Course Descriptions

ME 18 ab. Thermodynamics. 9 units (3-0-6); second, third terms. Prerequisites: Ph1 and Ph2 (may be taken concurrently)An introduction to classical thermodynamics with engineering applications. First term includes the first and second laws; closed and open systems; properties of a pure substance; availability and irreversibility; generalized thermodynamic relations. Second term emphasizes applications: gas and vapor power cycles; propulsion; mixtures; combustion and thermochemistry; chemical equilibrium. Instructor: Hunt.

ME 19 ab. Fluid Mechanics. 9 units (3-0-6); first, second terms. Prerequisites: Ma 2, Ph 1 abc. Properties of fluids, basic equations of fluid mechanics, theoreoms of energy, linear and angular momentum. Euler's equations, inviscid potential flow, surfaces waves, airfoil theory. Navier-Stokes equations, vorticity and vorticity transport. Flow of real fluids, similarity parameters, flow in ducts. Boundary layer theory for laminar and turbulent flow, transition to turbulence. Drag, lift and propulsion. Instructor: Colonius.

ME 20. Heat Transfer. 9 units (3-0-6); third term. Prerequisites: ME 18 ab, ME 19 ab. An introduction to heat transfer. Steady-state and transient conduction, including numerical solutions. Forced and natural convective-heat transfer. Heat exchangers. Radiative heat transfer and solar energy. Instructor: Not offered 2008-09.

ME 35 abc. Statics and Dynamics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ma 1 abc, Ph 1 abc. Introduction to statics and dynamics of rigid and deformable bodies. Equilibrium of force systems, principle of virtual work, distributed force systems, friction, static analysis of rigid and deformable structures, kinematics, particle dynamics, rigid-body dynamics, dynamics of deformable systems, and vibrating systems. Instructor: Lapusta.

ME 65. Mechanics of Materials. 9 units (3-0-6); first term. Prerequisites: ME 35 abc, Ma 2 ab. Introduction to continuum mechanics, principles of elasticity, plane stress, plane strain, axisymmetric problems, stress concentrations, thin films, fracture mechanics, variational principles, frame structures, finite element methods, composites, and plasticity. Taught concurrently with Ae/AM/CE/ME 102. Instructor: Daraio.

ME 66. Vibration. 9 units (3-0-6); third term. Prerequisites: ME 35 abc, MA 2 ab. Introduction to vibration and wave propagation in continuous and discrete multi-degree-of-freedom systems. Strings, mass-spring systems, mechanical devices, elastic continua. Equations of motion, Lagrange's equations, Hamilton's principle, and time-integration schemes. Instructor: Heaton.

ME 71. Introduction to Engineering Design. 9 units (3-5-1); third term. Prerequisite: ME 35 ab recommended. Enrollment is limited and will be based on responses to a questionnaire available in the Registrar’s Office during registration. Not offered on a pass/fail basis. Introduction to mechanical engineering design, fabrication, and visual communication. Concepts are taught through a series of short design projects and design competitions emphasizing physical concepts. Many class projects will involve substantial use of the shop facilities, and construction of working prototypes. Instructor: Staff.

ME 72. Engineering Design Laboratory. 9 units (3-4-2); first term; (1-8-0), second term. Prerequisites: ME 35 abc, ME 71, ME 18 ab, CS 1, or equivalent and instructor’s permission. Enrollment is limited. A project based course in which teams of students design, fabricate, analyze, test, and operate an electromechanical device to compete against devices designed by other student teams. The class lectures and the projects will stress the integration of mechanical design, sensing, engineering analysis, and computation to solve problems in engineering system design. The laboratory units of ME 72 can be used to fulfill a portion of the laboratory requirement for the ME or E&AS option. Not offered on a pass/fail basis. Instructor: Shepherd.

ME 73. Machine Component Design. 9 units (3-4-2); second term. Prerequisites: ME 35 abc, ME 72, or instructor’s permission. Basic machine components, including bearings, seals, shafts, gears, belts, chains, couplings, linkages, and cams. Analysis and synthesis of these devices, as well as their use in the design of larger engineering systems, will be examined. The laboratory section makes use of contemporary mechanical hardware to provide students with "hands-on’’ experience with the components discussed in class. Not offered 2008-09.

CS/EE/ME 75 abc. Introduction to Multi-Disciplinary Systems Engineering. 3 units (2-0-1) first term, 3-6 units second term; 12 units (2-9-1) or up to 18 units (2-15-1), with instructor's permission, third term. This course presents the fundamentals of modern multidisciplinary systems engineering in the context of a substantial design project. Students from a variety of disciplines will conceive, design, implement, and operate a system involving electrical, information, and mechanical engineering components. Specific tools will be provided for setting project goals and objectives, managing interfaces between component subsystems, working in design teams, and tracking progress against tasks. Students will be expected to apply knowledge from other courses at Caltech in designing and implementing specific subsystems. During the first two terms of the course, students will attend project meetings and learn some basic tools for project design, while taking courses in CS, EE, and ME that are related to the course project. During the third term, the entire team will build, document, and demonstrate the course design project, which will differ from year to year. Freshman must receive permission from the lead instructor to enroll. Instructor: Murray.

ME 90 abc. Senior Thesis, Experimental. 9 units; (0-0-9) first term; (0-9-0) second, third terms. Prerequisite: senior status; instructor’s permission. Experimental research supervised by an engineering faculty member. The topic selection is determined by the adviser and the student and is subject to approval by the Mechanical Engineering Undergraduate Committee. First and second terms: midterm progress report and oral presentation during finals week. Third term: completion of thesis and final presentation. The second and third terms may be used to fulfill laboratory credit for EAS. Not offered on a pass/fail basis. Instructor: Staff.

ME 91 abc. Senior Thesis, Analytical. 9 units (0-0-9); first, second, third terms. Prerequisite: senior status; instructor’s permission. Undergraduate research supervised by an engineering faculty member. The topic selection is determined by the adviser and the student and is subject to approval by the Mechanical Engineering Undergraduate Committee. First and second terms: midterm progress report and oral presentation during finals week. Third term: completion of thesis and final presentation. Not offered on a pass/fail basis. Instructor: Staff.

ME 96. Mechanical Engineering Laboratory. 9 units (0-9-0); third term. Prerequisites: ME 18 ab, ME 19 ab, ME 35 ab. A laboratory course with experiments drawn from diverse areas of mechanical engineering, including heat transfer, control, fluid mechanics, solid mechanics, atomic force microscopy, materials, combustion, turbomachinery, and dynamics. Instructor: Staff.

ME 100. Advanced Work in Mechanical Engineering. The faculty in mechanical engineering will arrange special courses on problems to meet the needs of qualified undergraduate students. Graded pass/fail for research and reading. A written report is required for each term.

Ae/APh/CE/ME 101 abc. Fluid Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisites: APh 17 or ME 18, and ME 19 or equivalent, ACM 95/100 or equivalent (may be taken concurrently). Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli’s equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; acoustics. Instructor: Pullin.

Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. 9 units (3-0-6); first, second, third terms. Prerequisite: ME 35 abc or equivalent. Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics. Instructor: Daraio.

E/ME 103. Management of Technology. 9 units (3-0-6); third term. A course intended for students interested in learning how rapidly evolving technologies are harnessed to produce useful products. Students will work through Harvard Business School Case Studies, supplemented by lectures to elucidate the key issues. There will be a term project. The course is team-based and designed for students considering working in companies (any size, including start-ups) or eventually going to business school. Topics include technology as a growth agent, financial fundamentals, integration into other business processes, product development pipeline and portfolio management, learning curves, risk assessment, technology trend methodologies (scenarios, projections), motivation, rewards and recognition. Industries considered will include electronics (hardware and software), aerospace, medical, biotech, etc. E 102 and E/ME 105 are useful but not required precursors. Instructor: Pickar.

E/ME 105. Product Design for the Developing World. 9 units (3-0-6); first term. Prerequisite: ME 71 or permission of instructor. The course will emphasize products appropriate for the developing world - for those people subsisting on less than one dollar a day. It will provide the student with a working knowledge of contemporary methods of product design to meet the constraints of cost, performance, quality, and time to market as applied to the developing world. Areas covered include design for X (X = manufacturability/assembly, environmental issues, including sustainability, failure modes and effects analysis, test, etc.). The integration of customer needs and financial return will be discussed with specific examples. Instructor: Pickar.

ME 110. Special Laboratory Work in Mechanical Engineering. 3–9 units per term; maximum two terms. Special laboratory work or experimental research projects may be arranged by members of the faculty to meet the needs of individual students as appropriate. A written report is required for each term of work. Instructor: Staff.

CDS 110ab Inroductory Control Theory. 9 units (3-0-6); first, second terms. Prerequisits: Ma 1 and Ma 2 or equivalents; ACM 95/100 may be taken concurrently. An introduction to analysis and design of feedbck control systems, including classical control theory in the time and frequency domain. Modeling of physical, biological, and information systems using linear and nonlinear differential equations. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. The first term of this course is taught concurrently with CDS 101, but includes additional lectures, reading, and homework that is focused on analytical techniques for design and synthesis of control systems. Instructor: Murray.

ME 115 ab. Introduction to Kinematics and Robotics. 9 units (3-0-6); second, third terms. Prerequisites: Ma 2, ACM 95/100 ab recommended. Introduction to the study of planar, rotational, and spatial motions with applications to robotics, computers, computer graphics, and mechanics. Topics in kinematic analysis will include screw theory, rotational representations, matrix groups, and Lie algebras. Applications include robot kinematics, mobility in mechanisms, and kinematics of open and closed chain mechanisms. Additional topics in robotics include path planning for robot manipulators, dynamics and control, and assembly. Course work will include laboratory demonstrations using simple robot manipulators. Not offered 2008-09.

ME 118. Thermodynamics. 9 units (3-0-6); first term. Prerequisites: ME 18ab, ME 19ab. Fundamentals of classical and statistical thermodynamics. Basic postulates, thermodynamic potentials, chemical and phase equilibrium, phase transitions, and thermodynamic properties of solids, liquids and gases. Not offered 2008-09.

ME 119 ab. Heat and Mass Transfer. 9 units (3-0-6); second, third terms. Prerequisites: ME 18ab, ME 19ab, ACM 95/100 (may be taken concurrently). Transport properties, conservation equations, conduction heat transfer, convective heat and mass transport in laminar and turbulent flows, phase change processes, thermal radiation. Not offered 2008-09.

Ae/ME 120 ab. Combustion Fundamentals. 9 units (3-0-6); second, third terms. Prerequisite: ME 119 a or equivalent. The course will cover thermodynamics of pure substances and mixtures, equations of state, chemical equilibrium, chemical kinetics, combustion chemistry, transport phenomena, and the governing equations for multicomponent gas mixtures. Topics will be chosen from non-premixed and premixed flames, the fluid mechanics of laminar flames, flame mechanisms of combustion-generated pollutants, and numerical simulations of multicomponent reacting flows. Instructor: Staff.

ME 122 ab. Sustainable Energy Engineering. 9 units (3-0-6); second, third terms. Prerequisites: ME18ab, ACM 95/100 (may be taken concurrently) . An in-depth examination of engineering systems to convert, store, transport, and use energy, with emphasis on technologies that reduce or eliminate dependence on fossil fuels and/or emission of greenhouse gases. Topics include: thermodynamics of energy conversion, energy resources, stationary power generation (vapor power cycles, combined cycles, solar thermal systems, nuclear fission and fusion, solar photovoltaics, fuel cells, wind), carbon sequestration, alternative fuels (hydrogen, biofuels), and transportation systems (internal combustion engines, gas turbines, fuel cell and electric vehicles). The course will emphasize using quantitative methods to assess and compare different technologies, and in the second term each student will prepare an independent analysis of a technology of his or her choice. Not offered 2008-09.

ME 131. Advanced Robotics: Manipulation and Sensing. 9 units (3-6-0); third term. Prerequisite: ME 115 ab. The course focuses on current topics in robotics research in the area of robotic manipulation and sensing. Past topics have included advanced manipulator kinematics, grasping and dextrous manipulation using multifingered hands, and advanced obstacle avoidance and motion planning algorithms. The lectures will be divided between a review of the appropriate analytical techniques and a survey of the current research literature. Course work will focus on an independent research project chosen by the student. Not offered 2008–09.

ME/CS 132. Advanced Robotics: Navigation and Vision. 9 units (3-6-0); third term. Prerequisite: ME 115 ab. The course focuses on current topics in robotics research in the area of autonomous navigation and vision. Topics will include mobile robots, multilegged walking machines, use of vision in navigation systems. The lectures will be divided between a review of the appropriate analytical techniques and a survey of the current research literature. Course work will focus on an independent research project chosen by the student. Instructor: Burdick.

ME 150 abc. Mechanical Engineering Seminar. 1 unit (1-0-0); each term. All candidates for the M.S. degree in applied mechanics and mechanical engineering are required to attend any graduate seminar in any division each week of each term. Graded pass/fail. Instructor: Goodwin.

Ae/Ge/ME 160 abc. Continuum Mechanics of Fluids and Solids. 9 units (3-0-6); first, second, third terms. Elements of Cartesian tensors. Configurations and motions of a body. Kinematics - study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics?balance laws. Linear and angular momentum, force, traction stress. Cauchy’s theorem, properties of Cauchy’s stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convective rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. Instructor: Ortiz.

MS/ME 161a. Imperfections in Crystals. 9 units (3-0-6); third term. Prerequisits: Graduate standing or MS 115a. The relation of lattice defects (vacancies, interstitials, dislocations) to the physical and mechanical properties of crystalline solids. Introduction to point imperfections, and their relationships to transport properties in metallic, covalent, and ionic crystals. Kroeger-Vink notation. Introduction to dislocations: geometric, crystallographic, elastic, and energetic properties of dislocations. Dislocation reactions and interactions including formation of locks, stacking faults, and surface effects. Relations between collective dislocation behavior and mechanical properties of crystals. Introduction to computer simulations of dislocations. Grain boundaries. The structure and properties of interfaces in solids. Emphasis on materials science aspects of role of defects in electrical, morphological, optical, and mechanical properties of solids. Instructor: Greer.

AM/ME 165 ab. Elasticity. 9 units (3-0-6); second, third terms. Prerequisites: Ae/Ge/ME 160 a and registered in Ae/Ge/ME 160 b. Fundamental concepts and equations of elasticity. Linearized theory of elastostatics and elastodynamics: basic theorems and special solutions. Finite theory of elasticity: constitutive theory, semi-inverse methods. Variational methods. Applications to problems of current interest. Not offered 2008–09.

ME 170. Introduction to Mechanical CAD. 4 units (1-0-3); third term. An introduction to the use of one or more mechanical computeraided design (CAD) packages via a series of weekly instructional exercises. Not offered 2008-09.

ME 171. Computer-Aided Engineering Design. 9 units (3-0-6); second term. Prerequisites: ACM 95/100 abc, ME 35 abc, ME 72, CS 1, or equivalent, working knowledge of the C computer programming language. Methods and algorithms for design of engineering systems using computer techniques. Topics include the design process; interactive computer graphics; curves and surfaces (including cubic and Bsplines); solid modeling (including constructive solid geometry and boundary models); kinematic and dynamic mechanism simulation; single and multivariable optimization; optimal design, and symbolic manipulation. Assessment of CAD as an aid to the design process. Not offered 2008-09.

ME 175. Fuzzy Sets in Engineering. 9 units (3-0-6); second term. Prerequisites: ACM 95/100 abc, working knowledge of the C computer programming language. The relatively new mathematics of fuzzy sets has recently been used to represent and manipulate vague and imprecise information in engineering. This course will present the basics of fuzzy sets and fuzzy mathematics and explore applications in the areas of data representation; function representation; filters and triggers; engineering design and optimization, including (fuzzy) set-based concurrent engineering. Not offered 2008–09.

ME 200. Advanced Work in Mechanical Engineering. The faculty in mechanical engineering will arrange special courses on problems to meet the needs of graduate students. Graded pass/fail; a written report is required for each term of work.

ME 202 abc. Engineering Two-Phase Flows. 9 units (3-0-6). Prerequisites: ACM 95/100 abc, Ae/APh/CE/ME 101 abc, or equivalents. Selected topics in engineering two-phase flows with emphasis on practical problems in modern hydro-systems. Fundamental fluid mechanics and heat, mass, and energy transport in multiphase flows. Liquid/vapor/gas (LVG) flows, nucleation, bubble dynamics, cavitating and boiling flows, models of LVG flows; instabilities, dynamics, and wave propagation; fluid/structure interactions. Discussion of two-phase flow problems in conventional, nuclear, and geothermal power plants, marine hydrofoils, and other hydraulic systems. Instructor: Brennen.

Ae/AM/MS/ME 213. Mechanics and Materials Aspects of Fracture. 9 units (3-0-6); second term. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and instructor’s permission. Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elastic-plastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, "dynamic" stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 2008-09.

Ae/AM/CE/ME 214 abc. Computational Solid Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisites: AM 125 abc or equivalent; ACM 100 abc or equivalent; CE/AM/Ae 108 abc or equivalent or instructor’s permission; Ae/AM/CE/ME 102 abc or equivalent; Ae/Ge/ME 160 ab desirable or taken concurrently. Introduction to the use of numerical methods in the solution of solid mechanics and materials problems. First term: Geometrical representation of solids. Automatic meshing. Approximation theory. Interpolation error estimation. Optimal and adaptive meshing. Second term: Variational principles in linear elasticity. Finite element analysis. Error estimation. Convergence. Singularities. Adaptive strategies. Constrained problems. Mixed methods. Stability and convergence. Variational problems in nonlinear elasticity. Consistent linearization. The Newton-Rahpson method. Bifurcation analysis. Adaptive strategies in nonlinear elasticity. Constrained finite deformation problems. Contact and friction. Third term: Time integration. Algorithm analysis. Accuracy, stability, and convergence. Operator splitting and product formulas. Coupled problems. Impact and friction. Subcycling. Space-time methods. Inelastic solids. Constitutive updates. Stability and convergence. Consistent linearization. Applications to finite deformation viscoplasticity, viscoelasticity, and Lagrangian modeling of fluid flows. Instructor: Ortiz.

Ae/AM/ME 215. Dynamic Behavior of Materials. 9 units (3-0-6); first term. Prerequisites: ACM 100 abc or AM 125 abc; Ae/AM/CE/ME 102 abc. Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Not offered 2008-09.

Ae/AM/ME 223. Plasticity. 9 units (3-0-6); third term. Prerequisite: Ae/AM/CE/ME 102 abc or instructor’s permission. Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stress-strain relations. Variational principles for incremental elastic-plastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and rate-sensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Not offered 2008-09.

Ae/AM/ME 225. Special Topics in Solid Mechanics. Units to be arranged. Subject matter will change from term to term depending upon staff and student interest but may include such topics as structural dynamics; aeroelasticity; thermal stress; mechanics of inelastic and composite materials; and nonlinear problems. Not offered 2008–09.

Ae/ACM/ME 232 abc. Computational Fluid Dynamics. 9 units (3-0-6), first, second, third terms. Prerequisites: Ae/APh/CE/ME 101abc or equivalent; ACM 100abc or AM 125abc, or equivalent; ACM 104, ACM 105, or equivalent. Introduction to the use of numerical methods in the solution of fluid mechanics problems. First term: review of basic numerical techniques: interpolation, integration, application for systems of ordinary differential equations, stability and accuracy. Treatment of partial differential equations in one space variable. Nonlinear convective-diffusive and convective-dispersive phenomena. Treatment of discontinuous solutions. Second term: survey of finite difference, finite element, and spectral approximations for the solution of the incompressible Navier-Stokes equations in two and three dimensions. Numerical study of problems of hydrodynamic stability, transition, and turbulence. Third term: methods for the numerical solution of the compressible Euler and Navier-Stokes equations in one, two, and three dimensions. Finite-difference and finite-volume methods. Methods based on solution of the Riemann problem. Flux-splitting. Shock-capturing methods and related stability problems. Implicit artificial viscosity for the Euler equations. Total variation diminishing approximations. Instructor: Staff.

ME/MS 260 abc. Micromechanics. 12 units (3-0-9). Prerequisites: ACM 95/100 or equivalent, and Ae/AM/CE/ME 102 abc or Ae 160 abc or instructor’s permission. The course gives a broad overview of micromechanics, emphasizing the microstructure of materials, its connection to molecular structure, and its consequences on macroscopic properties. Topics include phase transformations in crystalline solids, including martensitic, ferroelectric, and diffusional phase transformations, twinning and domain patterns, active materials; effective properties of composites and polycrystals, linear and nonlinear homogenization; defects, including dislocations, surface steps, and domain walls; thin films, asymptotic methods, morphological instabilities, self-organization; selected applications to microactuation, thin-film processing, composite materials, mechanical properties, and materials design. Open to undergraduates with instructor’s permission. Not offered 2008-09.

Ae/Ge/ME 266 ab. Dynamic Fracture and Frictional Faulting. 9 units (3-0-6), first, second terms. Prerequisites: Ae/AM/CE/ME 102abc or Ae/Ge/ME 160 or instructor's permission. Introduction to elastodynamics, waves in solids. Dynamic fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, dynamic rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Crack branching, faulting along nonplanar interfaces. Related dynamic phenomena such as adiabatic shear localization. Applications to engineering phenomena and physics and mechanics of earthquakes. Not offered 2008-09.

ME 300. Research in Mechanical Engineering. Hours and units by arrangement. Research in the field of mechanical engineering. By arrangement with members of the faculty, properly qualified graduate students are directed in research.