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Course Criteria
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3.00 Credits
3 SI Factorization of matrices, eigenvalues and eigenvectors, orthogonality. Applications of matrices to such topics as least-squares approximation, fast Fourier transform, difference and differential equations, linear programming, networks, game theory. Prereq: MAT 331 or MAT 485
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3.00 Credits
3 Y Theory of groups, rings, and fields, including the integers and polynomail rings. Prereq: MAT 531
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3.00 Credits
3 IR Prime numbers, greatest common divisors, congruences. Euler's function, Fermat's theorem, primitive roots, indices, quadratic residues, Legendre and Jacobi symbols, and the quadratic reciprocity law.Prereq: MAT 275 or CIS 275, and MAT 331 or permission of instructor
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3.00 Credits
3 Y Permutations, combinations, recurrence relations, generating functions, inclusion-exclusion and applications, introductory graph theory. Prereq: MAT 275 or CIS 275.
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3.00 Credits
3 IR Synthetic projective geometries. Coordinate systems for projective spaces. Algebraic representation of projective transformations; euclidean, non-euclidean, and affine geometries as real cases of projective geometry. Prereq: MAT 275 or CIS 275 and MAT 331
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3.00 Credits
3 IR Theory of curves in three-dimensional space, including Frenet's formula, Gaussian and mean curvature, geodesics, developable surfaces, special conformal mappings. Prereq: MAT 412 or 511 or permission of instructor
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3.00 Credits
3 IR Metrics and metric spaces, topologies and topological spaces, separation properties, compactness, connectedness, and continuity. Prereq: MAT 275 or CIS 275 and MAT 512
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3.00 Credits
3 Y Approximation methods for solution of nonlinear equations. Interpolation problems. Numerical integration. Solution of ordinary differential equations. Error analysis and writing computer programs. Primarily for mathematics and engineering students. Prereq: 12 credits of calculus and knowledge of a scientific programming language
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3.00 Credits
3 IR Mathematical concepts in their historical perspective. Character and contributions of t he great mathematicians and relation of mathematics to other sciences. Prereq: 12 credits of calculus and at least two 500-level mathematics courses
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3.00 Credits
3 Topic Chosen by the instructor. Permission of department.
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