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, MATH, STAT, SIEO course designations) 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 concentration in either energy systems or in micro/nanoscale engineering. The requirements for a special concentration are identical to those of the standard track, with one exception: a special concentration student must take at least 15 of his/her points from a list determined by a special concentration adviser in consultation with an advisory committee. The currently available special concentrations are listed below.

M.S. in Mechanical Engineering with Concentration in Energy Systems
Advisers: Professors Vijay Modi and Arvind Narayanaswamy

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: 30 points of graduate level course work, i.e., courses numbered 4000-level or higher, at least two of which must be a 6000-level (MECE E6100 Advanced mechanics of fluids and MECE E6313 Advanced heat transfer are strongly recommended).
Furthermore, students must take one course in statistics (STAT/SIEO designations) and at least five courses from the following list*:

    MECE E4210: Energy infrastructure planning
    MECE E4211: Energy: sources and conversion
    MECE E4302: Advanced thermodynamics
    MECE E4304: Turbomachinery
    MECE E4305: Mechanics and thermodynamics propulsion
    MECE E4312: Solar thermal engineering
    MECE E4314: Energy dynamics of green buildings
    MECE E4320: Intro to combustion
    MECE E4330: Thermofluid systems design
    MECE E6100: Advanced mechanics of fluids
    MECE E6104: Case studies in computational fluid dynamics
    MECE E6313: Advanced heat transfer
    EAEE E6126: Carbon sequestration

*One 3-point research course can be counted towards the concentration if the research is approved by the student’s adviser and is energy related.

M.S. in Mechanical Engineering with Concentration in Micro/Nanoscale Engineering
Advisers: Professors 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

M.S. in Mechanical Engineering with Concentration in Robotics and Control
Advisers: Professors Sunil Agrawal, Matei Ciocarlie, Hod Lipson, Richard Longman, and Fred Stolfi

The field of robotics is seeing unprecedented growth, in areas as diverse as manufacturing, logistics, transportation, health care, space exploration, and more. This program prepares students for a career in robotics and its many applications in society. Students perform in-depth study of topics such as robotic manipulation, navigation, perception, human interaction, medical robotics, assistance and rehabilitation. This concentration is a suitable preparation for joining established companies, information-age dominant players investing heavily in this field, or the new wave of robotics start-ups aiming to provide disruptive
innovations. Many of the acquired skills can be applied in other fields as diverse as automation, manufacturing, computer graphics or machine vision. This program can also be a foundation for a research career in robotics and related areas, in both academia and industry.

Candidates for the M.S. with concentration in Robotics and Control should simultaneously satisfy these two sets of requirements:

Take at least five courses from the list below during their M.S. (courses taken during undergraduate studies do not count):

Courses in the Mechanical Engineering Department
MECE E4058: Mechanics and embedded microcomputer control
MECE E4601: Digital control systems
MECE E4602: Intro to robotics
MECE E6400: Advanced machine dynamics
MECE E6601: Intro to control theory
MECE E6602: Modern control theory
MECE E6610: Optimal control theory
MECE E6614: Advanced topics in robotics and mechanism synthesis
MECE E4606: Digital manufacturing

Courses in the other Departments in the School of Engineering and Applied Science
ELEN E4501: Sensors, actuators and electromechanical systems
BMME E4702: Advanced musculoskeletal biomechanics
COMS W4731: Computer vision
COMS W4733: Computational aspects of robotics
ELEN E4810: Digital signal processing
COMS E6733: 3D photography

Satisfy the general requirements for the MS in mechanical engineering requirements, which are:

  1. All courses must be at the graduate level, i.e., numbered 4000 or higher, with at least two 6000-level courses included.
  2. Five (5) courses at least within the Mechanical Engineering department.
  3. At least one math course (APMA or MATH designator), covering material beyond what the student has taken previously. Examples of suitable courses are: APMA E4001y Principles of applied mathematics; APMA E4300y, Introduction to numerical methods; APMA E4301x Numerical methods for partial differential equations; and APMA E4204x Functions for complex variables.
  4. A total of 30 credits are required.

Express M.S. Application

The Express M.S. Application is offered to current seniors, including 3-2 students, who are enrolled in the BS program. In the Express M.S. Application, a master’s degree can be earned seamlessly. Graduate classes are available for seniors to apply toward their M.S. degree and the advanced courses that will be taken have been designed to have the exact prerequisites completed as an undergraduate. Other advantages include the opportunity for better course planning and creating a streamlined set of courses more possible. Additional benefits include simplified application process, no GRE is required and no reference
letters are required.To qualify for this program, your cumulative GPA should be at least 3.5. For more information on requirements and access to an application, please visit me.columbia.edu/ms-express-application-1.

Doctoral Degree Program

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 May, 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.