetic fields, Faraday's law, ac circuits, and Maxwell's equations) and optics (such as light, geometrical optics, and physical optics). Common exams
.

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Electric Charge and Electric Force
Electric Fields and Electric Potential
Magnetic Fields and Magnetic Flux
Gauss’s Law, Ampere’s Law, Faraday’s Law, Lenz’s Law
Maxwell’s Equations
Kirchhoff’s Rules
Series and Parallel Capacitors, Resistors, and Inductors
Circuit Analysis, single and multi-loop circuits
Dielectrics
Optical Lenses, lens equations, and ray tracing
Diffraction, refraction, reflection, interference, polarization

PHSX 224 Physics III: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: PHSX 222 or PHSX 242; M 172 or M 182. (F, Sp) Covers topics in thermodynamics (such as temperature, heat, laws of thermodynamics, and the kinetic theory of gases) and modern physics (such as relativity; models of the atom; quantum mechanics; and atomic, molecular, solid state, nuclear, and particle physics)

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explain and apply the postulates of special relativity, relativistic coordinate transformations, and relativistic momentum and energy for particles;
explain and apply the relationship between microscopic and macroscopic thermodynamic variables, processes in ideal gases, and the Laws of Thermodynamics;
explain and apply the results of fundamental quantum mechanics experiments and concepts, including wave-particle duality, wave functions, quantization, uncertainty relations, correspondence principle, particle-in-a-box, hydrogen atom, and spin and magnetic moment;
explain and apply the Pauli exclusion principle as it applies to multi-electron systems and atoms, and lasers and electron conduction in metals and semiconductors;
explain and apply basic phenomenology of nuclear and particle physics;
explain and apply the results of experiments in thermal and modern physics, and measurement uncertainties.

PHSX 240 Honors Gen & Mod Phys I: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: Restricted to Physics majors or Honors students or consent of instructor
COREQUISITE: M 171Q or M 181Q. (F) The honors equivalent of PHSX 220. The concepts are discussed in more depth and the range of applications is greater. Common final only
.

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Upon completion of this course, a student will be able to: - Explain how to apply the four kinematic equations to problems involving constant acceleration, in both linear and angular situations; - Correctly draw a free body diagram and solve Newton's second law, and identify third law action-reaction pairs; - Apply the conservation of momentum, the work energy theorem, and be able to differentiate when each is appropriate; - Apply torque and angular momentum concepts to rotation problems; - Explain wave mechanics and the difference between transverse and longitudinal waves. For standing waves, identify speed, wavelength, or frequency.

PHSX 242 Honors Gen & Mod Phys II: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: PHSX 220 or PHSX 240; M 171Q or M 181Q
COREQUISITE: M 172 or M 182. (Sp) Restricted to Physics majors or Honors students or consent of instructor. The honors section of PHSX 222. The concepts are discussed in more depth and the range of applications is greater
.

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Upon completion of PHSX 242, students should understand the nature of light, geometrical optics, and physical optics.
Electricity and magnetism, and the sources and properties of electromagnetic fields
Simple direct-current (DC) and alternating-current (AC) circuits.
Electromagnetic radiation, and experiments in optics and electricity & magnetism, and measurement uncertainties.

PHSX 256 Solving Problems with Python: 3 Credits (3 Lec)

PREREQUISITE: PHSX 220 or 240; or PHSX 205 and M 161Q or M 165Q or M 171Q or M181Q. (Sp) Introduction to the Python programming language and computational problem solving with emphasis on realistic problems in the physical sciences. Recommended for students in all STEM fields

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Set up a file system and Python development environment.
Construct basic Python computer code.
Translate physics problems into computer algorithms.
Identify errors in computer code representing physics problems.
Create graphical representations of solutions to physics problems.

PHSX 261 Laboratory Electronics I: 4 Credits (3 Lec, 1 Lab)

PREREQUISITE: PHSX 222 or PHSX 242, and PHSX 256. (Sp) Laboratory electronic measurements, analysis, and design of basic DC and AC circuits. Students will gain experience with linear circuit elements, semiconductor devices, and operational amplifiers. Prior command of complex numbers and Fourier analysis, or concurrent enrollment in PHSX 301 is recommended

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Analyze and Construct Circuits: Design and build basic analog circuits, including those with resistors, capacitors, and inductors, and predict their performance based on theoretical principles.
Master Lab Instrumentation: Effectively and safely operate standard electronics laboratory equipment, such as digital multimeters, power supplies, function generators, and oscilloscopes, to measure circuit properties and troubleshoot systems.
Apply Signal Processing Techniques: Experiment with and apply practical circuit solutions to common laboratory challenges, including filtering unwanted noise, boosting weak signals, and reducing systematic offsets in measurement apparatus.
Understand Active Components: Explain the function and apply key active components like transistors and operational amplifiers in common circuit configurations.

PHSX 262 Laboratory Electronics II: 2 Credits (1 Lec, 1 Lab)

PREREQUISITE: PHSX 261. (Sp) Analysis and design of basic digital circuits and advanced laboratory electronic measurements

PHSX 290R Undergraduate Research: 1-3 Credits (1-3 Other)

PREREQUISITE: Consent of instructor and approval of department head. Directed undergraduate research. Course will address responsible conduct of research
Repeatable up to 3 credits.

PHSX 291 Special Topics: 1-4 Credits ()

PREREQUISITE: None required but some may be determined necessary by each offering department. Courses not required in any curriculum for which there is a particular one time need, or given on a trial basis to determine acceptability and demand before requesting a regular course number
Repeatable up to 12 credits.

PHSX 292 Independent Study: 1-3 Credits (1-3 Other)

PREREQUISITE: Consent of instructor and approval of department head. Directed study on an individual basis
Repeatable up to 6 credits.

PHSX 301 Mathematical Methods in the Physical Sciences: 3 Credits (3 Lec)

PREREQUISITE: M 273 or M 283 ; PHSX 222 or PHSX 242
COREQUISITE: M 274 or M 284. (F, Sp) Survey of the most important mathematical techniques used in the physical sciences: power series, complex variables, linear algebra, vector calculus, Fourier analysis, series solutions of ordinary differential equations, and partial differential equations. Applications to specific problems in the various disciplines of the physical sciences are emphasized
.

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Expand functions using infinite series of both real and complex numbers.
Utilize linear algebra and representations of vectors and matrices to solve systems of equations. Identify and explain eigenvalues and eigenvectors.
Demonstrate facility with differential and integral calculus of several variables, with emphasis on the application of vector-calculus theorems.
Perform Fourier series expansions and Fourier transforms, and explain their significance.
Solve ordinary differential equations using series solutions.
Solve partial differential equations expressed as boundary-value problems.

PHSX 305RN Art and Science of Holography: 3 Credits (2 Lec, 1 Lab)

PREREQUISITE: M105Q or M121Q or equivalent math placement test; and Junior standing or instructor permission. (Sp) Beginner's course on creating holograms. Pictorial and geometric interpretations of lasers, interference, coherence, film, and holography enable students with limited science and M backgrounds to create their own holographic masterpieces. Lab techniques and documenting the creative process are emphasized

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Have an understanding of the basic principles and properties of light, including amplitude, wavelength, frequency, intensity, phase, interference, and polarization.
Have a conceptual understanding of diffraction, refraction, and spatial and temporal coherence
Have an understanding of the basic principles of constructive and destructive interference in index gratings and multi-slit gratings.
Be familiar with simple optics like spatial filters, beam splitters, mirrors, and lenses.
Have a conceptual understanding of film exposure and developing of holograms, including phase gratings.
Have an understanding of the basic set-up, techniques, and requirements for making, developing, and displaying white-light reflection, transmission, interference, and conical holograms.
Have a qualitative knowledge of the geometric model (mirror model) of holography developed by T. H. Jeong.
Have a conceptual understanding of magnification, orthoscopic, pseudoscopic, virtual, and real images.
Be able to perform optical ray-tracing with lenses and mirrors.
Understand the relationship between wavelengths and wavevectors and estimate the interference gratings produced by two interfering beams.
Demonstrate the ability to work independently in a lab setting with small groups of students without immediate instructor assistance
Be able to make and document quantitative measurements and qualitative scientific observations.
Research and write a moderate length paper on a current topic on holography.
Develop, execute, write-up, and present an appropriate independent project

PHSX 317 Instrument Building for Scientists: 1 Credits (1 Lab)

(F, Sp, Su) Junior standing required. Introduction to design, and fabrication of parts for laboratory experiments. Hands-on training in the safe use of band saw, drill press, milling machine, lathe, and CNC machinery use. Completion will allow students controlled access to machine shop.

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Identify and remediate unsafe work practices within a shop environment.
Plan, design, and sketch components.
Safely operate saws, drill presses, milling machines, lathes, 3D printers, and CNC machinery.
Import 2D and 3D models into a CAM software package and setup work coordinate systems, stock definitions, machine definitions, tool paths, and word address code generation.
Explain choice of tool speeds, feeds, and depth of cuts for various manual and CNC machining applications.
Use inspection equipment to measure dimensions, inspect parts, and adjustment of CNC machine tool parameters accordingly.

PHSX 320 Classical Mechanics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 301; PHSX 220 or PHSX 240. (F) Principles of Newtonian and Lagrangian mechanics including single particle motion, systems of particles, rigid body motion, moving coordinate systems, and small oscillations

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Apply Newtonian mechanics.
Demonstrate an understanding of conservation laws, and their use in studying dynamical systems.
Calculate the motion of particles, strings, and extended bodies.
Calculate motion under a central force.
Describe small oscillations about equilibrium.
Solve the harmonic oscillator problem (force and damped) and apply the results.
Calculate motion in translating and accelerating coordinate systems
Solve problems using Lagrangian methods.

PHSX 331 Methods of Computational Physics: 2 Credits (1 Lec, 1 Other)

PREREQUISITE: PHSX 301. (F) Introduction to the use of computational methods in physics. Emphasis will be placed on common methods of casting problems into forms amenable to numerical solution and for displaying numerical results. (1 cr. Lecture, 1cr. Recitation)

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Find the roots of a set of algebraic equations using either bisection or Newton’s method;
Solve simple, coupled, ordinary differential equations using either Euler’s method or the Runge-Kutta method;
Solve simple eigenvalue problems using the shooting method;
Apply least-squares fitting to, and extract statistical measures from, data sets;
Write well-documented, clear programs, and understand and modify existing programs;
Display numerical results in graphical format, and interpret those results.

PHSX 343 Modern Physics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 224, PHSX 301, and M 284 or M 274. (F) Waves in classical physics and quantum mechanics: complex representation, amplitude mechanics, and interference; Special relativity: postulates, Lorentz transformations, applications in nuclear and particle physics; Quantum mechanics: interpretation of key experiments, Schrodinger equation, particles in potentials, spin, the atom; Introduction to nuclear and particle physics

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Upon completion of this course, students should be able to: - Describe experiments that classical mechanics could not adequately predict. - Calculate length contractions and time dilations for objects moving at velocities comparable to the speed of light. - Calculate the classical and quantum mechanical behavior for blackbody radiation, the photoelectric effect, Rutherford backscattering, the electron two-slit experiment, and the Stern-Gerlach experiment. - Calculate the energies of bound states in an infinite square potential well and a simple harmonic oscillator potential well. - Describe the differences in the Thomson, Rutherford, and Bohr atom models. - Calculate the energy levels in the hydrogen atom. - Calculate the angular and radial probability densities of the atom. - Calculate the rotational energies of a diatomic molecule. - Describe how quantum mechanics adequately describes the temperature dependence of the heat capacity of a diatomic molecule. - Calculate the density of states of a gas in a container. - Describe the main postulate of statistical mechanics. - Calculate the average and most likely energy of a particle in the Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions. - Describe how the band theory of materials is used to define metals, insulators, semiconductors, and ferromagnets. - Calculate the binding energy of a nucleus. - Describe the difference between fission and fusion. - Describe the standard model of elementary particle physics. - Describe the concepts of black holes, dark matter, the cosmic microwave background, and the lifecycle of the universe

PHSX 423 Electricity and Magnetism I: 3 Credits (3 Lec)

PREREQUISITE: PHSX 343 or Graduate Standing. (Sp) Electrostatic and magnetostatic fields due to simple charge and current distributions, forces on charges and currents due to those fields, basic analog circuits, conductivity and resistivity, and Maxwell's Equations as applied to electromagnetic induction and waves

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Calculate and describe electric fields and scalar potentials from simple, static charge distributions.
Calculate and describe magnetic fields and vector potentials from simple, static current distributions.
Calculate and describe the forces on charges and currents due to electric and magnetic fields.
Describe and apply the differences between conductors, insulators, and semiconductors.
Develop and apply electromagnetic boundary conditions.
Utilize Maxwell's Equations to describe electromagnetic induction and the production of electromagnetic waves.
Characterize and apply capacitance and inductance in electrical circuits.

PHSX 425 Electricity and Magnetism II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 423 or Graduate Standing. (F) Electrostatic and magnetostatic fields and potentials in matter, electromagnetic conservation laws, propagation of electromagnetic waves in materials, potentials due to dynamic charge distributions, and electromagnetic radiation. This course is strongly recommended for students intending to study physics in graduate school

View Course Outcomes:

Calculate and explain electric fields in electrically polarizable materials.
Calculate and explain magnetic fields in magnetizable materials.
Exploit conservation of charge, energy, linear momentum, and angular momentum to determine the evolution of systems.
Determine the behavior of electromagnetic waves at boundaries between materials, and their propagation into those materials.
Calculate and describe gauge transformations and potentials due to time-dependent charge distributions.
Calculate and describe electromagnetic radiation from accelerating charges.

PHSX 427 Advanced Optics: 3 Credits (3 Lec)

PREREQUISITE: (PHSX 224; M 274 or M 284) or Graduate Standing. () Emphasis is on new developments in optics triggered by the laser. Provides a good foundation in wave optics, nonlinear optics, integrated optics, and spectroscopy

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Explain modern wave and quantum optics with consideration of new phenomena, devices, and processes resulting from the development of the laser.
Explain the principles and applications of geometrical optics (ray optics).
Explain the practical realizations of technology, including devices such as lenses, image brightness and depth of field, polarizers, diffraction gratings, interferometers and optical spectrometers, optical detectors, optical components, and component characteristics.

PHSX 437 Laser Applications: 3 Credits (3 Lec)

PREREQUISITE: PHSX 222 OR PHSX 242. () A survey of laser types and properties and applications for scientists and engineers who wish to use lasers in research or technology. Many demonstrations will be used to illustrate the principles

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Explain basic laser principles, laser designs, and the practical applications of lasers and optical devices to a broad range of scientific and engineering problems
Describe the connections to practical technology and devices and real corporate and laboratory situations
Explain the types of lasers, their varied design principles, and a broad range of applications

PHSX 441 Solid State Physics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 224 or graduate standing. () A treatment of the classification and electronic structure of solids. Properties of conductors, superconductors, insulators, and semiconductors will be discussed. This course is strongly recommended for students intending to study physics in graduate school

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Understand differences between ionic, covalent and van-der-Walls bonds between atoms.
Know typical structures of crystals, glasses, amorphous solids and polymers
Understand relations of electronic structure of solids and electrical properties of metals, isolators and semiconductors
Calculate the force due to the Coloumb interaction
Be familiar with physical principles of superconductivity, ferro- and antiferroelectricity, ferro-, ferri- and antiferromagnetism
Determine how materials effect electric and magnetic field
Know basic features and information abilities of modern research methods (X-ray analysis, electron transmission and tunneling microscopes, magnetic resonance and optical absorption)

PHSX 444 Advanced Physics Lab: 4 Credits (2 Lec, 2 Lab)

PREREQUISITE: PHSX 262 and PHSX 343
COREQUISITE: PHSX 461. (F, Sp) Introduction to methods, instrumentation, and data acquisition techniques used in modern physics research. Different experiments are offered in the two semesters. For students desiring a strong experimental exposure, taking both courses is recommended. Experiments in the fall semester are typically in the optical area and include interferometers, fiber optics, spectral measurement, polarization, and laser optics. Experiments in spring semester are typically in solid state physics and particle spectroscopy. Co-convened with PHSX 516
.
Repeatable up to 8 credits.

PHSX 446 Thermodynamics & Statistical Mechanics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 301 and PHSX 224 and PHSX 343, or Graduate Standing. (Sp) Statistical physics and thermodynamics and their applications to physical phenomena. This course is strongly recommended for students intending to study physics in graduate school and is a required course for the professional option

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Students will form a deeper understanding of thermodynamics, and how basic assumptions about the constituents of a system lead to very general thermodynamic rules.
Students will demonstrate an understanding of probability theory.
Students will demonstrate an understanding of how probabilistic concepts can be used to simplify the problem of understanding the behavior of a system with many interacting particles.
Students will demonstrate an ability to calculate the properties of physical systems using statistical methods.

PHSX 451 Elementary Particle Physics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 343 or Graduate Standing. () A survey of elementary particle physics, beginning with an historical viewpoint and leading up to today's remarkably successful "Standard Model" of quarks, leptons, and gauge bosons

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Upon completion of this course, students should be able to: - Describe the standard model of elementary particle physics. - Describe how elementary particles are created. - Describe how elementary particles are detected. - Discuss symmetries and resulting conservation laws in particle physics. - Discuss the history and impact of important experiments in particle physics - Use 4-vector notation to calculate particle energies and momenta. - Describe bound states of elementary particles. -  Describe the differences between the strong and weak interactions.

PHSX 461 Quantum Mechanics I: 3 Credits (3 Lec)

PREREQUISITE: PHSX 343. (F) The wave function, the Schrodinger equation in 1-D, formalism and Dirac notation, and 3-D effects including the hydrogen atom. Prior command of PHSX 320 material is recommended

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Discuss the impact of important experiments that led to development of Schrodinger’s Eq.
Describe the differences between states, eigenstates, operators, and observables.
Use Dirac notation and matrix notations.
Discuss Hermitian operators and significance of commuting and non-commuting operators.
Calculate expectation values and uncertainties of measurable observables.
Discuss and apply the Heisenberg Uncertainty Principle.
Use the Schroedinger equation to calculate position, momentum, energy, and time evolution.
Calculate eigenstates and eigenvalues of bound particles in 1D and 3D potential wells.
Calculate eigenstates, eigenvalues, and evolution of free particles.
Calculate reflection and transmission coefficients for step or finite-well potentials.
Describe the differences between the spin and the angular momentum operators.
Understand the behavior/ probabilities of particle spin in successive Stern-Gerlach expts.
Understand the basics concepts of addition of angular momentum.

PHSX 462 Quantum Mechanics II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 461 or Graduate Standing. (Sp) Identical particles, time independent perturbation theory, time dependent perturbation theory, and the variational principle

PHSX 464 Current Topics in Space Physics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 423 and PHSX 446. (F, Sp) This course will provide fundamental knowledge of processes underpinning space physics, such as the dynamics of charged particles, their interaction with electromagnetic fields, and their collective behavior in plasma waves, and discuss various applications in space and astrophysical environments

View Course Outcomes:

Identify fundamental properties of charged particles in electromagnetic fields.
Discuss current topics in space physics research and applications.
Analyze scientific literature.

PHSX 490R Undergraduate Research: 1-3 Credits (1-3 Other)

PREREQUISITE: Junior or senior standing and consent form with approved research plan signed by instructor/ research advisor and academic advisor. (F, Sp) Directed undergraduate research/creative activity, which may culminate in a research paper, journal article, or undergraduate thesis. Course will address responsible conduct of research. Typically only 1 credit per semester. May be repeated
Repeatable up to 6 credits.

View Course Outcomes:

Undergraduate Research: Student learning outcomes vary.

PHSX 491 Special Topics: 1-4 Credits (1-4 Lec)

PREREQUISITE: Course prerequisites as determined for each offering. Courses not required in any curriculum for which there is a particular one-time need, or given on a trial basis to determine acceptability and demand before requesting a regular course number
Repeatable up to 12 credits.

PHSX 492 Independent Study: 1-3 Credits (1 Other)

PREREQUISITE: Junior or senior standing, consent of instructor and approval of department head. (F, Sp) Max 6 cr. Directed study on an individual basis
Repeatable up to 6 credits.

PHSX 494 Seminar/Workshop: 1-4 Credits ()

PREREQUISITE: Junior or senior standing and as determined for each offering. (F, Sp) Max 4 cr. Topics offered at the upper division level which are not covered in regular courses. Students participate in preparing and presenting discussion material. Co-convened with PHSX 594
Repeatable up to 4 credits.

PHSX 499R Senior Capstone Seminar: 1 Credits (1 Other)

PREREQUISITE: PHSX 490R and Senior Standing. (Sp, Su) Senior capstone course. Participation in this course requires the completion of a senior project that integrates the student's knowledge and skills acquired during the undergraduate curriculum. Students will be required to complete: i) an APS-style abstract, ii) an APS-style 10-minute oral presentation, iii) a poster session, and iv) a written research report, based on their research/creative activity

View Course Outcomes:

conduct literature searches
update groups on the status of your research
understand issues concerning ethics in research
create an abstract of a research project suitable for a paper or presentation
make a professional presentation in front of a technically trained audience (either poster or oral).
structure a scientific paper according to standards of the Physics literature.

PHSX 501 Mathematical Methods and Their Applications in Classical Mechanics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 320 or graduate standing. (F) This course covers Lagrangian and Hamiltonian mechanics, small oscillations, strings and continua, and fluids. Relevant mathematical methods will include multivariate Taylor expansions, linear algebra, Sturm-Liouville theory, and Fourier theory

View Course Outcomes:

formulate and solve classical mechanics problems using Lagrangian and Hamiltonian methods.
linearize non-linear systems of equations about an equilibrium and solve the linearized system using normal modes.
use the calculus of variations to characterize the function that extremizes a function.
apply methods of classical mechanics, including conservation laws, to a continuum system such as a fluid.
use symmetries of a system to identify conserved quantities and predict the nature of normal modes of its linearization.

PHSX 506 Quantum Mechanics I: 3 Credits (3 Lec)

PREREQUISITE: PHSX 462 or graduate standing. (F) The graduate Quantum Mechanics-1 course covers foundational principles of quantum mechanics, with deeper emphasis on the more general and more formal structure of quantum physics. The main equations are developed from few underlying physical and mathematical concepts

View Course Outcomes:

Use linear algebra methods as a general approach to Quantum mechanics
Describe time evolution of states (Schrodinger) and observables (Heisenberg)
Identify and solve for bound and extended states of a quantum system
Recognize and find approximate solutions using perturbation approaches
Identify and use concepts of rotations and angular momentum in Quantum system
Simplify problems by employing symmetries of the system
Solve quantum problems with several particles

PHSX 507 Quantum Mechanics II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 506. (Sp) The graduate Quantum Mechanics-2 course covers applications of quantum formalism developed in QM-1. A more detailed description of angular momentum addition and applications to more complex systems. Time-dependent perturbations and transitions between quantum states. Application to radiation and scattering problems. Quantum mechanics in relativistic case

View Course Outcomes:

Analyze systems with complex angular momentum structure
Apply advanced approximation techniques for complex quantum systems
Solve problems involving transitions between quantum states
Quantitatively describe quantum scattering processes
Apply quantum mechanics to many-particle systems, atoms, and relativistic electrons

PHSX 511 Astronomy for Teachers: 3 Credits (3 Other)

(F) This is an online, distance education course primarily intended for science educators. Topics include: exploring the nature of light and matter, a survey of the solar system, stars and stellar formation and evolution, galaxies, Big Bang cosmology and observational astronomy.

View Course Outcomes:

Recognize and explain the movements of the Sun, Moon and planets, as viewed from Earth, over the course of time.
Explain the evolution of stars as well as the large scale of the Universe.
Identify the parts of the life cycle of stars, and describe the importance of the electromagnetic spectrum to astronomers.
Evaluate the evidence explaining the Big Bang Theory.
Describe the four forces of nature: gravity, electromagnetic, strong and weak force.

PHSX 512 General Relativity Online: 3 Credits (3 Lec)

PREREQUISITE: PHSX 222 or PHSX 242 or M 182 or PHSX 405 or equivalent. (Sp) This online course addresses the theory of general relativity, which underlies our understanding of gravity and the large-scale structure of the cosmos. Designed for practicing high school physics teachers. Assignments and discussions use electronic computer conferencing and simulation software. It is recommended that students take PHSX 343 or PSXH 405 or equivalent before taking this course. Offered Spring

View Course Outcomes:

define the principles of general relativity, black holes (event horizon, singularity, Hawking radiation), and Big Bang cosmology (Friedmann-Robertson-Walker models of the universe, comic background radiation, dark matter and dark energy)
describe spacetime geometry and derive particle trajectories from a metric
use a Penrose diagrams to study the causal structure of a black hole spacetime
understand astrophysical processes leading to the formation of black holes
learn various astronomical observations supporting Big Bang, dark matter, and dark energy
discover how different forms of energy can affect the evolution of a universe
write a movie review article applying the one’s understanding of black holes acquired in the course
summarize and submit a personal reflection of weekly discussion posts specific to course content

PHSX 513 Quantum Mechanics Online: 3 Credits (3 Lec)

This online course addresses the key ideas behind quantum mechanical observations and devices, including the fundamental behavior of electrons and photons. Designed for practicing high school physics teachers. Assignments and discussions use electronic computer conferencing and simulation software. Offered summer.

View Course Outcomes:

define the principles of quantum mechanics developed from quantum particle exploring all paths in space-time
identify and apply quantum mechanics to explain the behavior of photons and electrons and their interaction
compare and contrast the connection between Feynman’s approach and Schrodinger’s approach
define wave functions, evolution in space-time, and measurement consequences.
summarize and submit a personal reflection of weekly discussion posts specific to course content

PHSX 514 Comparative Planetology Online: 3 Credits (3 Lec)

(Su) This course gives a general overview of comparative planetology. Intended for classroom teachers, it emphasizes creating standards aligned classroom materials and using instructional best practices. Course participants build content knowledge by completing a series of planetary and space science units.

View Course Outcomes:

Explain the solar nebula theory for the formation of the solar system.
Compare and contrast the surface functions of terrestrial planets and moons
Compare and contrast the atmospheric formation and composition of solar system planets.
Evaluate the potential for future exploration and utilization of solar system resources.
Evaluate the potential of finding extra-terrestrial life or signs of past life in our solar system.

PHSX 515 Advanced Topics In Physics: 3 Credits (3 Lec)

PREREQUISITE: Graduate standing. Topics in astrophysics, condensed matter physics, optics, mathematical physics, or particle physics are presented as needed to supplement the curriculum
Repeatable up to 6 credits.

PHSX 516 Experimental Physics: 3 Credits (2 Lec, 1 Lab)

PREREQUISITE: (PHSX 261, PHSX 423, and PHSX 461) or graduate standing. (F, Sp) Experiments chosen from laser optics and atomic, solid-state, and nuclear physics are carried out in depth to introduce the graduate student to methods, instrumentation, and data acquisition techniques useful for experimental thesis projects. Co-convened with PHSX 444
Repeatable up to 6 credits.

PHSX 519 Mathematical Methods and Their Applications in Electromagnetic Theory: 3 Credits (3 Lec)

PREREQUISITE: PHSX 425 or graduate standing. (Sp) This course covers electro- and magnetostatics, fields in matter, induction, Maxwell's equations, and waves. Relevant mathematical methods will include PDE solutions to boundary value problems in three coordinate systems, Green's functions, and complex variables

View Course Outcomes:

Students will be able to fields in vacuum, linear media, and conductors.
find and describe the time evolution of fields, of charge distribution, and of current distribution.
find energies of the fields.
find interactions between charges, currents, and fields.
set up and solve standard boundary value problems.
fluent in constructing solutions to Laplace equations and Poissonequations with eigen functions in three-dimensional curvilinear coordinates.
derive approximate solutions with the multipoleexpansion skill and to estimate the accuracy of the solution.
reason solutions.
recover physically understandable and expectable solutions in limiting cases and in simplified or symmetric configurations.

PHSX 520 Electromagnetic Theory II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 519. (F) The second part of Electromagnetism course covers electromagnetic waves, their radiation and propagation (including media), and Special relativity

View Course Outcomes:

Quantitatively describe propagation of EM waves in dispersive media
Characterize different radiation sources and derive radiation patterns
Find scattering patterns of EM waves on objects
Identify key features of wave propagation in non-uniform environments
Use laws of special relativity to approach electromagnetic problems

PHSX 523 General Relativity I: 3 Credits (3 Lec)

PREREQUISITE: PHSX 519. (F) Tensor calculus, differential geometry, and an introduction to Einstein's theory of gravity. The Schwarzschild solution and black hole physics

PHSX 524 General Relativity II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 523. () Advanced topics in gravitation theory such as singularities, cosmological models, and gravitational waves

PHSX 525 Current Topics in General Relativity: 3 Credits (3 Lec)

PREREQUISITE: PHSX 523. () Current topics in general relativity will be explored

View Course Outcomes:

Understand current research topics in general relativity.

PHSX 531 Nonlinear Optics/Laser Spectroscopy: 3 Credits (3 Lec)

PREREQUISITE: PHSX 507. () Two-level atoms in laser fields and applications to nonlinear optics such as photon echoes, second harmonic generation, and stimulated Raman scattering. Atomic and molecular energy level structure, linear and nonlinear spectroscopy, and applications to gaseous and solid state laser materials

PHSX 535 Statistical Mechanics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 446 or graduate standing. (Sp) Basic concepts of equilibrium statistical mechanics, with application to classical and quantum systems, will be presented as well as theories of phase transitions in fluid, magnetic, and other systems

PHSX 544 Condensed Matter Physics I: 3 Credits (3 Lec)

PREREQUISITE: PHSX 446 or PHSX 506 or CHMY 557 or permission of instructor. (Spring, even years.) Introduction to concepts and methods used for understanding the properties of (solid) materials, with various interactions that involve electrons, ions, light, phonons, magnetism, etc. Students will recognize the main ideas behind solids, solve basic problems, and apply this to relevant research in condensed matter, materials, optics, chemistry

PHSX 545 Condensed Matter Physics II: 3 Credits (3 Lec)

PREREQUISITE: PHSX 544. () Applications to the transport, optical, dielectric, and magnetic properties of metals, semiconductors, and insulators

PHSX 555 Quantum Field Theory: 3 Credits (3 Lec)

PREREQUISITE: PHSX 507. () Techniques of canonical and path integral quantization of fields; renormalization theory. Quantum electrodynamics; gauge theories of the fundamental interactions

PHSX 560 Astrophysics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 425, PHSX 462, PHSX 446, and PHYS 435, or graduate standing. () The purpose of this course is to prepare graduate students for thesis-level research in astrophysics, solar physics or related fields. Topics covered include: fluid mechanics, hydrodynamics, plasma physics, radiation processes and stability of equilibrium states

PHSX 564 Current Topics in Space Physics: 3 Credits (3 Lec)

(F, Sp) This course will provide fundamental knowledge of processes underpinning space physics, such as the dynamics of charged particles, their interaction with electromagnetic fields, and their collective behavior in plasma waves, and discuss various applications in space and astrophysical environments.
Repeatable up to 6 credits.

View Course Outcomes:

Identify fundamental properties of charged particles in electromagnetic fields.
Discuss current topics in space physics research and applications.
Analyze scientific literature related to space physics.
Identify and examine gaps in the current literature and research areas inspace physics.

PHSX 565 Astrophysical Plasma Physics: 3 Credits (3 Lec)

PREREQUISITE: PHSX 501 and PHSX 519
COREQUISITE: PHSX 520. (F) An introduction to the physics of fluids and plasma relevant to astrophysical plasmas such as the solar corona. Topics covered include: magnetostatics, one-fluid (MHD) and two-fluid approaches, linear waves and instabilities, shocks, transonic flows and collisional effects
.

View Course Outcomes:

Derive conservation laws for a set of fluid equations
Linear a set of non-linear fluid equations and derive their normal modes
Derive the characteristic equations for a fluid equation
Compute magnetic field lines from a magnetic field, and describe when those are frozen to the fluid.
Identify all the waves in a magnetized plasma

PHSX 566 Mathematical Methods for Theoretical Physics: 3 Credits (3 Lec)

PREREQUISITE: M 349, M 472, and PHSX 320 or graduate standing. (F) This course will cover some of the advanced mathematical techniques to deal with realistic physical systems that have multiple, sometimes infinite, degrees of freedom. The focus will be on using general principles of linear algebra, vector spaces, geometry, symmetry and topology, that play special role in modern physics

View Course Outcomes:

Simplify systems with many degrees of freedom using symmetry principles.
Analyze spectra of quantum systems using point groups.
Apply rotations group to describe rotational properties of quantum and classical systems.
Use complex-valued functions and their calculus for advanced physics modeling.
Apply advanced math techniques to data analysis.

PHSX 567 Computational Physics: 3 Credits (3 Lec)

(Spring, even years.) Theory of computational techniques, and applications such as numerical integration, differential equations, Monte Carlo methods, and fast Fourier transforms.
Repeatable up to 3 credits.

View Course Outcomes:

Apply programming skills to diverse exercises in scientific modeling, data analysis, and visualization.
Compute solutions to problems that cannot be solved analytically.
Compare rates of algorithmic convergence.
Analyze data to separate physically meaningful information from random error (noise).
Devise and execute a term project that advances their educational and/or research interests.

PHSX 571 Electric Circuits and Magnetism for Teachers: 3 Credits (2 Lec, 1 Lab)

(Su) This course is designed for educators teaching electricity and magnetism. Participants will master core concepts and increase their understanding of the underlying physics. Participants will also engage with concepts using guided home inquiry experiments and online simulations, quizzes, and discussions.

View Course Outcomes:

Demonstrate a foundational understanding of the basic principles underlying electric circuits and magnets.
Generate and evaluate fundamental models of electric circuits and magnetism.
Identify and explain common phenomena using conceptual models of electricity and magnetism.
Apply electric and magnetic concepts to explain the behavior of modern technologies such as motors, generators, and wireless communication.
Engage in productive dialog with other science teachers about the relevance of a conceptual understanding of electricity and magnetism.

PHSX 572 Space Science for Elementary Teachers: 1 Credits (1 Lec)

(Fall, odd years.) This course builds elementary teachers’ content knowledge through space science and astronomy units. Participants experience classroom activities and learn teaching “best practices” before implementing them in their classrooms. Course materials are aligned to National Model Academic Standards in Space Science.

View Course Outcomes:

Accurately describe and model the phases of the Moon.
Demonstrate the difference in revolution and rotation and describe how they cause our days and seasons.
Create constellation diagrams and explain the history of major constellations.
Construct a scale model of the Solar System distances.
Use a model to demonstrate the causes of daily and annual changes in visible star patterns.

PHSX 574 World of Motion & Force for Elem/MS Teachers: 2 Credits (2 Lec)

(Su) In this 7-week, 2-credit course for elementary/MS teachers we will focus on the core ideas of measurement, motion, and forces as they appear in modern inquiry-oriented science education. Its broad purpose is to introduce elementary and middle school teachers to core ideas about motion and forces, as they relate to inquiry-oriented science curricular materials. The course aims to help teachers use modern curricular materials more effectively by increasing their understanding of the physics concepts. Offered Summer.

View Course Outcomes:

describe position and displacement using both coordinates and vectors, in one and two dimensions, and analyze the motion of an object using these descriptions;
distinguish between average and instantaneous velocities and accelerations;
calculate velocities and accelerations from position versus time information, in tabular or graphical form and, conversely, construct displacement information from graphs of velocity versus time;
analyze projectile and circular motions, as specific examples of motion in two dimensions;
recognize and creatively address common student difficulties – including common misconceptions – in the learning of kinematical ideas;
evaluate curricular materials for their effectiveness in developing student understanding of motions; and
be creative users of curricular materials related to motion, modifying them as required in order to meet the particular needs of their learners.

PHSX 579 Special Relativity for Teachers: 3 Credits (3 Other)

(F) An introduction to Special Relativity concepts and applications. Designed for practicing high school teachers seeking context, background, tools, and methods to enrich their professional knowledge and abilities. Participants should have an understanding of electricity and magnetism, optics, and calculus.

View Course Outcomes:

Compare and contrast standard Newtonian model of space and time and the special relativistic concept of a four dimensional “spacetime”.
Correctly draw “spacetime diagrams” as a tool to demonstrate and apply the concepts of special relativity including the two postulates of special relativity, invariant spacetime intervals, relativity of simultaneity, time dilation and length contraction, the relativistic Doppler shift, and basic relativistic particle interactions with regard to conservation of energy and momentum.
Explain the experimental and observational evidence for special relativity as it applies to modern experimental and observational physics.
Connect the Special Theory of Relativity to the General Theory of Relativity.
Create lesson plans which will help their students develop their own understanding of Special Relativity at an introductory level.

PHSX 580 Conceptual Physics for Teachers: 3 Credits (3 Lec)

(Su) This course is designed for middle and high school teachers who are covering some of the basic ideas of physics in their classrooms. At the conceptual level, the course investigates many of the fundamental concepts of physics and their relevance to the world around you. Topics include measurement, motion, force, momentum, energy, power, gravitation, torque, rotational motion, simple harmonic motion, mechanical waves, and sound. Offered Summer. On-Line Only.

View Course Outcomes:

Use research-based science teaching practices to create an engaged atmosphere of exploration and experimentation in their science curricula.
Perform experiments where they will collect data, display it graphically and analyze it to draw conclusions.
Develop lab handouts/guides, based on experiments done in this class, for use in their own classroom.
Explain basic physics principles – mechanics, waves, light, electricity, magnetism, and modern physics - from a conceptual point of view, demonstrating this ability in writing age/grade appropriate lesson plans.
Utilize web-based simulations, such as electric circuits software, to collect data and then deduce rules.
Produce a curated list of websites for each area of study.

PHSX 582 Astrobiology for Teachers Online: 3 Credits (3 Lec)

(Sp) Astrobiology is the interdisciplinary study of the origin, evolution, distribution, and possibility of life in the universe. This course covers the discovery of planetary systems and nature of habitable zones around stars, life in extreme environments, and possible extraterrestrial ecosystems.

View Course Outcomes:

Analyze key events in the history of the universe, Solar System formation, and Earth’s evolution that led to the development of life on Earth.
Evaluate the conditions that support habitability on Earth and assess how astronomers explore other worlds to look for habitability.
Describe the ways that scientists explore the Solar System and beyond to look for new places life might exist and the possible characteristics of that life.
Evaluate bodies in the solar system (including planets, moons, dwarf planets, asteroids, and comets for potential habitability based on information gathered by scientists.
Integrate course material and activities in their own teaching.

PHSX 584 Physics by Inquiry: Light & Color for Teachers: 2 Credits (2 Lab)

(Summer, even years.) An in-depth and hands-on exploration of physics principles. The course begins with an investigation of light and reflection of light, leading to an understanding of colored light, pigments, and how the two interact. For middle and high school science teachers.

View Course Outcomes:

Distinguish between colors of light and colors of pigment.
Predict the color of a screen with various colors of light shown on it.
Predict the color of pigment with various colors of light shown on it.
Recognize the key misconceptions associated with light and pigment identified in the Physics Education Research literature.
Structure their own classroom to support the active learning environment of the Physics by Inquiry curriculum.

PHSX 586 Physics by Inquiry: Heat & Temperature for Teachers: 2 Credits (2 Lab)

(Summer, odd years.) This course for middle/high school teachers focuses on core ideas of heat and temperature, as they appear in modern inquiry-oriented science education. The course will help teachers use modern curricular materials more effectively by increasing their understanding of physics concepts.

View Course Outcomes:

Predict the amount of heat transferred into a system verses the heat transferred out of a system and explain any apparent discrepancies.
Interpret graphs of temperature vs. heat for a system to find the heat capacity, heat of fusion, and heat of vaporization
Recognize the key misconceptions associated with heat and temperature
Explain the differences between heat capacity and specific heat, what happens as matter changes phases, and everyday experiences with heat. Use proportional reasoning with heat and temperature.
Structure their own classroom to support the active learning environment of the Physics by Inquiry curriculum.

PHSX 587 Physics by Inquiry: Geometric Optics for Teachers: 2 Credits (2 Lab)

(Summers, even years.) In this course for middle/high school teachers we focus on the core ideas of heat and temperature, as they appear in modern inquiry-oriented science education. The course helps teachers use curricular materials effectively by increasing their understanding of physics concepts.

View Course Outcomes:

Identify the difference between a real and a virtual image.
Differentiate between point sources of light and extended light sources.
Predict the location of an image for different types of lenses.
Predict the outcome of different combinations of colored light and pigments.
Structure a classroom to support the active learning environment of the Physics by Inquiry curriculum.

PHSX 589 Graduate Consultation: 3 Credits (3 Other)

PREREQUISITE: Master's standing and approval of the Dean of Graduate Studies. This course may be used only by students who have completed all of their coursework (and thesis, if on a thesis plan) but who need additional faculty or staff time or help

PHSX 590 Master's Thesis: 1-10 Credits (1 Other)

PREREQUISITE: Master's standing
Repeatable up to 99 credits.

PHSX 591 Special Topics: 1-4 Credits (4 Lec)

PREREQUISITE: Upper division courses and others as determined for each offering. Courses not required in any curriculum for which there is a particular one time need, or given on a trial basis to determine acceptability and demand before requesting a regular course number
Repeatable up to 12 credits.

PHSX 592 Independent Study: 1-3 Credits (1-3 Other)

PREREQUISITE: Graduate standing, consent of instructor, approval of department head and Dean of Graduate Studies. Directed research and study on an individual basis
Repeatable up to 6 credits.

PHSX 594 Seminar: 1 Credits (1 Other)

PREREQUISITE: Graduate standing or seniors by petition. (F, Sp) Course prerequisites as determined for each offering. Topics offered at the graduate level which are not covered in regular courses. Students participate in preparing and presenting discussion material
Repeatable up to 8 credits.

PHSX 597 Physics of Sustainable Energy for Teachers: 3 Credits (2 Lec, 1 Other)

(Su) During this course, high school physics teachers complete units centered on the physics of renewable energy sources and create standards aligned materials to use in their classrooms. Covered topics include fossil fuels, renewable energy, world energy consumption, sustainability, and more.

View Course Outcomes:

Discuss the advantages and disadvantages of a portfolio of renewable energy sources
Analyze projected world energy usage and renewable energy sources to justify alternatives to fossil fuels
Present calculations that put characteristics of energy sources in perspective.
Devise connections between course content and the ability to teach physics concepts.
Connect Next Generation Science Standards and local state standards in physics topics to concepts related to renewable energy sources.

PHSX 689 Doctoral Reading & Research: 3-5 Credits (3 Other)

PREREQUISITE: Doctoral standing. This course may be used by doctoral students who are reading research publications in the field in preparation for beginning doctoral thesis research
Repeatable up to 15 credits.

PHSX 690 Doctoral Thesis: 1-10 Credits (1 Other)

PREREQUISITE: Doctoral standing
Repeatable up to 99 credits.