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MATH M471: Numerical Analysis I
3.00 Credits
Indiana University-South Bend
P: MATH-M 301, MATH-M 311, CSCI-C 101, or consent of instructor. R: MATH-M 343. Numerical solutions of nonlinear equations; interpolation, including finite difference and splines; approximation, using various Hilbert spaces; numerical differentiation and integration; direct methods for linear systems; iterative techniques in matrix algebra. Knowledge of a programming language such as C, C++, or Fortran is a prerequisite of this course. I (odd years)
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MATH M471 - Numerical Analysis I
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MATH M472: Numerical Analysis II
3.00 Credits
Indiana University-South Bend
P: MATH-M 471 and MATH-M 343. Numerical solutions of nonlinear systems; solution of ordinary differential equations: initial-value problems, boundary-value problems; computation of eigenvalues and eigenvectors; introduction of numerical solutions for partial differential equations.
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MATH M472 - Numerical Analysis II
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MATH M491: Putnam Examination Seminar
1.00 Credits
Indiana University-South Bend
P: MATH-M 211 or MATH-M 215, or consent of instructor or department chair. The Putnam Examination is a national mathematics competition for college undergraduates at all levels of study. It is held in December each year. This problem seminar is designed to help students prepare for the examination. May be repeated twice for credit.
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MATH M491 - Putnam Examination Seminar
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MATH M546: Control Theory
3.00 Credits
Indiana University-South Bend
P: MATH-M 301, MATH-M 343. This course is an introduction to the analysis of feedback control systems. Topics may include: modeling of physical, biological, and information systems using linear and nonlinear differential equations; state=space description of systems; frequency and time domains; linear dynamic control systems; stability and performance of interconnected systems, including use of block diagrams, Bode plots, Nyquist criterion, and Lyapunov functions; optimal control, bang-bang control; discrete and digital control.
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MATH M546 - Control Theory
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MATH M551: Markets And Asset Pricing
3.00 Credits
Indiana University-South Bend
P: Two courses from the following: MATH-M 301, MATH-M 311, MATH-M 343, MATH-M 365, MATH-M 447. Interest theory; introduction to theory of options pricing; Black-Scholes theory of options; general topics in finance as the time value of money, rate of return of an investment, cash-flow sequence, utility functions and expected utility maximization, mean variance analysis, optimal portfolio selection, and the capital assets pricing model; topics in measurement of interest.
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MATH M551 - Markets And Asset Pricing
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MATH M560: Applied Stochastic Processes
3.00 Credits
Indiana University-South Bend
P: MATH-M 301, MATH-M 463 or MATH-M 365, or consent of instructor. Simple random walk as approximation of Brownian motion. Discrete-time Markov chains. Continuous-time Markov chains; Poisson, compound Poisson, and birth-and-death chains; Kolmogorov's backward and forward equations; steady state. Diffusions as limits of birth-anddeath processes. Examples drawn from diverse fields of application.
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MATH M560 - Applied Stochastic Processes
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MATH M562: Statistical Design of Experiments
3.00 Credits
Indiana University-South Bend
P: MATH-M 365, MATH-M 466, or consent of instructor. Latin square, incomplete blocks, and nested designs. Design and analysis of factorial experiments with crossing and nesting of factors, under fixed, random, and mixed effects models, in the balanced case. Blocking and fractionation of experiments with many factors at two levels. Exploration of response surfaces.
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MATH M562 - Statistical Design of Experiments
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MATH M565: Analysis Ofvariance
3.00 Credits
Indiana University-South Bend
P: MATH-M 466 and some matrix algebra. General linear hypothesis. Least squares estimation. Confidence regions. Multiple comparisons. Analysis of complete layouts. Effects of departures from underlying assumptions. Analysis of covariance.
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MATH M565 - Analysis Ofvariance
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MATH M569: Statistical Decision Theory
3.00 Credits
Indiana University-South Bend
Foundation of statistical analysis; Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; game theory and minimax rules; Bayesian design and sequential analysis. Comparison of statistical paradigms.
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MATH M569 - Statistical Decision Theory
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MATH M571: Analysis of Numerical Methods I
3.00 Credits
Indiana University-South Bend
P: CSCI-C 101, MATH-M 301, MATH-M 311, or consent of instructor. R: MATH-M 343. Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems; numerical methods for integral equations and ordinary differential equations; finite difference, finite element, and Galerkin methods for partial differential equations; stability of methods.
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MATH M571 - Analysis of Numerical Methods I
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