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Course Criteria
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3.00 Credits
Secure programming. Cryptograhic engineering and key handling. Access controls. Tradeoffs in security design. Design for security. - Steven Bellovin Prerequisites: COMS W4118; W4180 and/or W4119 recommended. General Education Requirement: Quantitative and Deductive Reasoning (QUA). 3 points
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3.00 Credits
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. - J. Gross Prerequisites: COMS W3203 General Education Requirement: Quantitative and Deductive Reasoning (QUA). Not offered in 2009-2010. Lect: 3. 3 pts.
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3.00 Credits
Sequences and recursions, calculus of finite differences and sums, elementary number theory, permutation group structures, binomial coefficients, Stilling numbers, harmonic numbers, generating functions. - J. Gross Prerequisites: COMS W3203 and a course in calculus. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 3. 3 pts.
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3.00 Credits
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. - M. Yannakakis, R. Servedio Prerequisites: COMS W3261. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 3. 3 pts.
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3.00 Credits
Modern theory and practice of computation on digital computers. Introduction to concepts of computational complexity. Design and analysis of numerical algorithms. Applications to computational finance, computational science, and computational engineering. - J. Traub Prerequisites: Knowledge of a programming language. Some knowledge of scientific computation is desirable. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 3. 3 pts.
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3.00 Credits
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. - R. Servedio Prerequisites: COMS W4231 or COMS W4236 or (COMS W3203 and permission of instructor) or (COMS W3261 and permission of instructor). General Education Requirement: Quantitative and Deductive Reasoning (QUA). lect: 3. 3pts
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3.00 Credits
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. - T. Malkin Prerequisites: Comfort with basic discrete math and probability. Recommended: COMS W3261 or COMS W4231. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 2.5. 3 pts.
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3.00 Credits
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. - H. Wozniakowski Prerequisites: Knowledge of linear algebra. Prior knowledge of quantum mechanics is not required although helpful. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 3. 3 pts
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3.00 Credits
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. - K. Ross Prerequisites: COMS W3137 and W3824. General Education Requirement: Quantitative and Deductive Reasoning (QUA). Lect: 3. 3 pts.
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3.00 Credits
An overview of the field of biomedical informatics, combining perspectives from medicine, computer science and social science. Use of computers and information in health care and the biomedical sciences, covering specific applications and general methods, current issues, capabilities and limitations of biomedical informatics. Biomedical Informatics studies the organization of medical information, the effective management of information using computer technology, and the impact of such technology on medical research, education, and patient care. The field explores techniques for assessing current information practices, determining the information needs of health care providers and patients, developing interventions using computer technology, and evaluating the impact of those interventions. - M. Chiang Prerequisites: Experience with computers and a passing familiarity with medicine and biology. Undergraduates in their senior or junior years may take this course only if they have adequate backgroud in mathematics and receive permission from the instructor General Education Requirement: Quantitative and Deductive Reasoning (QUA). 3 points
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