Electrical Engineering (MS)
Master of Science Degree
Candidates for the M.S. degree in electrical engineering must complete 30 points of credit beyond the bachelor’s degree. A minimum of 15 points of credit must be at the 6000 level or higher. No credit will be allowed for undergraduate courses (3000 or lower). At least 15 points must be in electrical engineering, defined as including all courses with an ELEN designator or a joint designator containing electrical engineering as a member, e.g., EECS, CSEE, EEME, ECBM, etc. And it is expected that at least 12 of the first 24 points taken will be in electrical engineering.
Not all technical courses can be applied toward the M.S. degree, and some have restrictions. Up to 6 points of research (such as ELEN E4998 INTERMEDIATE PROJECTS, ELEN E6001 ADVANCED PROJECTS, and ELEN E6002 ADVANCED PROJECTS) can be applied. Up to 1.5 points of fieldwork (ELEN E6999 FIELDWORK) can be used. No more than 3 points of courses that do not contain primarily engineering, math, or science content can be used, subject to the written pre-approval of the department. Any course that is not on the list of standard courses specified at ee.columbia.edu/masters-program requires prior written department approval, including during the summer session.
The general school requirements listed earlier in this bulletin, such as minimum GPA, must also be satisfied. All degree requirements must be completed within five years of the beginning of the first course credited toward the degree.
More details and a requirements checklist for approvals can be found at ee.columbia.edu/masters-program.
Optional M.S. Specializations
Students in the electrical engineering M.S. program often choose to use some of their electives to focus on a particular field. Students may pick one of a number of optional, formal specialization templates or design their own M.S. program in consultation with an adviser. These specializations are not degree requirements. They represent suggestions from the faculty as to how one might fill one’s programs so as to focus on a particular area of interest. Students may wish to follow these suggestions, but they need not. The degree requirements are quite flexible and are listed in the Master of Science Degree section, above. All students, whether following a formal specialization template or not, are expected to include breadth in their program. Not all of the elective courses listed here are offered every year. For the latest information on available courses, visit the Electrical Engineering home page at ee.columbia.edu.
Specialization in Data-Driven Analysis and Computation
Advisers: Professors Dimitris Anastassiou, Shih-Fu Chang, Pedrag Jelenkovic, Zoran Kostic, Aurel A. Lazar, Nima Mesgarani, John Paisley, John Wright, Xiaofan (Fred) Jiang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements | ||
| 2. Choose at least two courses from the following: | ||
| NEURAL NETWRKS ＆ DEEP LEARNING | ||
| IoT - INTELLIG ＆ CONNECTED SYS | ||
| DIGITAL SIGNAL PROCESSING | ||
| Machine Learning for Signals, Information and Data | ||
| CONVEX OPTIMIZATION | ||
| TOPICS-INFORMATION PROCESSING | ||
| 3. Choose at least one course from the following: | ||
| NEUR NET ＆ DEEP LEAR RSRCH | ||
| BAYESIAN MOD MACHINE LEARNING | ||
| IoT - SYS ＆PHY DATA ANALYTICS | ||
| TOPICS-INFORMATION PROCESSING | ||
| 4. Choose one course from the following: | ||
A second course from # 3 | ||
| INTRO-GENOMIC INFO SCI ＆ TECH | ||
| Computing with Brain Circuits of Model Organisms | ||
| TPC NEUROSCI ＆ DEEP LEARN | ||
| TOPICS DATA-DRIVEN ANAL ＆ COMP | ||
| Sparse and Low-Dimensional Models for High-Dimensional Data | ||
ELEN E9601 | ||
Specialization in Networking
Advisers: Professors Predrag Jelenkovic, Javad Ghaderi, Ethan Katz-Bassett, Debasis Mitra, Gil Zussman, Xiaofan (Fred) Jiang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Choose one basic networking course from the following: | ||
| COMPUTER COMMUNICATNS NETWORKS | ||
| COMPUTER NETWORKS | ||
| 3. Choose one basic systems or analytical course from the following: | ||
| NETWORKING LABORATORY | ||
| FUND-LARGE-SCALE DIST SYSTEMS | ||
| OPERATING SYSTEMS I | ||
| TOPICS IN NETWORKING | ||
| WIRELESS ＆ MOBILE NETWORKING I | ||
| Modeling and Performance | ||
| 4. Choose three courses from the following (courses cannot be used to fulfill both this requirement and any of the above requirements): 1 | ||
| Optical interconnects and interconnection networks | ||
| COMPUTER COMMUNICATNS NETWORKS | ||
| INTERNET ECON, ENG ＆ SOCIETY | ||
| TOPICS IN NETWORKING | ||
| TOPICS IN NETWORKING | ||
ELEN E6775 | ||
| TOPICS IN NETWORKING | ||
| WIRELESS ＆ MOBILE NETWORKING I | ||
| CONVEX OPTIMIZATION FOR ENG | ||
| CONVEX OPTIMIZATION | ||
| NETWORKING LABORATORY | ||
EECS E4951 | ||
| Modeling and Performance | ||
COMS W4180 | ||
| TOPICS IN COMPUTER SCIENCE | ||
| ADVANCED INTERNET SERVICES | ||
| TOPICS IN COMPUTER SCIENCE | ||
| QUEUING THEORY ＆ APPLICATIONS | ||
| STOCHASTIC MODELS | ||
| 5. At least two of the four courses used to fulfill requirements 3 and 4 must be 6000-level ELEN, EECS, CSEE, or EEOR courses. | ||
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With adviser approval, other relevant advanced topic courses on networking topics, other relevant advanced topic courses on networking topics from ELEN E677 x, COMS W4995 TOPICS IN COMPUTER SCIENCE, COMS E6998 TOPICS IN COMPUTER SCIENCE, or other course numbers may be used to fulfill this requirement.
Specialization in Wireless and Mobile Communications
Advisers: Professors Gil Zussman, Predrag Jelenkovic, Xiaodong Wang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Choose one basic circuits course from the following: | ||
| ANALOG ELECTRONIC CIRCUITS | ||
| COMMUNICATION CIRCUITS | ||
ELEN E6314 | ||
| ADV ANALOG INTEGRATED CIRCUITS | ||
| 3. Choose two communications or networking courses such as: | ||
| COMPUTER NETWORKS | ||
| DIGITAL COMMUNICATIONS | ||
| WIRELESS COMMUNICATIONS | ||
ELEN E6711 | ||
| DIGITAL SIGNAL PROCESSING | ||
| WIRELESS ＆ MOBILE NETWORKING I | ||
EECS E4951 | ||
| COMPUTER COMMUNICATNS NETWORKS | ||
| COMMUNICATION THEORY | ||
| Topics in communications | ||
| Classical and Quantum Information Theory | ||
ELEN E677X | ||
| 4. At least two additional approved courses in wireless communications or a related area. | ||
Specialization in Integrated Circuits and Systems
Advisers: Professors Peter Kinget, Harish Krishnaswamy, Mingoo Seok, Kenneth Shepard, Yannis Tsividis, Charles Zukowski
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Choose one digital course from the following: | ||
| DIGITAL VLSI CIRCUITS | ||
| Advanced digital electronic circuits | ||
| 3. Choose one analog course from the following: | ||
| ANALOG ELECTRONIC CIRCUITS | ||
| ADV ANALOG INTEGRATED CIRCUITS | ||
| Analog-Digital Interfaces in VLSI | ||
| COMMUNICATION CIRCUITS | ||
ELEN E6314 | ||
| MILLIMETER-WAVE IC DESIGN | ||
| 4. Choose two additional courses such as: | ||
Other courses from no. 2 and 3 | ||
| VLSI DESIGN LABORATORY | ||
ELEN E6304 | ||
| MICROWAVE CIRCUIT DESIGN | ||
| Seminar in electronic circuits | ||
| 5. At least one additional approved course in integrated circuits and systems or a related area. | ||
Specialization in Smart Electric Energy
Advisers: Professors Matthias Preindl, Xiaofan (Fred) Jiang, Gil Zussman, Kenneth Shepard, Xiaodong Wang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Choose at least two power conversion or power systems courses from the following: | ||
| POWER ELECTRONICS | ||
| TPCS-ELEC ＆ COMPUT ENGINEERING | ||
| TPCS-ELEC ＆ COMPUT ENGINEERING | ||
| POWER SYSTEMS ANALYSIS | ||
| SOL ENERGY/SMART GRID POWR SYS | ||
| 3. Choose at least one control or optimization course from the following: | ||
| DIGITAL CONTROL SYSTEMS | ||
| INTRO TO CONTROL THEORY | ||
| MODERN CONTROL THEORY | ||
| Statistical signal processing and learning | ||
| CONVEX OPTIMIZATION FOR ENG | ||
| CONVEX OPTIMIZATION | ||
| IoT - INTELLIG ＆ CONNECTED SYS | ||
| EMBEDDED SYSTEMS | ||
| 4. Choose at least one nonelectric energy class course from the following: | ||
| ENERGY INFRASTRUCTURE PLANNING | ||
| INTRO TO COMBUSTION | ||
| ENERGY SOURCES AND CONVERSION | ||
| ADVANCED THERMODYNAMICS | ||
| PHOTOVOLTAIC SYSTEMS ENGIN | ||
| ENVIR DATA ANALYSIS ＆ MODELING | ||
| CARBON STORAGE | ||
| CARBON CAPTURE | ||
| CLOSING THE CARBON CYCLE | ||
| 5. Not required, but consider taking one of the following energy policy or market nontechnical elective courses (this course will fill the quota of nontechnical courses on the M.S. Checklist) | ||
| INDUST ECOLOGY-EARTH RESOURCES | ||
| ALTERNATIVE ENERGY RESOURCES | ||
| Electricity Markets | ||
| Energy Systems Fundamentals | ||
| Energy Analysis for Energy Efficiency | ||
| The Economics of Energy | ||
| Global Energy Policy | ||
| Energy Policy | ||
| Renewable Energy Markets and Policy | ||
Specialization in Systems Biology and Neuroengineering
Advisers: Professors Dimitris Anastassiou, Christine Hendon, Pedrag Jelenkovic, Aurel A. Lazar, Nima Mesgarani, Kenneth Shepard, Xiaodong Wang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Take both: | ||
| INTRO-GENOMIC INFO SCI ＆ TECH | ||
| Computational neuroscience: circuits in the brain | ||
| 3. Choose at least one course from the following: | ||
| NEURAL CONTROL ENGINEERING | ||
| NEURAL NETWRKS ＆ DEEP LEARNING | ||
| Computing with Brain Circuits of Model Organisms | ||
| BRAIN COMPUTER INTERFACES LAB | ||
| COMPUTATIONAL GENOMICS | ||
| DESIGN PRIN FOR BIOL CIRCUITS | ||
| METHODS OF COMPUT NEUROSCIENCE | ||
BMEE E6030 | ||
| 4. Choose at least one course from the following: | ||
| NEUR NET ＆ DEEP LEAR RSRCH | ||
| TPC NEUROSCI ＆ DEEP LEARN | ||
ELEN E608X: | ||
| TPCS IN COMP NEUROSCI/ENGINEERING | ||
ELEN E6261 | ||
| Classical and Quantum Information Theory | ||
| ADV DIGITAL SIGNAL PROCESSING | ||
Specialization in Lightwave (Photonics) Engineering
Advisers: Professors Keren Bergman, Ioannis (John) Kymissis, Michal Lipson
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Take both: 1 | ||
| FUNDAMENTALS OF PHOTONICS | ||
| LIGHTWAVE DEVICES | ||
| 3. Choose one of the following device/circuits/photonics courses such as: | ||
| LIGHTWAVE SYSTEMS | ||
| PHOTONIC INTEGRATED CIRCUITS | ||
| COMMUNICATION CIRCUITS | ||
| OPTICAL SYSTEMS | ||
| Optical interconnects and interconnection networks | ||
| MOD DISPLAY SCI ＆ TECHNOLOGY | ||
| 4. Choose at least two additional approved courses in photonics or a related area. Options also include courses outside EE such as: | ||
APPH E4090 | ||
| QUANTUM PHYSICS OF MATTER | ||
| MODERN OPTICS | ||
| STATISTICAL MECHANICS AND COMP METHODS | ||
| LASER PHYSICS | ||
| PHYSICS/SOLAR ENERGY | ||
| SOLID STATE PHYSICS I | ||
APPH E6082 | ||
| Magnetism and magnetic materials | ||
APPH E6110 | ||
| KINETICS OF TRANSFORMATIONS | ||
| ELEC ＆ MAGNETIC PROP OF SOLIDS | ||
| LATTICE VIBES ＆ CRYSTAL DEFCTS | ||
MSAE E6120 | ||
MSAE E6220 | ||
| ENERGY/PART-BEAM PROCES-MATRLS | ||
MSAE E6225 | ||
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Or an E&M course, such as APPH E4300 APPLIED ELECTRODYNAMICS or PHYS GR6092 ELECTROMAGNETIC THEORY.
Specialization in Microelectronic Devices
Advisers: Professors Dion Khodagholy, Ioannis (John) Kymissis, Michal Lipson, James Teherani, Wen Wang
| Code | Title | Points |
|---|---|---|
| 1. Satisfy M.S. degree requirements. | ||
| 2. Choose one basic course such as: | ||
| INTRO-SEMICONDUCTOR DEVICES | ||
| FUNDAMENTALS OF PHOTONICS | ||
| 3. Choose one advanced course such as: | ||
| ELEN E4193 | MOD DISPLAY SCI ＆ TECHNOLOGY | |
| ELEN E4944 | PRNCPLS OF DEVICE MICROFABRCTN | |
| ELEN E4503 | ||
| ELEN E6151 | ||
| ELEN E6331 | PRINCPLS SEMICONDUCTR PHYSCS I | |
| ELEN E6332 | ||
| ELEN E6333 | Semiconductor device physics | |
| ELEN E6945 | DEVICE NANOFABRICATION | |
| 4. Choose at least two other approved courses in devices or a related area. Options also include courses outside EE such as: | ||
APPH E4090 | ||
| QUANTUM PHYSICS OF MATTER | ||
| MODERN OPTICS | ||
| STATISTICAL MECHANICS AND COMP METHODS | ||
| LASER PHYSICS | ||
| PHYSICS/SOLAR ENERGY | ||
| SOLID STATE PHYSICS I | ||
APPH E6082 | ||
| Magnetism and magnetic materials | ||
APPH E6110 | ||
| KINETICS OF TRANSFORMATIONS | ||
| ELEC ＆ MAGNETIC PROP OF SOLIDS | ||
| LATTICE VIBES ＆ CRYSTAL DEFCTS | ||
MSAE E6120 | ||
MSAE E6220 | ||
| ENERGY/PART-BEAM PROCES-MATRLS | ||
MSAE E6225 | ||