# 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 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 E4720: Machine learning for signals, information, and data; 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 E4070; ECBM: E607x: Topics in neuroscience and deep learning, ELEN E6690: Topics in data-driven analysis and computation; ELEN E6876: Sparse and low-dimensional models for high-dimensional geometry; ELEN E9601: Seminar in data-driven analysis and computation*.

### Concentration in Networking

Advisers: Professors Predrag Jelenkovic, Javad Ghaderi, Ethan Katz-Bassett, Debasis Mitra, Gil Zussman, Xiaofan (Fred) Jiang

- Satisfy M.S. degree requirements.
- One basic networking course from the following:
*ELEN E6761: Computer communication networks I, CSEE W4119: Computer networks*. - One basic systems or analytical course from the following:
*Systems courses: CSEE E4140: Networking laboratory; COMS W4113: Fundamentals of large-scale distributed systems; COMS W4118: Operating systems I;*Analytical courses:*ELEN E6772: Topic: network algorithms; ELEN E6950: Wireless and mobile networking, I; CSEE E6180: Modeling and performance evaluation.*. - Three courses from the following list (courses cannot be used to fulfill both this requirement and any of the above requirements):
*ELEN E6488: Optical interconnects and interconnection networks; ELEN E6761: Computer communication networks I; ELEN E6767: internet economics, energy, and society; ELEN E6770: Topic: next generation networks; ELEN E6772: Topic: network algorithms; ELEN E6775: Topic: computer networks: a systems approach; ELEN E6776: Topic: content distribution networks; ELEN E6950: Wireless and mobile networking I; EEOR E4650: Convex optimization for EE; EEOR E6616: Convex optimization; CSEE E4140: Networking laboratory; EECS E4951: Wireless networks and systems; CSEE E6180: Modeling and Performance Evaluation; COMS W4180: Network security; COMS W4995: Internet technology, economics, and policy, COMS E6181: Advanced internet services; COMS E6998: Cloud computing and big data; IEOR E6704: Queueing theory; IEOR E4106: Stochastic models; with adviser approval, other relevant advanced topic courses on networking topics from ELEN E677x, COMS W4995, COMS E6998, or other course numbers may be used to fulfill this requirement.*. - At least two of the four courses used to fulfill requirements 3 and 4 must be 6000-level ELEN, EECS, CSEE, or EEOR courses.

### Concentration in Wireless and Mobile Communications

Advisers: 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.*. - Two 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; EECS E4951: Wireless networks and systems; 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 digital interfaces 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 no. 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 Smart Electric Energy

Advisers: Professors Matthias Preindl, Xiaofan (Fred) Jiang, Gil Zussman, Kenneth Shepard, Xiaodong Wang

- Satisfy M.S. degree requirements.
- Take at least two power conversion or power systems courses from:
*ELEN E4361: Power electronics; ELEN E6902 Renewable power systems; ELEN E6904: Motor drive systems; ELEN E4511: Power systems analysis and control; ELEN E4510: Solar energy and smart grid power systems.* - Take at least one control or optimization course from:
*EEME E4601: Digital control systems; EEME E6601: Introduction to control theory; EEME E6602: Modern control theory; ELEN E6873: Detection and estimation theory; EEOR E4650: Convex optimization for electrical engineering; EEOR E6616: Convex optimization; EECS E4764: IoT—intelligent and connected systems; CSEE W4840: Embedded system Design.* - Take at least one nonelectric energy class course from:
*MECE E4210: Energy infrastructure planning; MECE E4320: Intro to combustion; MECE E4211: Energy: sources and conversions; MECE E4302: Advanced thermodynamics; EAEE E4190: Photovoltaic systems engineering and sustainability; EAEE E4257: Environmental data analysis and modeling; EAEE E4301: Carbon storage; EAEE E4302: Carbon capture; EAEE E4304: Closing the carbon cycle.* - 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):
*EAEE E4001: Industrial ecology of earth resources; EAIA W4200: Alternative energy resources; INAF U6057 Electricity markets; INAF U6072: Energy systems fundamentals; SUMA K4135: Energy analysis for energy efficiency; INAF U6065: The economics of energy; INAF U6061: Global energy policy; INAF U6242: Energy policy; INAF U6135: Renewable energy markets and policy.*

### Concentration in Systems Biology and Neuroengineering

Adviser: Professors Dimitris Anastassiou, Christine Hendon, Pedrag Jelenkovic, Dion Khodagholy, 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 E4070; 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 Lightwave (Photonics) Engineering

Advisers: Professors Keren Bergman, Ioannis (John) Kymissis, Michal 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 Microelectronic Devices

Advisers: Professors Dion Khodagholy, Wen Wang, Ioannis (John) Kymissis, Michal Lipson, James Teherani

- 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.*