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Course Criteria
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3.00 Credits
(Prerequisite, MA 421 or consent of department.) Projective geometry of one and two dimensions, its axiomatic foundation, and the fundamental ideas of the projective plane. Duality, harmonic forms, coordinates, conics, polarities, and a brief introduction to geometry of higher dimensions.
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3.00 Credits
(Prerequisite, MA 421 or consent of department.) A comparison of non Euclidean geometries with Euclidean geometry. Hilbert's axioms, history of the parallel postulate, elementary theorems of hyperbolic plane geometry and a brief introduction to elliptic geometry.
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3.00 Credits
(Prerequisites, MA 322 and MA 425 or consent of the mathematics department.) The properties of groups, rings and fields with emphasis on the algebraic structure and morphisms. Algebraic and transcendental field extensions.
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3.00 Credits
(Prerequisite, MA 322 and MA 425 or consent of department.) The structure of vector spaces, algebras and fields. Transformations, linear independence, bases and other topics are studied.
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3.00 Credits
This course provides an overview of a wide array of concepts and methods of statistical analysis, and how these methods can be implemented using SAS to perform data analysis. Concepts typically covered are graphical summaries of data, populations and samples, measures of central tendency, measures of dispersion and variability, probability, the normal distribution, an introduction to hypothesis testing, assessing normality, simple t-tests, two-sample hypotheses, analysis of variance and multiple comparisons, and modern regression analysis. Programming assignments in SAS are an important component of the course. The course should be of interest to mathematics majors and to graduate students in other disciplines with an interest in statistical analysis of data. It is recommended that students who enroll in this course have already taken at least one course in statistics.
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3.00 Credits
(Prerequisite, MA 532.) Probability, distributions, expected values, moments, sampling distribution and point estimation. Multivariate normal distribution, maximum likelihood estimation, interval estimation, test of hypotheses, linear regression, experimental design and analysis of variance.
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3.00 Credits
(Prerequisite, MA 263.) A study of the complex plane, holomorphic functions, the elementary functions, complex integration. Taylor¿s series and the Laurent expansion, the calculus of residues and conformal mapping.
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3.00 Credits
(Prerequisite, MA 262 and MA 425 or permission of instructor.) This course rigorously proves the results of Calculus I and II. Topics include an axiomatic characterization of the real numbers, sequences, functions, limits, continuity, differentiation, Riemann integration, and infinite series.
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3.00 Credits
(Prerequisite, MA 735.) As a continuation of Advanced Calculus I, this course provides a rigorous treatment of multi-variable calculus. Topics include topology, convergence, differentiability, and integration on Rn.
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3.00 Credits
(Prerequisite, MA 425 or consent of department.) Properties of numbers, prime and composite, Euclid's algorithm, indeterminate problems. Diophantine problems, congruences and residues, Buler's Theorem, Fermat's Theorem, classical problems.
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