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Course Criteria
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3.00 Credits
This is the second of a two course sequence designed to provide students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics covered include integration of functions of one variable, pointwise and uniform convergence, integration and differentiation of series, differentiable mappings of several variables, chain rule, product rule and gradients, Mean Value Theorem, Taylor's Theorem, Inverse Function Theorem, Implicit Function Theorem.
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3.00 Credits
Formulation, development, testing and reporting of mathematical models of various real world problems. Deterministic and stochastic models, optimization, simulation. Emphasis on the careful mathematical formulations and the appropriate use of computer software, both as an aid in the solution of mathematical problems and as a tool in the process of model evaluation, simulation, reporting. A term project will be an important component of this course. The course is taught in a laboratory setting with computers as lab equipment.
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3.00 Credits
An introduction to the mathematical theory of counting. Basic counting principles, permutations and combinations, partitions, recurrence relations, and a selection of more advanced topics such as generating functions, combinatorial designs, Ramsey theory, or group actions and Poyla theory.
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3.00 Credits
Historical survey of the general development of mathematics with a balance of historical perspective and mathematical structure.
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3.00 Credits
An introduction to group theory and ring theory. Topics include permutations and symmetries, subgroups, quotient groups, homomorphisms, as well as examples of rings, integral domains, and fields.
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3.00 Credits
A continuation of MA 413 focusing on rings and fields. Topics include rings, ideals, integral domains, fields and extension fields. Geometric constructions and Galois theory are introduced.
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3.00 Credits
An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification and quotient spaces. Credit for both MA 434 and MA 542 is not allowed.
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3.00 Credits
Selected numerical algorithms are analyzed. Topics include error analysis, machine arithmetic, roundoff, root finding using fixed point methods, interpolation, numerical integration, differential equations, eigenvalue/eigenvector problems, least squares analysis, boundary value problems.
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3.00 Credits
Arithmetic of complex numbers; regions in the complex plane, limits, continuity and derivatives of complex functions; elementary complex functions; mapping by elementary functions; contour integration, power series, Taylor series, Laurent series, calculus or residues; conformal representation; applications. Credit for both MA 437 and MA 537 not allowed.
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3.00 Credits
A comprehensive introduction to probability, the mathematical theory used to model uncertainty, covering the axioms of probability, random variables, expectation, classical discrete and continuous families of probability models, the law of large numbers and the central limit theorem. Credit for both MA 451 and MA 550 is not allowed.
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