Graduate Programs
Master of Science Degree Program
The program leading to the Master of Science degree in mechanical engineering requires completion of a minimum
of 30 points of approved course work consisting of no fewer than ten courses. A thesis based on either experimental, computational, or analytical research is optional and may be counted in lieu of up to 6 points of course work. In general, attainment of the degree requires one academic year of full-time study, although it may also be undertaken on a part-time basis over a correspondingly longer period. A minimum grade point average of 2.5
is required for graduation.
The M.S. degree in mechanical engineering requires a student to take a sequence of courses that shows a “clearly discernible specialty or concentration.” In consultation with his/her adviser an M.S. student can develop a concentration specifically tailored to his/her interests and objectives, and we refer to this as the standard track. Alternatively, M.S. students can pick from a set of predefined concentrations, or special tracks.
Typical choices of concentration in the standard track include such subjects as mechanics of solids and fluids, thermodynamics, heat transfer, manufacturing engineering, robotics, kinematics, dynamics and vibrations, controls, and power generation. Nevertheless, the following guidelines must be adhered to:
1. The sequence of courses selected must not be haphazard, but rather show a clearly discernible specialty.
2. All courses must be at the graduate level, i.e., numbered 4000 or higher, with some 6000-level courses included.
3. Every program must contain at least one course in mathematics (APMA or MATH designators) or their equivalent, covering material beyond what the student has taken previously. It should appear early in the sequence in order to serve as a basis for the technical course work.
4. Out-of-department study is encouraged, but at least five courses should be in mechanical engineering.
Rather than apply for the standard track, students can apply for a special track in either energy systems or in micro/nanoscale engineering. The requirements for a special track are identical to those of the standard track, with one exception: a special track student must take at least 15 of his/her points from a list determined by a special track adviser in consultation with a special track advisory committee. The name of the special track will be listed on a student’s transcript. The currently available special tracks are listed below.
M.S. in Mechanical Engineering with Concentration in Energy Systems
Advisors: Profs. Daniel Attinger and Vijay Modi
The concentration in energy systems provides the M.S. candidate with a global understanding of current energy challenges. Advanced thermofluidic knowledge is provided to design and optimize energy systems, with a strong emphasis on renewable energies. Courses related to energy and environmental policy, two strong areas of Columbia as a global university, can be integrated into the course sequence. This concentration is a suitable preparation for careers in energy production and energy consultation.
Requirements: While satisfying the general mechanical engineering requirements, take at least five courses from:
MECE E4211: Energy: sources and conversion
MECE E4302: Advanced thermodynamics
MECE E4312: Solar thermal engineering
MECE E4314: Energy dynamics of green buildings
MECE E6100: Advanced mechanics of fluids
MECE E6104: Case studies in computational fluid dynamics
MECE E6313: Advanced heat transfer
APPH E4130: Physics of solar energy
EAEE E6126: Carbon sequestration
EAEE E6208: Combustion chemistry or processes
INTA W4200: Alternative energy resources
ARCH A4684: Sustainable design
SIPA U4727: Environmental politics and policy management
SIPA U6060: International energy systems and business structures
M.S. in Mechanical Engineering with Concentration in Micro/Nanoscale Engineering
Advisors: Profs. James Hone and Jeff Kysar
The concentration in micro/nanoscale engineering provides the M.S. candidate with an understanding of engineering challenges and opportunities in micro- and nanoscale systems. The curriculum addresses fundamental issues of mechanics, fluid mechanics, optics, heat transfer, and manufacturing at small-size scales. Application areas include MEMS, bio-MEMS, microfluidics, thermal systems, and carbon nanostructures.
Requirements: While satisfying the general mechanical engineering requirements, take at least five courses from:
MECE E4212: Microelectromechanical systems
MECE E4213: BioMEMS
MECE E6105: Transport phenomena in the presence of interfaces
MECE E6700: Carbon nanotubes
MECE E6710: Nanofabrication laboratory
MECE E6720: Nano/microscale thermal transport processes
MECE E8990: Small scale mechanical behavior
ELEN E4503: Sensors, actuators, and electromechanical systems
ELEN E6945: Device nanofabrication
BMEN E4590: BioMEMS: cellular and molecular applications
MSAE E4090: Nanotechnology
Doctoral/Professional Degree Programs
Students who wish to continue their studies beyond the master’s degree level but are unwilling to embark upon a program of research of the kind required for a doctoral degree may continue in a program leading to the professional degree of Mechanical Engineer (MECE). The course of study consists of a minimum of 30 points of work beyond the master’s degree, combining courses of an analytical nature with those emphasizing the applied aspects of one or more fields in mechanical engineering. For the professional degree, the student must have a grade point average of 3.0 or better.
When a student becomes a prospective candidate for either the Doctor of Engineering Science (Eng.Sc.D.) or Doctor of Philosophy (Ph.D.) degree, a faculty adviser is assigned whose task is to help choose a program of courses, provide general advice on academic matters, and monitor academic performance.
The doctoral candidate is expected to attain a level of mastery in some area of mechanical engineering, and must therefore choose a field and concentrate in it by taking the most advanced courses offered. This choice of specialty is normally made by the time the student has completed 30 points of credit beyond the bachelor’s degree, at which time a complete course program is prepared and submitted to the departmental doctoral committee for approval. The student must maintain a grade point average of 3.2 or better in graduate courses.
The department requires the prospective candidate to pass a qualifying examination. Given once a year, in January, it is usually taken after the student has completed 30 points beyond the bachelor’s degree. However, it may not be delayed past the next examination given after completion of 45 points. The examination comprises a written test, given in two parts over two days, in which questions may be selected from a broad set in all areas of mechanical engineering and applied mathematics, devised to test the candidate’s ability to think creatively. There is also an oral examination based on some research project the student has undertaken. A candidate who fails the examination may be permitted to repeat it once in the following year.
After passing the qualifying examination, the student chooses a faculty member in the pertinent area of specialization who then serves as the research adviser. This adviser helps select a research problem and supervises the research, writing, and defense of the dissertation. Once a specific problem has been identified and a tentative plan for the research prepared, the student submits a research proposal and presents it to a faculty committee. The committee considers whether the proposed problem is suitable for doctoral research, whether the plan of attack is well formulated and appropriate to the problem, and whether the student is adequately prepared. It may approve the plan without reservation, or it may recommend modifications or additions. This is the last formal requirement until the dissertation is submitted for approval.
All doctoral students are required to successfully complete four semesters
of the mechanical engineering seminar MECE E9500.