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Courses - Fall 2025
ENAE
Engineering, Aerospace Department Site
Open Seats as of
10/02/2025 at 10:30 PM
ENAE100
(Perm Req)
The Aerospace Engineering Profession
Credits: 1
Grad Meth: Reg, P-F, Aud
Recommended: ENES100 and MATH140.
Overview of salient aspects of professional practice of Aerospace Engineering. Introduction to the range of technical expertise needed to succeed in the profession and the objectives of the various parts of the Aerospace Engineering program at UMCP in supporting students' efforts in gaining the required knowledge and skills. Familiarization with departmental faculty and their areas of research, creation of links with other students, professional society student chapters, and available resources. Discussion of ethical issues, business requirements, and their interactions with technical developments.
ENAE202
(Perm Req)
Computing Fundamentals for Engineers
Credits: 3
Grad Meth: Reg, P-F, Aud
Corequisite: MATH141.
Credit only granted for: ENAE202 or ENME202.
Introduction to computer programming for the solution of engineering problems. Python & MATLAB languages including flow control, functions, file handling, arrays, and data structures. Students will be introduced to computing fundamentals, principles of software engineering, object-oriented programming, and algorithms.
ENAE283
Introduction to Aerospace Systems
Credits: 3
Grad Meth: Reg
Prerequisite: Minimum grade of C- or better in PHYS161 and MATH141; and must have completed or be concurrently enrolled in ENAE222.
Restriction: Must be in Engineering: Aerospace program.
Credit only granted for: (ENAE281 and ENAE282) or ENAE283.
Formerly: ENAE281 and ENAE282.
Introduction to the fundamental disciplines of aerospace engineering, and the systems concepts that integrate these into conceptual designs for flight vehicles. Course covers the foundations of aerodynamics, propulsion, aerospace materials, flight mechanics, orbital mechanics, vehicle stability and control.
ENAE283H
(Perm Req)
Introduction to Aerospace Systems
Credits: 3
Grad Meth: Reg
Prerequisite: Minimum grade of C- or better in PHYS161 and MATH141; and must have completed or be concurrently enrolled in ENAE222.
Restriction: Must be in Engineering: Aerospace program.
Credit only granted for: (ENAE281 and ENAE282) or ENAE283.
Formerly: ENAE281 and ENAE282.
Introduction to the fundamental disciplines of aerospace engineering, and the systems concepts that integrate these into conceptual designs for flight vehicles. Course covers the foundations of aerodynamics, propulsion, aerospace materials, flight mechanics, orbital mechanics, vehicle stability and control.
ENAE288B
Topics in Aerospace Engineering; Student Initiated Course Failures in Human Spaceflight
Credits: 1
Grad Meth: Reg, P-F, Aud
Failures in Human Spaceflight: Apollo 1, Challenger, & Columbia provides an introduction to fatal accidents in American spaceflight history. Students will study the engineering failures and management decisions leading to each disaster. Additionally, they will consider the investigations, public responses, and impacts prompted by the accidents.Readings will include official accident reports, internal NASAcommunications, and personal accounts. Students will discuss how these disasters shaped modern risk management and what lessons were learned - or ignored - along the way.
ENAE301
Dynamics of Aerospace Systems
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: PHYS271, MATH461, PHYS270, MATH246, ENAE283, ENAE202, ENES102, and MATH241.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Kinematics and dynamics of three dimensional motion of point masses and rigid bodies with introduction to more general systems. Primary emphasis on Newtonian methods. Practice in numerical solutions and computer animation of equations of motion using MATLAB.
ENAE311
Compressible Aerodynamics
Credits: 3
Grad Meth: Reg
Prerequisite: PHYS271, (MATH240 or MATH461), PHYS270, MATH246, ENAE283, ENES220, ENAE202, MATH241, and ENES232.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department; and junior standing or higher.
Credit only granted for: ENAE410 or ENAE311.
Fundamentals of aerodynamics. Elements of compressible flow. Normal and oblique shock waves. Flows through nozzles, diffusers and wind tunnels. Elements of the method of characteristics and finite difference solutions for compressible flows. Aspects of hypersonic flow.
Prerequisite: ENAE311 or enrolled in hypersonics graduate certificate program. Corequisite: ENAE481 or ENAE483.
ENAE311H
(Perm Req)
Compressible Aerodynamics
Credits: 3
Grad Meth: Reg, P-F
Prerequisite: PHYS271, (MATH240 or MATH461), PHYS270, MATH246, ENAE283, ENES220, ENAE202, MATH241, and ENES232.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department; and junior standing or higher.
Credit only granted for: ENAE410 or ENAE311.
Fundamentals of aerodynamics. Elements of compressible flow. Normal and oblique shock waves. Flows through nozzles, diffusers and wind tunnels. Elements of the method of characteristics and finite difference solutions for compressible flows. Aspects of hypersonic flow.
ENAE362
Aerospace Instrumentation and Experimentation
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: MATH246 and ENAE283.
Restriction: Must be in Engineering: Aerospace program; and junior standing or higher.
Basic instrumentation electronics including DC electronics, AC electronics, semiconductors, electro-optics and digital electronics. Sensing devices used to carry out experiments in Aerospace Engineering includes metrology, machine tool measurements, bridge circuits, optical devices, and introduction to computer based data acquisition. Topics chosen to support measurements in aerodynamics, flight structures and flight control.
ENAE380
Flight Software Systems
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE283 and ENAE202.
Restriction: Must be in Engineering: Aerospace program; and junior standing or higher.
Avionics using advanced sensor and computing technologies are at the heart of every modern Aerospace vehicle. Advanced software systems to improve cockpit safety and enable unmanned and deep-space missions. Object-oriented programming and software engineering concepts required to design and build complex flight software systems. Software validation, verification and real-time performance analysis to assess flight software system reliability and robustness. Human-machine interface design for piloted systems. Automatic onboard data acquisition and decision-making for unmanned air and space vehicles.
ENAE398H
(Perm Req)
Honors Research Project
Credits: 1 - 3
Grad Meth: Reg
Contact department for information to register for this course.
ENAE403
Aircraft Flight Dynamics
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE414 and ENAE432.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Study of motion of aircraft, equations of motion, aerodynamic force representation, longitudinal and lateral motions, response to controls and to atmospheric disturbances, handling qualities criteria and other figures of merit.
ENAE414
Incompressible Aerodynamics
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: PHYS271, (MATH240 or MATH461), PHYS270, MATH246, ENAE283, ENES220, ENAE202, MATH241, and ENES232.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department; and junior standing or higher.
Credit only granted for: ENAE310 or ENAE414.
Aerodynamics of inviscid incompressible flows. Aerodynamic forces and moments. Fluid statics/buoyancy force. Vorticity, circulation, the stream function and the velocity potential. Bernoulli's and Laplace's equations. Flows in low speed wind tunnels and airspeed measurement. Potential flows involving sources and sinks, doublets, and vortices. Development of the theory of airfoils and wings.
ENAE423
Vibration and Aeroelasticity
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE324.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Dynamic response of single and multiple degrees of freedom systems, finite element modeling, wing divergence, aileron reversal, wing and panel flutter.
ENAE423H
(Perm Req)
Vibration and Aeroelasticity
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE324.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Dynamic response of single and multiple degrees of freedom systems, finite element modeling, wing divergence, aileron reversal, wing and panel flutter.
ENAE441
Space Navigation and Guidance
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: Minimum grade of C- or better in ENAE432; and must have completed or be concurrently enrolled in ENAE404.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Principles of navigation. Celestial, radio, and inertial navigation schemes. Navigational and guidance requirements for orbital, planetary, and atmospheric entry missions. Fundamentals of estimation theory, linear and nonlinear filtering techniques.
ENAE455
Aircraft Propulsion and Power
Credits: 3
Grad Meth: Reg, P-F
Prerequisite: ENES232, ENAE414, and ENAE311.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of piston, turbojet, fanjet, and other variations of airbreathing aircraft power units.
ENAE457
Space Propulsion and Power
Credits: 3
Grad Meth: Reg, P-F
Prerequisite: PHYS271, ENES232, PHYS270, and ENAE311.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department. And senior standing.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of rocket, ion, and other exoatmospheric power units.
ENAE457H
(Perm Req)
Space Propulsion and Power
Credits: 3
Grad Meth: Reg, P-F
Prerequisite: PHYS271, ENES232, PHYS270, and ENAE311.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department. And senior standing.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of rocket, ion, and other exoatmospheric power units.
ENAE472
Introduction to Hypersonics
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE311 or enrolled in hypersonics graduate certificate program.
Corequisite: ENAE481 or ENAE483 (if not enrolled in hypersonics graduate certificate program).
Restriction: Students must be in the Hypersonic Graduate Certificate Program (code: Z165) or receive permission from the department.
Credit only granted for: ENAE488N or ENAE472.
Formerly: ENAE488N.
Introduces students to the various key aspects of flight at hypersonic speeds. Critical aerodynamic phenomena to be covered includes the qualitative behavior of flow fields in the high-Mach-numberlimit, approximate methods for quantifying surface pressure, and estimates of viscous drag and heating. High-speed air-breathing propulsion systems will be discussed, including cycle analysis and performance metrics for propulsion, with a main emphasis onthe fundamentals of ramjet and scramjet engines. Key Guidance, Navigation and Control (GNC) concepts for various hypersonic vehicle types will also be introduced, including the design of appropriate flight trajectories and control algorithms to achieve mission goals. Finally, students will be provided with an overview of high-temperature materials, structures, and thermal protection systems.
ENAE481
(Perm Req)
Principles of Aircraft Design
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE324, ENAE362, and ENAE432.
Corequisite: ENAE414.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Credit only granted for: ENAE481 or ENAE491.
Aircraft design principles blending both synthesis and analysis. The iterative nature of the design process. Applied aerodynamics. Elements of aircraft performance calculation and optimization. Design of aircraft including payload, crew and avionics provisions, propulsion selection and sizing, aerodynamic configuration optimization, mass properties, stability and control characteristics, and vehicle subsystems. Individual student projects in aircraft design.
Restricted to students in the Vertical Flight Society Helicopter Design Competition and requires permission of the instructor to enroll.
ENAE483
Principles of Space Systems Design
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisite: ENAE404, ENAE324, ENAE362, and ENAE432.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department.
Credit only granted for: ENAE483 or ENAE493.
Principles of space systems analysis and vehicle design. Launch vehicle performance analysis and optimization. Design of vehicle systems including avionics, power, propulsion, life support, human factors, structures, actuator and mechanisms, and thermal control. Design processes and design synthesis. Individual student projects in vehicle design.
ENAE488I
Topics in Aerospace Engineering; Wind Turbine Aeromechanics
Credits: 1 - 4
Grad Meth: Reg, P-F, Aud
This course will cover the aerodynamics, hydrodynamics and structural dynamics of onshore and offshore wind turbines. The first part of the course will concentrate on wind turbine aerodynamics, covering details of blade element momentum theory. In addition, various simulation tools will be examined and utilized for practical applications. A brief introduction to the use of Computational Fluid Dynamics will be covered. The second part will look in detail at hydrodynamic effects on fixed and floating offshore wind platforms. In addition, interference effects for wind-plants will be introduced and several techniques for inclusion in wind plant design. The third part of the course will examine the structural dynamics of wind turbine blades, including aeroelastic effects, as well as wind turbine fixed and floating foundations. A final small team project will tie the various portions of the course together.
ENAE488V
(Perm Req)
Topics in Aerospace Engineering; DTEVV Fundamentals
Credits: 3
Grad Meth: Reg, P-F, Aud
Prerequisites: ENAE432 or ENME361 (or equivalent); or permission of instructor. Corequisite: ENAE403 (or equivalent); or permission of instructor

Course is designed to give students a basic understanding of Development, Test & Evaluation, Verification & Validation process used to produce new aviation systems.
ENAE499
(Perm Req)
Credits: 3
Grad Meth: Reg
Contact department for information to register for this course.
ENAE601
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENAE404; or permission of ENGR-Aerospace Engineering department.
Mathematics and applications of orbit theory, building upon the foundations developed in ENAE 404 and ENAE 441. Topics include two body orbits, solutions of Kepler's equation, the two-point boundary value problem, rendezvous techniques, and Encke's method.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE603
(Perm Req)
Near-Earth Object Exploration
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENAE601.
Restriction: Must be in one of the following programs (ENGR: MS/PhD-Aerospace Engineering (Master's); ENGR: MS/PhD-Aerospace Engineering (Doctoral)).
Credit only granted for: ENAE788N or ENAE603.
Formerly: ENAE788N.
An overview of the near-Earth objects (NEOs) of our solar system--the asteroids and comets whose orbits closely approach Earth's orbit--and what we know about them, what we're learning about them, and how to design spacecraft missions to interact with them.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE631
(Perm Req)
Helicopter Aerodynamics I
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENAE414 and ENAE311. Or permission of ENGR-Aerospace Engineering department; and permission of instructor.
A history of rotary-wing aircraft, introduction to hovering theory, hovering and axial flight performance, factors affecting hovering and vertical flight performance, autorotation in vertical descent, concepts of blade motion and control, aerodynamics of forward flight, forward flight performance, operational envelope, and introduction to rotor acoustics.
Those sections that begin with a letter are taught via ITV and are not intended for College Park campus students.

Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE636
Helicopter Dynamics II
Credits: 3
Grad Meth: Reg, Aud
Credit only granted for: ENAE788R or ENAE636.
Formerly: ENAE788R.
Aerodynamics, dynamics and aeromechanics of helicopters and tilt rotor aircraft. Experimental testing and mathematical modeling required for the design and analysis of such aircraft.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE641
Linear System Dynamics
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENAE432.
Linear systems; state space, multi-input, multi-output models; eigenstructure; controllability, observability, singular value analysis; multivariable Nyquist condition; observer design; introduction to Kalman filtering. Full state feedback techniques including pole placement and LQR/LQG techniques; introduction to loop shaping and robustness.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE642
Atmospheric Flight Control
Credits: 3
Grad Meth: Reg, Aud, S-F
Prerequisite: ENAE403 and ENAE432; or students who have taken courses with comparable content may contact the department.
Exposure to flight guidance and control. Draws heavily from vehicle dynamics as well as feedback theory, and careful treatment of the non-linear aspects of the problem is critical. Conventional sythesis techniques are stressed, although modern methods are not ignored. Multivariable system analysis is included, along with flight-control design objectives and hardware limitations. Emphasis on aircraft and missiles.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE655
Structural Dynamics
Credits: 3
Grad Meth: Reg, Aud
Advanced principles of dynamics necessary for structural analysis; solutions of eigenvalue problems for discrete and continuous elastic systems, solutions to forced response boundary value problems by direct, modal, and transform methods.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE661
(Perm Req)
Aircraft Propulsion and Power
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENES232, ENAE414, and ENAE311.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department; and must have Senior or graduate standing.
Jointly offered with: ENAE455.
Credit only granted for: ENAE455 or ENAE661.
An introduction to air-breathing jet propulsion with the main emphasis on the fundamentals of gas turbine engines. It is intended for students with prerequisite knowledge of elementary fluid mechanics, gas dynamics, and thermodynamics.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE662
Space Propulsion and Power
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: ENES232 and ENAE311; or equivalents.
Restriction: Must be in Engineering: Aerospace program; or permission of ENGR-Aerospace Engineering department; and must have senior or graduate standing.
Jointly offered with: ENAE457.
Credit only granted for: ENAE457, ENAE457H, ENAE662.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of rocket, ion, and other exoatmospheric power units.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE673
Aerodynamics of Incompressible Fluids
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: Undergraduate courses in differential equations, incompressible, and compressible flow (ENAE311; and one course from ENAE414; ENME331, OR ENME640, or equivalent).
Restriction: Must be in ENGR: MS/PhD-Aerospace Engineering (Master's) program.
Introduces the fundamental concepts of incompressible flows. Topics to be addressed include the conservation equations, potential flow, lift and drag, Navier-Stokes equations, boundary layers and similarity solutions, and solutions to classical problems.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE681
Engineering Optimization
Credits: 3
Grad Meth: Reg, Aud
Methods for unconstrained and constrained minimization of functions of several variables. Sensitivity analysis for systems of algebraic equations, eigenvalue problems, and systems of ordinary differential equations. Methods for transformation of an optimization problem into a sequence of approximate problems. Optimum design sensitivity analysis.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE682
(Perm Req)
Hypersonic Aerodynamics
Credits: 3
Grad Meth: Reg, Aud
Restriction: Permission of ENGR-Aerospace Engineering department.
Hypersonic shock and expansion waves, Newtonian theory, Mach methods, numerical solutions to hypersonic inviscid flows, hypersonic boundary layer theory, viscous interactions, numerical solutions to hypersonic viscous flows. Applications to hypersonic vehicles.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE684
(Perm Req)
Computational Fluid Dynamics I
Credits: 3
Grad Meth: Reg, Aud
Restriction: Permission of ENGR-Aerospace Engineering department.
Partial differential equations applied to flow modelling, fundamental numerical techniques for the solution of these equations, elliptic, parabolic, and hyperbolic equations, elements of finite difference solutions, explicit and implicit techniques. Applications to fundamental flow problems.
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE686
Computational and Experimental Methods for Hypersonic Flows
Credits: 3
Grad Meth: Reg, Aud
Recommended: ENAE682.
Restriction: Permission of ENGR-Aerospace Engineering department.
Provides a comprehensive framework on computational and experimental methods for investigating hypersonic flows, covering essential topics and providing a balanced mix of theory and practical applications.
ENAE692
Introduction to Space Robotics
Credits: 3
Grad Meth: Reg, Aud, S-F
Prerequisite: ENAE301 or ENES221.
Recommended: ENAE432.
Introduction to the kinematics, dynamics, and control of robot manipulators. DH parameters, serial and parallel manipulators, kinematic redundancy, sensors, actuators, and mechanism design. Control concepts introduced ranging from independent joint control to impedance control. Examples drawn from space robotics, wearable robotics, and other areas.
ENAE788D
Selected Topics in Aerospace Engineering; Advanced Space Systems Design
Credits: 3
Grad Meth: Reg, Aud
ENAE788F
Selected Topics in Aerospace Engineering; Development, Test & Evaluation, Verification & Validation (DTEVV) Fundamentals for Aviation
Credits: 3
Grad Meth: Reg, Aud, S-F
Campus - University System of Maryland at Southern Maryland Address - 44219 Airport Road, Building 3, California, MD 20619 Room - 2256
ENAE788I
Selected Topics in Aerospace Engineering; Wind Turbine Aeromechanics
Credits: 3
Grad Meth: Reg, Aud
This course will cover the aerodynamics, hydrodynamics and structural dynamics of onshore and offshore wind turbines. The first part of the course will concentrate on wind turbine aerodynamics, covering details of blade element momentum theory. In addition, various simulation tools will be examined and utilized for practical applications. A brief introduction to the use of Computational Fluid Dynamics will be covered. The second part will look in detail at hydrodynamic effects on fixed and floating offshore wind platforms. In addition, interference effects for wind-plants will be introduced and several techniques for inclusion in wind plant design. The third part of the course will examine the structural dynamics of wind turbine blades, including aeroelastic effects, as well as wind turbine fixed and floating foundations. A final small team project will tie the various portions of the course together.
ENAE788K
Selected Topics in Aerospace Engineering; Estimation and Control of Stochastic Systems
Credits: 1 - 3
Grad Meth: Reg, Aud, S-F
Those sections that begin with a letter are designated for Master of Engineering students and are not intended for Master of Science or Ph.D.Students.
ENAE788P
Selected Topics in Aerospace Engineering; Optical Remote Sensing
Credits: 3
Grad Meth: Reg, Aud
Prerequisites: Programming experience, orbital dynamics (ENAE404 or ENAE601, can be co-requisite).

This course will cover topics in electromagnetic radiation, sensor systems, sensing architectures, and sensor data processing. Focus application areas include earth observation from space sensors and detections of space objects from ground sensors. Students will be introduced to practical approaches to common design and analysis problems in optical remote sensing.
ENAE799
Master's Thesis Research
Credits: 1 - 6
Grad Meth: S-F
Contact department for information to register for this course.
ENAE898
Pre-Candidacy Research
Credits: 1 - 8
Grad Meth: Reg
Contact department for information to register for this course.
ENAE899
(Perm Req)
Doctoral Dissertation Research
Credits: 6
Grad Meth: S-F
Contact department for information to register for this course.