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MATH M420: Metric Space Topology
3.00 Credits
Indiana University-South Bend
P: MATH-M 347. Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology.
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MATH M435: Introduction to Differentialgeometry
3.00 Credits
Indiana University-South Bend
P: MATH-M 301 and MATH-M 311. An introduction to the geometry of curves and surfaces. Topics include arc length, torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas.
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MATH M435 - Introduction to Differentialgeometry
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MATH M436: Introduction to Geometries
3.00 Credits
Indiana University-South Bend
P: MATH-M 347. R: MATH-M 403. Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes. Perspectives, coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations.
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MATH M447: Mathematical Models And Applications I
3.00 Credits
Indiana University-South Bend
P: MATH-M 301. Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth. Suitable for secondary school teachers. I (even years)
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MATH M448: Mathematical Models And Applications II
3.00 Credits
Indiana University-South Bend
P: MATH-M 447. Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth. Suitable for secondary school teachers.
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MATH M451: The Mathematics of Finance And Interesttheory
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, MATH-M 463. 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. II (odd years)
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MATH M463: Introduction to Probabilitytheory
3.00 Credits
Indiana University-South Bend
C: MATH-M 311. The meaning of probability. Random experiment, probability models, combinatoric techniques, conditional probability, independence. Random variables, distributions, densities, expectation, moments, transformation of random variables. Important discrete and continuous distributions. Multivariate distributions, correlations. Moment generating functions, laws of large numbers, central limit theorem, normal approximation. I (odd years)
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MATH M463 - Introduction to Probabilitytheory
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MATH M466: Introduction to Mathematical Statistics
3.00 Credits
Indiana University-South Bend
P: MATH-M 463. Theory of sampling distribution, Chebyshev's inequality, convergence in probability. Estimation theory, maximum likelihood estimators, method of moments, goodness of point estimators, confidence intervals. Hypothesis testing, power function, error types, likelihood ratio tests. Non-parametric methods. Regression. Analysis of variance. Sufficient statistics. Bayesian estimation, asymptotic distribution of maximum likelihood estimators. II (even years)
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MATH M466 - Introduction to Mathematical Statistics
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MATH M467: Advanced Statistical Techniques I
3.00 Credits
Indiana University-South Bend
P: MATH-M 466 or consent of instructor. Statistical techniques of wide application, developed from the least-squares approach: fitting of lines and curves to data, multiple regression, analysis of variance of one- and two-way layouts under various models, multiple comparison.
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MATH M468: Advanced Statistical Techniques II
3.00 Credits
Indiana University-South Bend
P: MATH-M 466 or consent of instructor. Analysis of discrete data, chi-square tests of goodness of fit and contingency tables, Behrens-Fisher problem, comparison of variances, nonparametric methods, and some of the following topics: introduction to multivariate analysis, discriminant analysis, principal components.
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MATH M468 - Advanced Statistical Techniques II
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