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 lecture courses in SEAS 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 but must be taken in consultation with a faculty 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 biomechanics energy systems, micro/nanoscale engineering, or robotics and control. The requirements for a concentration 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 concentrations are listed below.

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

The 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 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 concentration is a suitable preparation for careers in the biomedical devices industry or engineering and scientific consulting.

To choose this concentration, select "Mechanical Engineering Biomechanics Master of Science" in the Program field when filling in the online application for the M.S. program. The name of this program will be listed on graduates’ transcripts.

Requirements: Requirements: While satisfying the requirements for a Master of Science in Mechanical Engineering, take at least five courses from:

MEBM E4703: Molecular mechanics in biology
MEBM E4710: Morphogenesis: shape and structure in biological materials
MECE E4100: Mechanics of fluids
MECE E6100: Advanced mechanics of fluids
MECE E6106: Finite element method for fluid flow and fluid-structure interactions
MEBM E6310-E6311: Mixture theories for biological tissues I and II
MECE E6422-E6423 Introduction to the theory of elasticity I and II
MECE E8501: Advanced continuum biomechanics

When offered by the Biomedical Engineering Department, the following courses may also count toward the Biomechanics track:
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 E4350: Biomechanics of developmental biology
BMEN E4570: Science and engineering of body fluids
BMEN E4750: Sound and hearing
BMEN E6301: Modeling of biological tissues with finite elements
BMME E4702: Advanced musculoskeletal biomechanics

One 3-credit research course can be counted toward the 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 Michael Burke, 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 specialization is a suitable preparation for careers in energy production and energy consultation.

Requirements: While satisfying the requirements for a Master of Science in Mechanical Engineering, take at least five courses from:

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

Furthermore, students must take one course in statistics (STAT or SIEO designations). One 3-credit research course can be counted toward 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, Jeffrey Kysar, and P. James Schuck

The concentration in micro/nanoscale engineering provides the M.S. candidate with an understanding of engineering challenges and opportunities in microand nanoscale systems. The curriculum addresses fundamental issues of mechanics, fluid mechanics, optics, heat transfer, and manufacturing at smallsize scales. Application areas include MEMS, bio-MEMS, microfluidics, thermal systems, and carbon nanostructures.

Requirements: The requirements for the micro/nanoscale engineering track ensures that students obtain an education in micro/nanoscale engineering that is both broad and deep. Students will be required to take at least five classes from a selected pool that covers many aspects of micro/ nanoengineering. Currently, eight classes are compatible with the general requirements for the Master of Science degree in Mechanical Engineering. These include:

MECE E4058: Mechatronics
MECE E4212: Microelectromechanical systems (MEMS)
MECE E4213: BioMEMS
MECE E4214: MEMS production and manufacturing
MECE E6137: Nanoscale actuation and sensing
MECE E6432: Small scale mechanical behavior

When offered by other departments, the following courses may also count toward the micro/nanoscale concentration:

APPH E6081: Solid state physics 1
ELEN E4106: Advanced solid state device materials
ELEN E4411: Fundamentals of photonics
ELEN E4944: Principles of device microfabrication
ELEN E6331: Principles semiconductor physics
ELEN E6414: Photonic integrated circuits
ELEN E6945: Device nano fabrication
ELEN E6414: Photonic integrated circuits
MSAE E4090: Nanotechnology
MSAE E4100: Crystallography
PHYS W4018: Solid state physics

One 3-credit research course can be counted toward the concentration if the research is approved by the student's adviser and is micro/nanoscale related.

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.

Requirements: While satisfying the requirements for a Master of Science in Mechanical Engineering, take at least five courses from:

MECE E4058: Mechanics and embedded microcomputer control
MECE E4602: Intro to robotics
MECE E4606: Digital manufacturing
MECE E6400: Advanced machine dynamics
MECE E6614: Advanced topics in robotics and mechanism synthesis
MECS E4510: Design automation
MECE E6615: Robotic manipulation
MECE E6616: Robot learning
EEME E4601: Digital control systems
EEME E6601: Introduction to control theory
EEME E6602: Modern control theory
EEME E6610: Optimal control theory
ELEN E4810: Digital signal processing
BMME E4702: Advanced musculoskeletal biomechanics

 

When offered by the Computer Science Department, these courses may also be used to satisfy the robotics requirements:
COMS W4731: Computer vision
COMS W4733: Computational aspects of robotics
COMS E6733: 3D photography

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

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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