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Course Criteria
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3.00 Credits
S. A study of Euclidean and hyperbolic geometries from an axiomatic viewpoint. Additional topics include transformations, and the construction of models for geometries. Prerequisite: Mathematics 256 or permission of the instructor.
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4.00 Credits
F, odd years. An introduction to the study of manifolds, including both the geometric topology and the differential geometry of manifolds. The emphasis is on lowdimensional manifolds, especially curves and surfaces. Topics include the topology of subsets of Euclidean space, curves and surfaces in Euclidean space, the topological classification of compact connected surfaces, smooth curves and surfaces, curvature, geodesics, the Gauss-Bonnet Theorem and the geometry of space. Prerequisites: Vector Calculus (Mathematics 232 or 261) and Linear Algebra (Mathematics 231, 232, 256 or 355) Not offered 2008-2009.
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4.00 Credits
F, even years. An introduction to first-order logic, computability and computational complexity. Topics covered include soundness and completeness of a formal proof system, computability and non-computability, and computational complexity with an emphasis on NP-completeness. Also listed as Computer Science 312. Prerequisite: Mathematics 256.
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2.00 Credits
S. This course introduces prospective teachers to important curricular and pedagogical issues related to teaching secondary school mathematics. These issues are addressed in the context of mathematical topics selected from the secondary school curriculum. The course should be taken during the spring preceding student teaching. Prerequisite: A 300-level course in Mathematics.
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4.00 Credits
F. An Introduction to partial differential equations and their applications. Topics Include mathematical modeling with partial differential equations, nondimensionalization, orthogonal expansions, solution methods for linear Initial and boundary-value problems, asymptotic expansions, and numerical solution of partial differential equations. Prerequisites: Mathematics 231 and either 261 or 232.
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4.00 Credits
S, odd years. Theory and practice of computational procedures Including principles of error analysis and scientific computation, root-finding, polynomial Interpolation, splines, numerical Integration, applications to ordinary differential equations, computational matrix algebra, orthogonal polynomials, least square approximations, and other applications. Also listed as Computer Science 372. Prerequisites: Computer Science 104 or 108 and Mathematics 256 or 232.
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4.00 Credits
F. Probability, probability density functions; binomial, Poisson, and normal distributions; central limit theorem, limiting distributions, sample statistics, hypothesis tests, and estimators. Prerequisite: Mathematics 231, 232, 256, or 261.
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4.00 Credits
S. A continuation of Mathematics 343 including theory of estimation, hypothesis testing, nonparametric methods, regression analysis, and analysis of variance. Prerequisite: Mathematics 343.
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4.00 Credits
S. An Introduction to abstract algebraic systems, including groups, rings, and fields, and their applications. Prerequisite: Mathematics 361.
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4.00 Credits
S, odd years. Vector spaces, linear transformations, eigenvalues and eigenvectors, inner product spaces, spectral theory, singular values and pseudoinverses, canonical forms, and applications. Prerequisite: Mathematics 256, or Mathematics 232, or both Mathematics 231 and 261.
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