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Course Criteria
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4.00 Credits
Vector spaces and dimension, linear transformations, dual spaces, adjoints of transformations, multilinear forms, eigenvectors, the CayleyHamilton theorem, inner product spaces, orthogonality, similarity transformations, the spectral theorem, Jordan form. 4 lecture/problemsolving. Prerequisite: C or better in MAT 208 or consent of instructor.
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4.00 Credits
The Frenet formulas, covariant derivatives, frame fields, the structure equations, differential forms on a surface, normal curvature, Gaussian curvatures; intrinsic geometry of surfaces in E3, the Gauss and Bonnet theorem. 4 lecture/problemsolving. Prerequisite: C or better in MAT 314 and MAT 216 or consent of instructor.
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4.00 Credits
Algebra and geometry of complex numbers; analyticity, mappings of elementary functions; Cauchy integral formula, Taylor and Laurent series, the residue theorem; conformal mapping with applications. 4 lectures/problemsolving. Prerequisite: C or better in MAT 314 or consent of instructor.
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4.00 Credits
Check with Department. Continuation of Topics in MAT 428. 4 lecture/problemsolving. Prerequisite: C or better in MAT 428 or consent of instructor.
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4.00 Credits
Partial differential equations with applications to wave actions, heat transfer and fluid flow. Ordinary differential equations; linear with variable coefficients, linear systems; stability and qualitative behavior of solutions. 4 lecture/problemsolving. Prerequisite: C or better in MAT 216 and 208 or consent of instructor.
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4.00 Credits
An integrated course in the algebra and calculus of vectors and tensors; topics in differential geometry; applications to mechanics of deformable media, hydrodynamics, general relativity. 4 lecture/problemsolving. Prerequisite: C or better in MAT 208 and 216 or consent of instructor. PHY 321 is recommended.
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4.00 Credits
Introduction to axiom systems including consistency, independence, satisfiability and completeness; transfinite arithmetic; the continuum hypothesis; wellordering and its equivalents. 4 lecture/problemsolving. Prerequisite: C or better in MAT 310 or consent of the instructor.
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2.00 Credits
Selection and completion of a project under faculty supervision. Projects typical of problems which graduates must solve in their fields of employment. Project results are presented in a formal report. Minimum of 120 hours total time.
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2.00 Credits
Discussions through seminar methods of new developments in the fields of student's particular interests. 2 lecture/discussion. Prerequisite: senior standing in mathematics.
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4.00 Credits
Study of enumeration techniques, permutations, combinations, principle of inclusion and exclusion, finite fields, combinatorial designs, errorcorrecting codes. 4 lecture/problemsolving. Prerequisite: C or better in Mat 208 or consent of instructor.
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