# 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 courses, visit the Electrical Engineering home page at www.ee.columbia.edu.

### Concentration in Multimedia Networking

Advisers: Professors Henning Schulzrinne, Predrag Jelenkovic

- Satisfy M.S. degree requirements.
- Both
*ELEN E6761: Computer communication networks, I*and*ELEN E6950: Wireless and mobile networking, I*. - Either
*COMS W4118: Operating systems*or*COMS W4111: Database systems.* *COMS E6181: Advanced Internet services*or*ELEN E6776: Topic: content distribution networks.*

With an adviser’s approval, any of the courses above can be replaced by the following closely related subjects: *CSEE E4140: Networking laboratory; CSEE W4119: Computer networks; COMS W4180: Network security; ELEN E6762: Computer communication networks, II; ELEN E6850: Visual information systems; ELEN E6951: Wireless and mobile networking, II.*

### Concentration in Telecommunications Engineering

Advisers: Professors Henning Schulzrinne, Pedrag Jelenkovic, Ed Coffman, Gil Zussman

- Satisfy M.S. degree requirements.
- One basic hardware or software course such as:
*EECS E4321: Digital VLSI circuits; ELEN E4411: Fundamentals of photonics; COMS W4118: Operating systems, I; COMS W4111: Database systems.* - One basic systems course such as:
*ELEN E4702: Communication theory; ELEN E4703: Wireless communications; CSEE W4119: Computer networks; ELEN E6761: Computer communication networks, I.* - At least two approved courses from a focus area such as Signal/Image Processing and Telecommunications/Multimedia Networks.

### Concentration in Lightwave (Photonics) Engineering

Advisers: Professors Keren Bergman, Ioannis (John) Kymissis, Michael Lipson

- Satisfy M.S. degree requirements.
- Take both
*ELEN E4411: Fundamentals of photonics*and*ELEN E6412: Lightware devices*(or an E&M course, such as*APPH E4300: Applied electrodynamics*or*PHYS GR6092: Electromagnetic theory*). - One more device/circuits/photonics course such as:
*ELEN E6413: Lightwave systems; ELEN E6414: Photonic integrated circuits; ELEN E4314: Communication circuits; ELEN E4488: Optical systems; ELEN E6488: Optical interconnects and interconnection networks; ELEN E4193: Modern display science and technology.* - At least two additional approved courses in photonics or a related area. Options also include courses outside EE such as
*APPH E4090: Nanotechnology; APPH E4100: Quantum physics of matter; APPH E4110: Modern optics; CHAP E4120: Statistical mechanics; APPH E4112: Laser physics; APPH E4130: Physics of solar energy; APPH E6081: Solid state physics, I; APPH E6082: Solid state physics, II; APPH E6091: Magnetism and magnetic materials; APPH E6110: Laser interactions with matter; MSAE E4202: Thermodynamics and reactions in solids; MSAE E4206: Electronic and magnetic properties of solids; MSAE E4207: Lattice vibrations and crystal defects; MSAE E6120: Grain boundaries and interfaces; MSAE E6220: Crystal physics; MSAE E6229: Energy and particle beam processing of materials; MSAE E6225: Techniques in X-ray and neutron diffraction.*

### Concentration in Wireless and Mobile Communications

Adviser: Professors Gil Zussman, Predrag Jelenkovic, Xiaodong Wang

- Satisfy M.S. degree requirements.
- One basic circuits course such as:
*ELEN E4312: Analog electric circuits; ELEN E4314: Communication circuits; ELEN E6314: Advanced communication circuits; ELEN E6312: Advanced analog ICs.* *T*wo communications or networking courses such as:*CSEE W4119: Computer networks; ELEN E4702: Digital communications; ELEN E4703: Wireless communications; ELEN E6711: Stochastic signals and noise; ELEN E4810: Digital signal processing; ELEN E6950: Wireless and mobile networking, I; ELEN E6951: Wireless and mobile networking, II; ELEN E6761: Computer communication networks, I; ELEN E6712: Communication theory; ELEN E6713: Topics in communications; ELEN E6717: Information theory; ELEN E677x: Topics in telecommunication networks.*- At least two additional approved courses in wireless communications or a related area.

### Concentration in Integrated Circuits and Systems

Advisers: Professors Peter Kinget, Harish Krishnaswamy, Mingoo Seok, Kenneth Shepard, Yannis Tsividis, Charles Zukowski

- Satisfy M.S. degree requirements.
- One digital course from:
*EECS E4321: Digital VLSI circuits*or*EECS E6321: Advanced digital electronic circuits.* - One analog course from:
*ELEN E4312: Analog electronic circuits; ELEN E6312: Advanced analog integrated circuits; ELEN E6316: Analog circuits and systems in VLSI; ELEN E4314: Communication circuits; ELEN E6314: Advanced communication circuits; ELEN E6320: Millimeter-wave IC design.* - Two additional courses such as: Other courses from 2. and 3.;
*ELEN E6350: VLSI design laboratory; ELEN E6304: Topics in electronic circuits; ELEN E6318: Microwave circuit design; ELEN E9303: Seminar in electronic circuits.* - At least one additional approved course in integrated circuits and systems or a related area.

### Concentration in Microelectronic Devices

Advisers: Professors Wen Wang, Ioannis (John) Kymissis

- Satisfy M.S. degree requirements.
- One basic course such as:
*ELEN E4301: Introduction to semiconductor devices*or*ELEN E4411: Fundamentals of photonics.* - One advanced course such as:
*ELEN E4193: Modern display science and technology; 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; ELEN E6945: Nanoscale fabrication and devices.* - At least two other approved courses in devices or a related area. Options also include courses outside EE such as
*APPH E4090: Nanotechnology; APPH E4100: Quantum physics of matter; APPH E4110: Modern optics; CHAP E4120: Statistical mechanics; APPH E4112: Laser physics; APPH E4130: Physics of solar energy; APPH E6081: Solid state physics, I; APPH E6082: Solid state physics, II; APPH E6091: Magnetism and magnetic materials; APPH E6110: Laser interactions with matter; MSAE E4202: Thermodynamics and reactions in solids; MSAE E4206: Electronic and magnetic properties of solids; MSAE E4207: Lattice vibrations and crystal defects; MSAE E6120: Grain boundaries and interfaces; MSAE E6220: Crystal physics; MSAE E6229: Energy and particle beam processing of materials; MSAE E6225: Techniques in X-ray and neutron diffraction.*

### Concentration in Systems Biology and Neuroengineering

Advisers: Professors Dimitris Anastassiou, Christine Hendon, Pedrag Jelenkovic, Aurel A. Lazar, Nima Mesgarani, Kenneth Shepard, Xiaodong Wang

- Satisfy M.S. degree requirements.
- Take both
*ECBM E4060: Introduction to genomic information science and technology*and*BMEB W4020: Computational neuroscience, circuits in the brain*. - Take at least one course from
*BMEE E4030: Neural control engineering; ECBM E4040: Neural networks and deep learning; ECBM E4090: Brain computer interfaces (BCI) laboratory; CBMF W4761: Computational genomics; ELEN E6010: Systems biology: design principles for biological circuits; EEBM E6020: Methods in computational neuroscience; BMEE E6030: Neural modeling and neuroengineering*. - Take at least one course from
*ECBM E6040: Neural networks and deep learning research; ECBM E607x: Topics in neuroscience and deep learning; ELEN E608x: Topics in systems biology; EEBM E609x: Topics in computational neuroscience and neuroengineering; ELEN E6261: Computational methods of circuit analysis ELEN E6717: Information theory; ELEN E6860: Advanced digital signal processing*.

### Concentration 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

- Satisfy M.S. degree requirements.
- Take at least two courses from
*ECBM E4040: Neural networks and deep learning; EECS E4764: Internet of things - intelligent and connected systems; ELEN E4810: Digital signal processing; ELEN E4903: Topic: machine learning (or equivalent); EEOR E6616: Convex optimization; EECS E6893: Topic: big data analytics*. - Take at least one courses from
*ECBM E6040: Neural networks and deep learning research; EECS E6720: Bayesian models for machine learning; EECS E6765: Internet of things - systems and physical data analytics; EECS E6895: Topic: advanced big data analytics*. - Take a second course from #3 or one course from
*ECBM E4060: Introduction to genomic information science and technology; ECBM: 6070: Topics in neuroscience and deep learning, ELEN E6690: Topics in data-driven analysis and computation; ELEN E6886: Sparse representation and high-dimensional geometry; ELEN E9601: Seminar in data-driven analysis and computation*.