Graduate Programs
The Department of Electrical
Engineering offers graduate programs leading to the degree of Master of Science (M.S.),
the graduate professional degree of Electrical Engineer (E.E.), and the degrees of
Doctor of Engineer-ing Science (Eng.Sc.D.) and Doctor of Philosophy (Ph.D.). The
Graduate Record Examination (General Test only) is required of all applicants except
special students. An undergraduate grade point average equivalent to B or better from an
institution comparable to Columbia is expected.
Applicants who, for good reasons,
are unable to submit GRE test results by the deadline date but whose undergraduate
record is clearly superior may file an application without the GRE scores. An
explanatory note should be added to ensure that the application will be processed even
while incomplete. If the candidate’s admissibility is clear, the decision may be made
without the GRE scores; otherwise, it may be deferred until the scores are received.
There are no prescribed course
requirements in any of the regular graduate degree programs. Students, in consultation
with their faculty advisers, design their own programs, focusing on particular fields of
electrical engineering. Among the fields of graduate study are microelectronics,
communications and signal processing, integrated circuit and system analysis and
synthesis, photonics, electromagnetic theory and applications, plasma physics, and
quantum electronics.
Graduate course charts for several
focus areas can be found at www.ee.columbia.edu.
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 taken in EE courses (i.e., courses listed by the Electrical Engineer-ing Department) or courses designated COMS, of which at least 10 points must be EE courses. Courses to be credited toward the M.S. degree can be taken only upon prior approval of a faculty adviser in the Department of Electrical Engineering. This applies to the summer session as well as the autumn and spring terms. Certain 4000-level courses will not be credited toward the M.S. degree, and no more than 6 points of research may be taken for credit. Up to 3 points of credit for approved graduate courses outside of engineering and science may be allowed. 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 checklist for adviser approvals can be found at www.ee.columbia.edu/academics/masters.
Professional Degree
The professional degree in
electrical engineering is intended to provide specialization beyond the level of the
M.S. degree, in a focused area of electrical engineering selected to meet the
professional objectives of the candidate. A minimum of 30 points of credit is required.
The prospective E.E. candidate follows a program of study formulated in consultation
with, and approved by, a faculty adviser. At least three courses will be in a specific,
focused area of electrical engineering, and at least two-thirds of the entire program
will be in electrical engineering or computer science. No thesis is required, but the
program may optionally include a seminar or project or research for which a report is
produced; up to 6 points of such projects may be credited toward the degree. The level
of the courses will generally be higher than is typical of a master’s degree program,
although courses at the 4000 level may be included to prepare for more advanced work. A
candidate is required to maintain a grade-point average of at least 3.0. All degree
requirements must be completed within five years of the beginning of the first course
credited toward the degree.
Doctoral Degree
The requirements for the Ph.D.
and Eng.Sc.D. degrees are identical. Both require a dissertation based on the
candidate’s original research, conducted under the supervision of a faculty member. The
work may be theoretical or experimental or both. Students who wish to become candidates
for the doctoral degree in electrical engineering have the option of applying for
admission to the Eng.Sc.D. program or the Ph.D. program. Students who elect the
Eng.Sc.D. degree register in the School of Engineering and Applied Science; those who
elect the Ph.D. degree register in the Graduate School of Arts and Sciences. Doctoral
candidates must obtain a minimum of 60 points of formal course credit beyond the
bachelor’s degree. A master’s degree from an accredited institution may be accepted as
equivalent to 30 points. A minimum of 30 points beyond the master’s degree must be
earned while in residence in the doctoral program. More detailed information regarding
the requirements for the doctoral degree may be obtained in the department office and at
www.ee.columbia.edu/academics/phd.
Optional M.S. Concentrations
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 concentration
templates or design their own M.S. program in consultation with an adviser. These
concentrations 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 concentration 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 concentrations, contact the Department of Electrical Engineering or visit the
Electrical Engineering home page at www.ee.columbia.edu.
Concentration in Multimedia
Networking
Advisers: Prof. Henning
Schulzrinne, Prof. Predrag Jelenkovic 1. Satisfy the basic M.S. degree requirement.
2. Both ELEN E6711: Stochastic signals and noise and ELEN E6761: Computer communication networks.
3. Either COMS W4118: Operating systems or COMS W4111: Database systems.
4. COMS E6181: Advanced Internet services.
5. Either ELEN E6960: Multimedia networking or ELEN E6970: Resource allocation and networking games.
With the adviser’s approval, any of the courses above can be replaced by the following closely related subjects: ELEN E4720: Networking laboratory; CSEE W4119: Computer networks; COMS W4995: Network security; ELEN E6762: Broadband networks; ELEN E6850: Visual information systems; ELEN E6940: Telecommunication networks control and management; ELEN E6950: Wireless and mobile networking.
Concentration in Telecommunications
Engineering
Advisers: Prof. Henning
Schulzrinne, Prof. Pedrag Jelenkovic, Prof. Ed Coffman, Prof. Nicholas Maxemchuk, Prof.
Dan Rubenstein 1. Satisfy the basic M.S. degree requirements.
2. One basic hardware or software course such as: ELEN E4321: VLSI circuits; ELEN E4411: Fundamentals of photonics; COMS W4118: Operating systems, I; COMS W4111: Database systems.
3. One basic systems course such as: ELEN E4702: Communication theory; ELEN E4703: Wireless communications; CSEE W4119: Computer networks; ELEN E6761: Computer communication networks.
4. At least two approved courses from a focus area such as Signal/Image Processing and Telecommunications/ Multimedia Networks.
Concentration in Media Engineering
Advisers: Prof. Shi-Fu Chang,
Prof. Alexandros Eleftheriadis, Prof. Dan Ellis, Prof. Xiaodong Wang 1. Satisfy the basic M.S. degree requirements.
2. Both ELEN E4810: Digital signal processing and ELEN E4830: Digital image processing.
3. Either ELEN E6761: Computer communication networks or CSEE W4119: Computer networks.
4. At least two approved advanced courses such as: ELEN E4890: Music signal processing; ELEN E6820: Speech and audio processing and recognition; ELEN E6850: Visual information systems; ELEN E6860: Advanced digital signal processing; ELEN E6880: Topics in signal processing; ELEN E6762: Broadband networks; ELEN E6960: Multimedia networking; COMS E6181: Advanced Internet services; or ELEN E6001-E6002: Advanced projects in electrical engineering with an appropriate project. A cross-disciplinary project in areas related to new media technology is especially encouraged.
Concentration in Lightwave (Photonics) Engineering
Advisers: Prof. Keren Bergman, Prof. Paul Diament, Prof. Richard Osgood, Prof. Amiya Sen, Prof. Tony Heinz1. Satisfy the basic M.S. degree requirements.
2. Take both ELEN E4411: Fundamentals of photonics and ELEN E6403: Classical electromagnetic theory or equivalent.
3. One more device/circuits/photonics course such as: ELEN E4401: Wave transmission and fiber optics; ELEN E6412: Lightwave devices; ELEN E6413: Lightwave systems; ELEN E4405: Classical nonlinear optics; ELEN E6414: Photonic integrated circuits; ELEN E4306: Communication circuits; ELEN E4501: Electromagnetic devices and energy conversion.
4. At least two approved courses in photonics or a related area.
Concentration in Wireless and Mobile
Communications
Adviser: TBA 1. Satisfy the basic M.S. degree requirements.
2. One basic circuits course such as: ELEN E4303: Analog electric circuits; ELEN E4314: Communication circuits; ELEN E6314: RF ICs; ELEN E6312: Design of analog integrated circuits.
3. Two communications courses such as: ELEN E4702: Communication theory; ELEN E4703: Wireless communications; ELEN E6711: Stochastic signals and noise; ELEN E4810: Digital signal processing; ELEN E6950: Wireless and mobile networking; ELEN E6761: Computer communication networks.
4. At least two approved courses in wireless communications or a related area.
Concentration in Microelectronic Circuits
Advisers: Prof. Yannis Tsividis, Prof. Charles Zukowski, Prof. Kenneth Shepard, Prof. Peter Kinget1. Satisfy the basic M.S. degree requirements.
2. One digital course: ELEN E4321: VLSI circuits.
3. One analog course such as: ELEN E4312: Analog electronic circuits; ELEN E4215: Analog filter synthesis and design; ELEN E6312: Advanced analog integrated circuits; ELEN E6316: Analog circuits and systems in VLSI; ELEN E4314: Communication circuits; ELEN E6314: Advanced communication circuits.
4. One additional course such as: ELEN E4332: VLSI design laboratory; ELEN E6261: Computational methods of circuit analysis; ELEN E6304: Topics in electronic circuits.
5. At least two additional approved courses in circuits or a related area.
Concentration in Microelectronic
Devices
Advisers: Prof. Wen Wang, Prof.
Richard Osgood 1. Satisfy the basic M.S. degree requirements.
2. One basic course such as: ELEN E4301: Introduction to semiconductor devices or ELEN E4411: Fundamentals of photonics.
3. One advanced course such as: ELEN E4944: Principles of device microfabrication; ELEN E4503: Sensors, actuators, and electromechanical systems; ELEN E6151: Surface physics and analysis of electronic materials; ELEN E6331: Principles of semiconductor physics, I; ELEN E6332: Principles of semiconductor physics, II; ELEN E6333: Semiconductor device physics.
4. At least two approved courses in devices or a related area.
Concentration in Systems Biology
Advisers: Prof. Dimitris
Anastassiou, Prof. Ed Coffman, Prof. Pedrag Jelenkovic, Prof. Aurel Lazar, Prof. Kenneth Shepard, Prof. Xiaodong Wang, Prof. Charles Zukowski
1. Satisfy the basic M.S. degree requirements.
2. Take both ECBM E4060: Introduction to genomic information science and technology and BMEB W4011: Computational neuroscience, I: circuits in the brain
3. Take at least one course from CBMF W4761: Computational genomics; BIOL W4037: Bioinformatics of gene regulation; Biomedical Informatics G4015: Computational biology, bioinformatics; APMA E4400: Introduction to biophysical modeling; BMEN E6480: Computa-tional neuroscience, II: neural modeling and neuroengineering; CHEN E4700: Principles of genomic technologies.
4. Take at least one course from ELEN E608x: Topics in systems biology; ELEN E6717: Information theory; ELEN E6201: Linear systems theory; EEME E6601: Introduction to control theory; ELEN E6711: Stochastic models in information systems; ELEN E6860: Advanced digital signal processing.