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Course Criteria
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3.00 Credits
Prerequisites: MTH 312 Analysis of curves and surfaces. Frenet-Serret formulae. Fist and second fundamental forms for surfaces, Gaussian and mean curvature, theorems of Meusnier and Rodriques and the Gauss-Bonnet theorem are also studied.
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3.00 Credits
Prerequisites: MTH 211 or MTH 213 A survey of the history of geometry, emphasizing the scholars of antiquity. Topics from modern (college) geometry, projective and non-Euclidean geometries.
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3.00 Credits
Prerequisites: MTH 312 An introduction to point-set and combinatorial topology.
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3.00 Credits
Selected topics from the areas of linear programming, dynamic programming, Markov chains and game theory. Mathematical model building will be developed through the use of numerous case studies from the natural and social sciences, e.g., ecological models, network models, scheduling models, urban structure, traffic flow, growth, etc.
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3.00 Credits
Deterministic and nondeterministic simulation.& Random number generators, Monte Carlo techniques, discrete simulation techniques and simulation computer languages (e.g. GPSS, SIMSCRIPT) are studied.& Standard Simulations Models, such as the national economy model, inventory control, banking, blackjack, etc., will also be covered.
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3.00 Credits
Prerequisites: MTH 212 Introduction to partial differential equations. Topics include: the classification of partial differential equations, the heat equation, the potential equation, separation of variables, Fourier series, the wave equation, and Sturm-Liouville eigenvalue problems.
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3.00 Credits
Prerequisites: MTH 362, 471; or permission of instructor Numerical methods for solving parabolic, hyperbolic, and elliptic partial differential equations. The course will emphasize the concepts of consistency, convergence and stability. Topics include: implicit and explicit methods, truncation error, Von Newmann stability analysis, and the Lax equivalence theorem.
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3.00 Credits
Prerequisites: MTH 353, 361; or permission of instructor An introduction to numerical linear algebra. Numerical linear algebra is fundamental to all areas of computational mathematics. This course will cover direct numerical methods for solving linear systems and linear least squares problems, stability and conditioning, computational methods for finding eigenvalues and eigenvectors, and iterative methods for both linear systems and eigenvalue problems.
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3.00 Credits
Prerequisites: MTH 353, 361; or permission of instructor An introduction to constrained and unconstrained optimization. Numerical optimization is an essential tool in a wide variety of applications. The course covers fundamental topics in unconstrained optimization and also methods for solving linear and nonlinear constrained optimization problems.
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3.00 Credits
Prerequisites: MTH 212 Course is conducted as a seminar. An elementary question is posed to the students who must generate their own mathematics in an attempt to find a solution. The aim is to develop student independence and creativity.
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