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COMS W4187: Security architecture and engineering
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W4118; W4180 and/or W4119 recommended. Secure programming. Cryptograhic engineering and key handling. Access controls. Tradeoffs in security design. Design for security.
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COMS W4203: Graph theory
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W3203 General introduction to graph theory. Isomorphism testing, algebraic specification, symmetries, spanning trees, traversability, planarity, drawings on higher-order surfaces, colorings, extremal graphs, random graphs, graphical measurement, directed graphs, Burnside-Polya counting, voltage graph theory.
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COMS W4236: Introduction to computational complexity
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W3261. Develops a quantitative theory of the computational difficulty of problems in terms of the resources (eg. time, space) needed to solve them. Classification of problems into complexity classes, reductions and completeness. Power and limitations of different modes of computation such as nondeterminism, randomization, interaction and parallelism.
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COMS W4236 - Introduction to computational complexity
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COMS W4252: Introduction to computational learning theory
3.00 Credits
Columbia University in the City of New York
Prerequisites: CSOR W4231 or COMS W4236 or (COMS W3203 and permission of instructor) or (COMS W3261 and permission of instructor). Possibilities and limitations of performing learning by computational agents. Topics include computational models of learning, polynomial time learnability, learning from examples and learning from queries to oracles. Computational and statistical limitations of learning. Applications to Boolean functions, geometric functions, automata.
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COMS W4252 - Introduction to computational learning theory
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COMS W4261: Introduction to cryptography
3.00 Credits
Columbia University in the City of New York
Prerequisites: Comfort with basic discrete math and probability. Recommended: COMS W3261 or CSOR W4231. An introduction to modern cryptography, focusing on the complexity-theoretic foundations of secure computation and communication in adversarial environments; a rigorous approach, based on precise definitions and provably secure protocols. Topics include private and public key encryption schemes, digital signatures, authentication, pseudorandom generators and functions, one-way functions, trapdoor functions, number theory and computational hardness, identification and zero knowledge protocols.
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COMS W4261 - Introduction to cryptography
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COMS W4281: Introduction to quantum computing
3.00 Credits
Columbia University in the City of New York
Prerequisites: Knowledge of linear algebra. Prior knowledge of quantum mechanics is not required although helpful. Introduction to quantum computing. Shor's factoring algorithm, Grover's database search algorithm, the quantum summation algorithm. Relationship between classical and quantum computing. Potential power of quantum computers.
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COMS W4281 - Introduction to quantum computing
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COMS W4444: Programming and problem solving
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W3137 and CSEE W3827. Hands-on introduction to solving open-ended computational problems. Emphasis on creativity, cooperation, and collaboration. Projects spanning a variety of areas within computer science, typically requiring the development of computer programs. Generalization of solutions to broader problems, and specialization of complex problems to make them manageable. Team-oriented projects, student presentations, and in-class participation required.
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COMS W4701: Artificial intelligence
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W3137. Provides a broad understanding of the basic techniques for building intelligent computer systems. Topics include state-space problem representations, problem reduction and and-or graphs, game playing and heuristic search, predicate calculus, and resolution theorem proving, AI systems and languages for knowledge representation, machine learning and concept formation and other topics such as natural language processing may be included as time permits.
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COMS W4705: Natural language processing
3.00 Credits
Columbia University in the City of New York
Prerequisites: COMS W3133, or W3134, or W3137, or W3139, or the instructor's permission. Computational approaches to natural language generation and understanding. Recommended preparation: some previous or concurrent exposure to AI or Machine Learning. Topics include information extraction, summarization, machine translation, dialogue systems, and emotional speech. Particular attention is given to robust techniques that can handle understanding and generation for the large amounts of text on the Web or in other large corpora. Programming exercises in several of these areas.
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COMS W4706: Spoken language processing
3.00 Credits
Columbia University in the City of New York
Prerequisites: Prerequisites: COMS W3133, or W3134, or W3137, or the instructor's permission. Computational approaches to speech generation and understanding. Topics include speech recognition and understanding, speech analysis for computational linguistics research, and speech synthesis. Speech applications including dialogue systems, data mining, summarization, and translation. Exercises involve data analysis and building a small text-to-speech system.
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