Mechanical Engineering (MS)
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, for domestic students, over a correspondingly longer period. A minimum grade-point average of 2.5 is required for graduation.
The M.S. degree in mechanical engineering allows a student to take a sequence of courses tailored to their interests and objectives; this is referred to 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:
- All courses must be at the graduate level, i.e., numbered 4000 or higher, with at least two 6000-level lecture courses in SEAS. At least one of the 6000-level courses must be in Mechanical Engineering.
- 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. Alternatively, any one of the following courses may be taken to satisfy the math requirement:
Course List Code Title Points BMEN E4110 BIOSTATISTICS FOR ENGINEERS COMS W4701 ARTIFICIAL INTELLIGENCE COMS W4771 MACHINE LEARNING IEOR E4150 INTRO-PROBABILITY ＆ STATISTICS 1 MECE E4520 DATA SCIENCE FOR MECHANICAL SYSTEMS ORCA E4500 FOUNDATIONS OF DATA SCIENCE - 1
Same as STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS.
- Out-of-department study is encouraged, but must be taken in consultation with a faculty adviser.
- At least five courses must be in Mechanical Engineering.
Students who are not on the standard track can select a concentration 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 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: While satisfying the requirements for a Master of Science in Mechanical Engineering, take at least five courses from:
| Code | Title | Points |
|---|---|---|
| MEBM E4703 | MOLECULAR MECHANICS IN BIOLOGY | |
| MEBM E4710 | MORPHOGENESIS:BIOL MAT SHP/STR | |
| 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 - MEBM E6311 | and MIXT THEORIES FOR BIOL TISSUES | |
| MECE E6422 - MECE E6423 | INTRO-THEORY OF ELASTICITY I and INTRO-THEORY OF ELASTICITY II | |
| MECE E8501 | ADVNCD CONTINUUM BIOMECHANICS |
When offered by the Biomedical Engineering Department, the following courses may also count toward the Biomechanics track:
| Code | Title | Points |
|---|---|---|
| BMEN E4301 | ||
| BMEN E4302 | BIOMECHANICS OF MUSCULOSKELETAL SOFT TIS | |
| 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 | ||
| BMEN E4750 | SOUND AND HEARING | |
| BMEN E6301 | MODELING OF BIOL TISS WITH FEM | |
| BMME E4702 |
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:
| Code | Title | Points |
|---|---|---|
| MECE E4210 | ENERGY INFRASTRUCTURE PLANNING | |
| MECE E4211 | ENERGY SOURCES AND CONVERSION | |
| MECE E4302 | ADVANCED THERMODYNAMICS | |
| MECE E4304 | TURBOMACHINERY | |
| MECE E4305 | MECH ＆ THERMODYNAMICS OF PROPULSION | |
| MECE E4312 | SOLAR THERMAL ENGINEERING | |
| MECE E4314 | ENERGY DYNAMICS OF GREEN BLDGS | |
| MECH E4320 | INTRO TO COMBUSTION | |
| MECE E4330 | THERMOFLUID SYSTEMS DESIGN | |
| MECE E6100 | ADVANCED MECHANICS OF FLUIDS | |
| MECE E6104 | CASE STUDIES-COMPUT FLUID DYN | |
| MECE E6313 | ADVANCED HEAT TRANSFER | |
| EAEE E6126 |
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 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: 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:
| Code | Title | Points |
|---|---|---|
| MECE E4058 | MECHATRONICS ＆ EMBEDDED MICRO | |
| MECE E4212 | MICROELECTROMECHANICAL SYSTEMS | |
| MECE E4213 | BIOMEMS: DESIGN FAB ＆ ANALYSIS | |
| MECE E4214 | MEMS Sensors and Systems | |
| MECE E6137 | NANOSCALE ACTUATION ＆ SENSING | |
| MECE E6432 | SMALL-SCALE MECH BEHAVIOR |
When offered by other departments, the following courses may also count toward the micro/nanoscale concentration:
| Code | Title | Points |
|---|---|---|
| APPH E6081 | SOLID STATE PHYSICS I | |
| ELEN E4106 | Advanced Solid State Devices and Materials | |
| ELEN E4411 | FUNDAMENTALS OF PHOTONICS | |
| ELEN E4944 | PRNCPLS OF DEVICE MICROFABRCTN | |
| ELEN E6331 | PRINCPLS SEMICONDUCTR PHYSCS I | |
| ELEN E6414 | PHOTONIC INTEGRATED CIRCUITS | |
| ELEN E6945 | DEVICE NANOFABRICATION | |
| MSAE E4090 | NANOTECHNOLOGY | |
| MSAE E4100 | CRYSTALLOGRAPHY | |
| PHYS W4018 |
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, and Hod Lipson
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:
| Code | Title | Points |
|---|---|---|
| MECE E4058 | MECHATRONICS ＆ EMBEDDED MICRO | |
| MECE E4602 | INTRODUCTION TO ROBOTICS | |
| MECE E4606 | DIGITAL MANUFACTURING | |
| MECE E4611 | ROBOTICS STUDIO | |
| MECE E6400 | ADVANCED MACHINE DYNAMICS | |
| MECE E6614 | ADV TPC:ROBOTICS/MECH SYNTHES | |
| MECS E4510 | EVOLUTIONARY COMPUTATION＆DESIGN AUTOMATI | |
| MECS E6615 | Robotic Manipulation: Sensing, Planning, Design and Execution | |
| MECS E6616 | ROBOT LEARNING | |
| EEME E4601 | DIGITAL CONTROL SYSTEMS | |
| EEME E6601 | INTRO TO CONTROL THEORY | |
| EEME E6602 | MODERN CONTROL THEORY | |
| EEME E6610 | ||
| ELEN E4810 | DIGITAL SIGNAL PROCESSING | |
| BMME E4702 |
When offered by the Computer Science Department, these courses may also be used to satisfy the robotics requirements:
| Code | Title | Points |
|---|---|---|
| COMS W4731 | Computer Vision I: First Principles | |
| COMS W4733 | COMPUTATIONAL ASPECTS OF ROBOTICS | |
| COMS E6733 |
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.