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Course Criteria
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3.00 Credits
Thorough treatment of linear programming and combinatorial optimization. Topics include matching theory, network flow, matroid optimization, and how to deal with NP-hard optimization problems. Prior exposure to discrete mathematics (such as 18.310) helpful.
Prerequisite:
Prereq: 18.06, 18.700, or 18.701
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3.00 Credits
Topics vary from year to year. Students present and discuss the subject matter. Instruction and practice in written and oral communication provided. Enrollment limited.
Prerequisite:
Prereq: 18.404, 18.410
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3.00 Credits
Provides an introduction to the theory and practice of quantum computation. Topics covered: physics of information processing; quantum algorithms including the factoring algorithm and Grover's search algorithm; quantum error correction; quantum communication and cryptography. Knowledge of quantum mechanics helpful but not required.
Prerequisite:
Prereq: Permission of instructor
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3.00 Credits
Examines quantum computation and quantum information. Topics include quantum circuits, quantum Fourier transform and search algorithms, the quantum operations formalism, quantum error correction, stabilizer and Calderbank-Shor-Steans codes, fault tolerant quantum computation, quantum data compression, entanglement, capacity of quantum channels, and proof of the security of quantum cryptography. Prior knowledge of quantum mechanics required.
Prerequisite:
Prereq: 18.435
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3.00 Credits
Design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks. Process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation.
Prerequisite:
Prereq: 6.046
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3.00 Credits
Advanced treatment of combinatorial optimization with an emphasis on combinatorial aspects. Non-bipartite matchings, submodular functions, matroid intersection/union, matroid matching, submodular flows, multicommodity flows, packing and connectivity problems, and other recent developments.
Prerequisite:
Prereq: 18.433 or permission of instructor
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3.00 Credits
Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem.
Prerequisite:
Prereq: Calculus II (GIR)
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3.00 Credits
A broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics: hypothesis testing and estimation. Confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.
Prerequisite:
Prereq: 18.440 or 6.041
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3.00 Credits
Basics of stochastic processes. Markov chains, Poisson processes, random walks, birth and death processes, Brownian motion.
Prerequisite:
Prereq: 18.440 or 6.041
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3.00 Credits
Topics vary from term to term.
Prerequisite:
Prereq: Permission of instructor
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