MATH 407 Linear Optimization (3) NW Maximization and minimization of linear functions subject to constraints consisting of linear equations and inequalities; linear programming and mathematical modeling. Simplex method, elementary games and duality. Prerequisite: either 2.0 in MATH 136, 2.0 in MATH 308, 2.0 in MATH 318, or 2.0 in AMATH 352. Offered: AWS. MATH 408 Nonlinear Optimization (3) NW Maximization and minimization of nonlinear functions, constrained and unconstrained; nonlinear programming problems and methods. Lagrange multipliers; Kuhn-Tucker conditions, convexity. Quadratic programming. Prerequisite: either 2.0 in MATH 308 or 2.0 in MATH 318; either 2.0 in MATH 327 or 2.0 in MATH 334. Offered: W. MATH 409 Discrete Optimization (3) NW Maximization and minimization problems in graphs and networks (shortest paths, minimum spanning trees, maximum flows, minimum cost flows); transportation and trans-shipment problems, NP-completeness. Prerequisite: 2.0 in MATH 407. Offered: Sp. MATH 509 Theory of Optimal Control (3) Trajectories from ordinary differential equations with control variables. Controllability, optimality, maximum principle. Relaxation and existence of solutions. Techniques of nonsmooth analysis. Prerequisite: real analysis on the level of MATH 426; background in optimization corresponding to MATH 515. Offered: jointly with AMATH 509; even years. MATH 514 Networks and Combinatorial Optimization (3) Networks and directed graphs. Paths and trees. Feasible and optimal flows and potentials. Transportation problems, matching and assignment problems. Algorithms and applications. Prerequisite: MATH 308 or AMATH 352 and MATH 324. Offered: jointly with AMATH 514. MATH 515 Fundamentals of Optimization (5) Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Prerequisite: linear algebra and advanced calculus. Offered: jointly with IND E 515/AMATH 515. MATH 516 Numerical Optimization (3) Methods of solving optimization problems in finitely many variables, with or without constraints. Steepest descent, quasi-Newton methods. Quadratic programming and complementarity. Exact penalty methods, multiplier methods. Sequential quadratic programming. Cutting planes and nonsmooth optimization. Prerequisite: MATH 515. Offered: jointly with AMATH 516. MATH 517 Optimization Under Uncertainty (3) Sequential optimization problems involving random variables. Dynamic programming, stochastic programming. Control of uncertain dynamic systems in finite, discrete time. Risk, feedback, adaptivity. Problems with imperfect state information. Applications such as to optimal stopping, inventory control, resource management. Prerequisite: MATH 308, MATH 324 and an introduction to basic concepts of probability, such as MATH 390 or MATH 394, MATH 395. Offered: jointly with AMATH 517. CSE 521 Design and Analysis of Algorithms I (3) Principles of design of efficient algorithms: recursion, divide and conquer, balancing, dynamic programming, greedy method, network flow, linear programming. Correctness and analysis of algorithms. NP-completeness. Prerequisite: CSE major and CSE 326 or equivalent. CSE majors only. CSE 522 Design and Analysis of Algorithms II (3) Analysis of algorithms more sophisticated than those treated in 521. Content varies and may include such topics as algebraic algorithms, combinational algorithms, techniques for proving lower bounds on complexity, and algorithms for special computing devices such as networks or formulas. Prerequisite: CSE major and CSE 521. CSE 523 Computational Geometry (3) Algorithms for discrete computational geometry. Geometric computation, range searching, convex hulls, proximity, Vornoi diagrams, intersection. Application areas include VLSI design and computer graphics. Prerequisite: CSE major and CSE 521; recommended: CSE 457 or equivalent. CSE 524 Parallel Algorithms (3) Design and analysis of parallel algorithms: fundamental parallel algorithms for sorting, arithmetic, matrix and graph problems and additional selected topics. Emphasis on general techniques and approaches used for developing fast and efficient parallel algorithms and on limitations to their efficacy. Prerequisite: CSE major and CSE 521. CSE 525 Randomized Algorithms and Probabilistic Analysis (3) Beane, Guruswami, Karlin, Lee Examines algorithmic techniques: random selection, random sampling, backwards analysis, algebraic methods, Monte Carlo methods, and randomized rounding; random graphs; the probabilistic method; Markov chains and random walks; and analysis tools: random variables, moments and deviations, Chernoff bounds, martingales, and balls in bins. Prerequisite: CSE 521 or equivalent; CSE majors only. Offered: WSp. CSE 527 Computational Biology (3) Introduces computational methods for understanding biological systems at the molecular level. Problem areas such as mapping and sequencing, sequence analysis, structure prediction, phylogenic inference, regulatory analysis. Techniques such as dynamic programming, Markov models, expectation-maximization, local search. Prerequisite: graduate standing in biological, computer, mathematical or statistical science, or permission of instructor