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Course Criteria
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4.00 Credits
4 hours, 4 credits. Inventory theory, queuing theory, linear programming, integer linear programming, nonlinear programming, the transportation problem, network analysis, and applications to industrial models. Software packages for linear programming. PREREQ: MAT 313 and CMP 230.
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4.00 Credits
4 hours, 4 credits. Methods for transforming information into cryptic messages and for deciphering secret code. Review of selected topics in elementary number theory. Construction of linear, quadratic, and exponential ciphers, as well as key exchange protocols. PREREQ: MAT 313.
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4.00 Credits
4 hours, 4 credits. Algebra and geometry of complex numbers, analytic functions, elementary functions, and conformal mapping. Cauchy integral theorem and applications. Taylor and Laurent series, calculus of residues, and classification of functions by singularities. Computer applications, including conformal mapping. PREREQ: MAT 320.
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4.00 Credits
4 hours, 4 credits. Study of the wave equation, heat equation, and Laplace's equation, with an emphasis on problems in one and two dimensions. Topics to include: harmonic functions and the Dirichlet problem, mixed boundary conditions, and Fourier series, Fourier transform and convolution. Computer-based projects. PREREQ: MAT 226.
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4.00 Credits
4 hours 4 credits. Metric spaces, Curves in Euclidian 3 space (E3): Curvature, torsion, fundamental theorem of ordinary differential equations, fundamental existence theorem for space curves. Surfaces in E3: geometry on a surface, Inverse Function Theorem, Implicit Function Theorem, and Gauss curvature. Coordinate charts, Fubini's Theorem, orientation and introduction to Riemannian Geometry, PREREQ: MAT 313 and MAT 320.
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4.00 Credits
4 hours 4 credits. Sets, functions, metric spaces, topological spaces, neighborhoods, Hausdorff spaces, discrete spaces, continuity, connectedness, path connectedness, compactness, homeomorphisms, homotopy, simply connected spaces, locally simply connected spaces, fundamental groups and universal covers. PREREQ: MAT 314 and MAT 320
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4.00 Credits
4 hours, 4 credits. Inverse and Implicit Function Theorems, Manifolds, Differential Forms, Fubini's Theorem, Partition of Unity, Integration on Chains, Stokes and Green's Theorems, and an introduction to Riemannian geometry. PREREQ: One course each in linear algebra and advanced calculus.
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4.00 Credits
4 hours, 4 credits. Axiomatic approach to the theory of sets. Relations, functions, the axiom of choice, ordinal numbers, well-ordering, Zorn's lemma, cardinal numbers and transfinite arithmetic, and transfinite induction. PREREQ: Any two courses chosen from linear algebra, modern algebra, or advanced calculus.
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4.00 Credits
4 hours, 4 credits. Propositional logic, logic with quantifiers, and with equality. Proof techniques such as Hilbert systems, tableaus, and others. Models, and the extent to which the notion of model embodies and generalizes the various structures studied by mathematicians. G?del's Completeness Theorem, and consequences such as Compactness and L?wenheim-Skolem Theorems. The incompleteness results of Tarski, G?del, and others. PREREQ: MAT 314.
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3.00 Credits
3 hours, 3 credits. Selected topics from algebra and number theory. Students will be expected to make oral presentations and work with periodical literature. PREREQ: MAT 314.
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