# MS Elective Specializations

MS Students in the electrical engineering department can participate in a number of elective specializations or can design their own MS program in consultation with an adviser. These specializations are not degree requirements. They represent suggestions from the faculty as to how one can structure their program to focus on a particular area of interest. All specializations are open to all EE MS students, except for the Specialization in Research for which a student needs to apply for and be admitted into (see below). The MS degree requirements are quite flexible and are listed in the Master of Science Degree section. All students, whether following elective specializations or not, are advised to include breadth in their program. Not all of the elective courses listed here are offered every year.

**Advisers:** Dimitris Anastassiou, Shih-Fu Chang, Predrag 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 course 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 E6070: 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

**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 4113: Distributed Systems
- COMS W4118: Operating systems I

- Analytical courses:
- ELEN E6772: Topic: Network Algorithms
- ELEN E6950: Wireless and mobile networking
- ICSEE 6180: Modeling and Performance Evaluation

- Systems courses:
- Three courses from the following list (but a course 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 Econ, Eng & Society
- ELEN E6770: Topic: Next Gen 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
- CSEE E4951: Wireless and mobile networks and systems.
- CSEE 6180: Modeling and Performance Evaluation
- COMS W4180: Network security
- COMS 4995: Internet Technology, Economics and Policy
- COMS 6181: 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 E677*, COMS 4995, 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.

**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;
- 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.

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

- Satisfy M.S. degree requirements.
- One digital course from:
- 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.

**Advisers: **M. Preindl, X. Jiang, G. Zussman, K. Shepard, Xiaodong Wang

- Satisfy EE M.S. degree requirements
- Take at least two [power conversion or power systems] courses from:
- ELEN E4361 Power electronics
- ELEN E4511 Power systems analysis
- ELEN E4510 Solar energy and smart grid power systems
- ELEN E4901 Photovoltaic Systems Eng. and Sustainability
- EAEE E4220 Energy system economics and optimization
- ELEN E6901 Energy Storage for the Electric Grid
- ELEN E6901 Smart Grid Technologies
- ELEN E6902 Renewable power systems
- ELEN E6904 Motor drive systems
- ELEN E6906 Future Energy: Economics, Systems, Policies

- 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 Systems

- Take at least one [non-electric energy class] course from:
- EAEE 4002 Alternative energy resources
- CHEN E4201 Engineering applications of electrochemistry
- EAEE E4180 Electrochemical energy storage systems
- MECE E4430 Automotive dynamics
- MECE E4210 Energy infrastructure planning
- MECE E4211 Energy: sources and conversion
- MECH E4320 Intro to combustion
- MECE E4302 Advanced thermodynamics
- EAEE E4190 Photovoltaic systems engineering and sustainability
- EAEE E4257 Environmental data analysis and modeling
- EAEE E4302 Carbon capture

- Recommended to take one of the following [energy policy or market] non-technical elective courses (this course will fill the quota of non-technical courses of the MS 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

**Advisers: **Professors Dimitris Anastassiou, Christine Fleming, 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

**Advisers:** Professors Keren Bergman, Ioannis (John) Kymissis

- Satisfy M.S. degree requirements.
- Take both
- 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.

**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.

Advisers: full-time EE faculty

The Department of Electrical Engineering offers qualified MS students the option to pursue the MS Research Specialization. This specialization is merit-based; each student needs to find a full-time faculty member in Electrical Engineering who is willing to supervise their research. Students need to first do at least 3 credits of ELEN 6001/6002 (as part of the 24 credits in their first two semesters) under the supervision of a research advisor and then needs the recommendation from their research advisor to apply and be considered for admission into the specialization by the department.

Admitted students will typically take a 6-credit (zero tuition) research course ENGI E4990 in their third semester, in addition to the remaining 6 credits of their other third-semester courses, to achieve a total of 12 credits and full-time status in their third semester. They then need to take another 6-credit (zero tuition) research course ENGI E4990 in their fourth semester and thereby be enrolled full time in the Columbia program as a student in residence. The course is a letter-grade course and can be taken in the fall or spring. The grades will be included on the transcript. ENGI E4990 credits do not count as credits for the MS degree. Although 30 credits satisfying the MS program have to be completed within the first three semesters of studies, the MS degree will be granted to students in this specialization only at the end of successfully and fully completing the fourth semester at Columbia. See https://bulletin.engineering.columbia.edu/interdisciplinary-engineering-courses for the bulletin description.