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Course Criteria
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4.00 Credits
Plane and space curves, Frenet-Serret formula surfaces. Local differential geometry, Gauss-Bonnet formula, introduction to manifolds. Prereq: MATH 281, 341.
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4.00 Credits
Theory of vector spaces over arbitrary fields, theory of a single linear transformation, minimal polynomials, Jordan and rational canonical forms, quadratic forms, quotient spaces. Prereq: MATH 342.
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3.00 Credits
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory. Prereq: MATH 342.
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4.00 Credits
Fundamentals of modern combinatorics; graph theory; networks; trees; enumeration, generating functions, recursion, inclusion and exclusion; ordered sets, lattices, Boolean algebras. Prereq: MATH 231 or 346.
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4.00 Credits
Linear and nonlinear first-order dynamical systems; equilibrium, cobwebs, Newton's method. Bifurcation and chaos. Introduction to higher-order systems. Applications to economics, genetics, ecology. Prereq: MATH 256.
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4.00 Credits
Discrete and continuous probability models; useful distributions; applications of moment-generating functions; sample theory with applications to tests of hypotheses, point and confidence interval estimates. Prereq: MATH 252.
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4.00 Credits
Multinomial distribution and chi-square tests of fit, simple and multiple linear regression, analysis of variance and covariance, methods of model selection and evaluation, use of statistical software. Prereq: MATH 462/562.
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3.00 Credits
Random variables; generating functions and characteristic functions; weak law of large numbers and central limit theorem; point and interval estimation; Neyman-Pearson theory and likelihood tests; sufficiency and exponential families; linear regression and analysis of variance. Pre- or coreq: MATH 282, 342.
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1.00 - 3.00 Credits
{VOID}
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1.00 - 3.00 Credits
{VOID}
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