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Course Criteria
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3.00 Credits
Systems of linear equations, matrix algebra, vectors and vector spaces, linear transformations, inner product spaces, determinants, characteristic values and vectors. Prerequisites: MTH 145-146. (Offered each fall.)
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3.00 Credits
Linear differential operators and equations. Existence and uniqueness of solutions: initial-value problems. The Wronskian, homogeneous equations and non homogeneous equations: variation of parameters, the method of undetermined coefficients. The Euler equation, the Laplace transform, normal systems, eigen values and eigenvectors. Series solutions. Prerequisite: MTH 245. (Offered each spring.)
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3.00 Credits
Elementary properties of integers, divisibility and related concepts, methods of representing integers, functions of number theory, simple diophantine equations, special sequences and series. Prerequisite: three semesters of mathematics or permission of the department chair. (Offered every other fall.)
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3.00 Credits
Some classical puzzles of recreational mathematics; enumeration techniques; combinatorial designs; graph theory and network flows. Prerequisite: three semesters of mathematics or permission of the department chair.
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3.00 Credits
Basic probability theory, combinatorial analysis, independence and dependence. Discrete and continuous distributions, random variables, random vectors, multivariate distributions. Expectations and moment generating functions. Binomial, normal, Poisson and related distributions. Sums and sequences of random variables. Central Limit Theorem. Prerequisites: MTH 245 or permission of department. (Offered each fall.)
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3.00 Credits
Distributions related to the normal. Estimation: consistency, unbiasedness, mean square error, sufficiency, method of moments, maximum likelihood estimates, confidence limits and intervals. Bayesian intervals. Tests of hypotheses: tests of simple hypotheses, Neyman-Pearson lemma, Bayes procedures, composite hypotheses, generalized likelihood ratio tests. Non-parametric procedures. Simple linear regression. Prerequisite: MTH 311 . (Offered each spring.)
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3.00 Credits
Review of statistical methods. Simple and multiple linear regression. Regression diagnostics. Time series models. Moving average, autoregressive and ARIMA models. Forecasting with regression and time series models. Prerequisite: MTH 311 . (Offered every other spring.)
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4.00 Credits
An introduction to techniques of mathematical proof, with emphasis on the recognition and evaluation of problem structures common to all areas of mathematics. Application of these techniques to a detailed description of the Real Number system. Examination of the algebraic, set-theoretic and topological structures of the Real Number system (completeness, compactness, connectedness) and real sequences. Prerequisites: MTH 245, MTH 261. (Offered each spring.)
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3.00 Credits
Introduction to group theory. Cyclic, Abelian, symmetric and product groups. Subgroups, equivalence relations, homomorphisms. Prerequisite: MTH 261 or permission of the department chair. (Offered each fall.)
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3.00 Credits
The general linear programming problem. The simplex algorithm: theoretical and computational aspects. Duality and relationships to sensitivity analysis. Specialized algorithms. Extensions to some nonlinear programming problems. Prerequisite: MTH 261.
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