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Course Criteria
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3.00 Credits
09W, 10W: 10A Biomedical informatics is an emerging discipline that coalesces the health science knowledges including medicine, dentistry, pharmacy, nursing, radiology and biological sciences with computer science, mathematics, statistics, engineering, information technologies and management. The objective of this course is to provide the theoretical foundations and the current applications of biomedical informatics in health sciences, and health care delivery systems. The course contents include structures, algorithms and design of algorithms necessary to organize, store, retrieve and analyze data and develop computational solutions to produce new knowledge and understanding about, and representation of biomedical knowledge, management of health care/hospital systems, clinical decision making, research in biomedical and pharmaceutical systems, and design and development of interactive and distributive multimedia systems for education. Prerequisites: Math 3 and permission of instructor. Dist: TAS. McGrath.
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3.00 Credits
08F, 09F: 11 Concepts and methods used in the treatment of linear equations with emphasis on matrix operations, differential equations, and eigenvalue problems will be developed following a brief review of analytic function theory. Topics include the Fourier integral, finite and infinite dimensional vector spaces, boundary value problems, eigenfunction expansions, Green's functions, transform techniques for partial differential equations, and series solution of ordinary differential equations. Properties and uses of orthogonal polynomials and special functions such as the hypergeometric, Bessel, Legendre, and gamma functions are included. Applications in engineering and physics are emphasized. Prerequisite: Engineering Sciences 92 or Mathematics 33 or 43, with permission of instructor, or the equivalent. Lotko.
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3.00 Credits
09W: 11 09S: 12 10W: 11 10S: 12 The application of statistical techniques and concepts to maximize the amount and quality of information resulting from experiments. After a brief introductory summary of fundamental concepts in probability and statistics, topics considered will include probability distributions, sampling distributions, estimation and confidence intervals for parameters of statistical distributions, hypothesis testing, design and analysis of variance for single and multiple-factor experiments, regression analysis, estimation and confidence intervals for parameters of non-statistical models, and statistical quality control. Prerequisites: Mathematics 13 or equivalent. Borsuk (winter), Lasky (spring).
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3.00 Credits
09W, 10W: 12 An introduction to various methods of optimization and their uses in modern engineering. Students will learn to formulate and analyze optimization problems and apply optimization techniques in addition to learning the basic mathematical principles on which these techniques are based. Topic coverage includes linear programming, nonlinear programming, dynamic programming, combinatorial optimization and Monte Carlo methods. Prerequisite: Mathematics 22 and Engineering Sciences 27 or equivalents, or permission of instructor. Cybenko.
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3.00 Credits
09W, 10W: 11 This course concentrates on the numerical solution of partial differential equations commonly encountered in Engineering Sciences. Finite difference and finite element methods are used to solve problems in heat flow, wave propagation, vibrations, fluid mechanics, hydrology, and solid mechanics. The course materials emphasize the systematic generation of numerical methods for elliptic, parabolic, and hyperbolic problems, and the analysis of their stability, accuracy, and convergence properties. Weekly computer exercises will be required to illustrate the concepts discussed in class. Prerequisite: Mathematics 23 and Engineering Sciences 91 (Mathematics 26 or Computer Science 26), or equivalents. Lynch.
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3.00 Credits
Not offered in the period from 08F through 10S The course examines in the context of modern computational practice algorithms for solving linear systems Ax = b and Az = x. Matrix decomposition algorithms, matrix inversion, and eigenvector expansions are studied. Algorithms for special matrix classes are featured, including symmetric positive definite matrices, banded matrices, and sparse matrices. Error analysis and complexity analysis of the algorithms are covered. The algorithms are implemented for selected examples chosen from elimination methods (linear systems), least squares (filters), linear programming, incidence matrices (networks and graphs), diagonalization (convolution), sparse matrices (partial differential equations). Prerequisite: Computer Science 26, Mathematics 26, or Engineering Sciences 91. Students are to be familiar with approximation theory, error analysis, direct and iterative technique for solving linear systems, and discretization of continuous problems to the level normally encountered in an undergraduate course in numerical analysis. Zomordian.
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3.00 Credits
08F, 09F: 10A This course will provide students with an introduction to the current and emerging technologies used in homeland security and the practitioners who use them. Topics covered in class include personal protective equipment, physical and cyber security systems, communications and information technologies, information assurance, WMD detection, robotics, simulation, exercise and training technologies. Students will gain a detailed understanding of the role technology plays in protecting the homeland. Dist: TAS. McGrath.
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3.00 Credits
09S, 10S: 10 Continuous and discrete-time signals and systems. The Discrete Fourier Transform and the Fast Fourier Transform. Linear filtering of signals and noise. Characterization of random signals using correlation functions and power spectral densities. Problems will be assigned that require the use of the computer. Prerequisite: Engineering Sciences 61 and 92 or equivalents. Hansen.
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3.00 Credits
09S, 10S: 11 This course covers current and emerging information technologies, focusing on their engineering design, performance and application. General topics such as distributed component and object architectures, wireless networking, web computing and information security will be covered. Specific subjects will include Java, CORBA, JINI public key cryptography, web search engine theory and technology, and communications techniques relevant to wireless networking such as Code Division Multiple Access protocols and cellular technology. Prerequisites: Engineering Sciences 20, Engineering Sciences 103 and 27 or Computer Science 78. Engineering Sciences 103 can be taken concurrently. Cybenko.
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3.00 Credits
09S, 10S: 2A Design and analysis of networked systems comprised of interacting dynamic agents will be considered. Inspired by the cohesive behavior of flocks of birds, we design self-organizing engineering systems that mimic a sense of coordinated motion and the capability of collaborative information processing similar to flocks of birds. Examples include multi-robot networks, social networks, sensor networks, and swarms. The course combines concepts in control theory, graph theory, and complex systems in a unified framework. Prerequisite: Engineering Sciences 26, Mathematics 23, or equivalents plus familiarity with MATLAB. Olfati-Saber.
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