Graduate Programs

The Department of Mechanical Engineering offers two doctoral degrees: Doctor of Philosophy (Ph.D.) and Doctor of Engineering Science (Eng.Sc.D.), and the Master of Science degree. The Ph.D. degree is confered by the Graduate School of Arts and Science, and the Eng.Sc.D. degree is conferred by the Fu Foundation School of Engineering and Applied Science.

M.S. students must complete the professional development and leadership course, ENGI E4000, as a graduation requirement. Ph.D. candidates are strongly encouraged to complete ENGI E6001–6004 and should consult their program for PDL requirements.

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 coursework 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 coursework. 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 focus.” In consultation with his/her adviser an M.S. student can develop a focus 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 tracks.

Typical choices 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. All courses must be at the graduate level, i.e., numbered 4000 or higher, with some 6000-level courses chosen in consultation with an adviser. At least one of the 6000- level courses must be in Mechanical Engineering.
  2. Every program must contain at least one course in mathematics (APMA, MATH, STAT course designations) covering material beyond what the student has taken previously. It is recommended to be taken early in the sequence in order to serve as a basis for the technical coursework.
  3. Out-of-department study is encouraged, must be taken in consultation with adviser.
  4. At least five courses must be in Mechanical Engineering.

Rather than selecting the standard option, students can select an elective specialization in either energy systems, micro/nanoscale engineering, or robotics and control. The requirements for a specialization are identical to those of the standard track, with one exception: students must take at least 15 points from a list determined by an adviser in consultation with an advisory committee. The currently available elective specializations are listed below.

M.S. in Mechanical Engineering with Elective Concentration in Biomechanics
Advisers: Professors Gerard Ateshian, Karen Kasza, and Kristin Myers

The elective concentration in biomechanics is developed in coordination with the Department of Biomedical Engineering. It provides the M.S. candidate with knowledge of the mechanics of biological tissues. The 4000-level courses offered in this elective concentration provide foundations of fluid and solid mechanics applicable to biomechanics, as well as applications of mechanics to specific cell, tissue and organ systems. The higher-level courses provide deeper foundations on theoretical and computational approaches relevant to biomechanics. This elective concentration is a suitable preparation for careers in the biomedical devices industry or engineering and scientific consulting.

Requirements: While satisfying the requirements for a Master of Science in Mechanical Engineering, take at least five courses from the below list.
The highlighted courses below are considered foundational courses for the Robotics and Control track and are strongly recommended to be included in your program:

    MECE E4100: Mechanics of Fluids
    ENME E4113: Advanced Mechanics of Solids
    ENME E4332: Finite Element Analysis, I
    BMEN E4301: Structure, mechanics, and adaptation of bone
    BMEN E4302: Biomechanics of Musculoskeletal Soft Tissues
    BMEN E4305: Cardiac Mechanics
    BMEN E4310: Solid Biomechanics
    BMEN E4320: Fluid Biomechanics
    BMEN E4340: Biomechanics of Cells
    BMEN E4570: Science and Engineering of Body Fluids
    BMME E4702: Advanced Musculoskeletal Biomechanics
    MEBM E4703: Molecular Mechanics in Biology
    MEBM E4710: Morphogenesis: Shape and Structure in Biological Materials
    BMEN E4750: Sound and Hearing
    BMEN E4750: Sound and Hearing
    MECE E6100: Advanced Mechanics of Fluids
    MECE E6104: Case Studies in CFD
    BMEN E6301: Modeling of Biological Tissues with Finite Elements
    MEBM E6310-6311: Mixture Theories for Biological Tissues I and II
    MECE E6400: Advanced Machine Dynamics
    MECE E6422-6423: Introduction to the Theory of Elasticity I and II
    MECE E8501: Advanced Continuum Biomechanics

One 3-credit research course can be counted towards the elective concentration if the research is approved by the student’s adviser and is biomechanics related.

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

The specialization 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 specialization is a suitable preparation for careers in energy production and energy consultation.

Requirements: 30 points of graduate level coursework, 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 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 E6103: Compressible flow
    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 toward the specialization 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 P. James Schuck

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, and Richard Longman

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 specialization 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 specialization 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
MEBM E4439: Modeling & id of dynamic system
MECE E4058: Mechanics and embedded microcomputer control
MECE E4510: Geometrical modeling
MECE E4601: Digital control systems
MECE E4602: Intro to robotics
MECE E4603: Applied robotics: algorithm & software
MECE E4606: Digital manufacturing
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 E6615: Robotic manipulation
MECE E6620: Applied signal recognition

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
EEME E6601: Introduction to control theory**
EEME E6602: Modern control theory**
EEME E6610: Optimal control theory**
COMS E6733: 3D photography*

*Registration rectrictions may apply.
**Count as MECE.

Examples of suitable APMA 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.

Doctoral Degree Program

All applications to the doctoral program in mechanical engineering are administered by The Fu Foundation School of Engineering and Applied Science. Students who matriculate into the doctoral program without a master's degree earn a Master of Science degree while pursuing their doctoral degree.

Doctoral candidates are expected to attain a level of mastery in an area of mechanical engineering and must therefore choose a field and take the most advanced courses offered in that field. Candidates are assigned a faculty adviser whose task is to help choose a program of courses, provide general advice on academic matters, and monitor academic performance. Candidates also choose a faculty member in the pertinent area of specialization to serve as their research adviser. This adviser helps select a research problem and supervises the research, writing, and defense of the dissertation.

Program Requirements

  1. 30 credits beyond master's degree
  2. GPA of 3.2 or better in graduate courses
  3. 4 semesters of graduate seminar MECE E9500
  4. Completion of all milestones

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