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Course Criteria
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3.00 Credits
3 hours; 3 credits This course presents a rigorous treatment of the limit, continuity, differentiability, and differential of a function of one variable. Other topics include real numbers and the axiom of continuity; convergence of a sequence of real numbers; elements of point set topology; and extensions and generalizations of the law of the mean. Prerequisite: MTH 3020 or 3030.
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3.00 Credits
3 hours; 3 credits This course presents rigorous treatment of the limit, continuity, differentiability, and differential of a function of two or more variables. Other topics include integration; multiple, improper, line, and surface integrals; and implicit function theorems. Prerequisite: MTH 4010.
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3.00 Credits
3 hours; 3 credits Topics to be included are Gauss-Jordan reduction, linear independence, linear vector spaces, linear transformations, similarity of matrices, diagonalizable matrices, characteristic values and vectors, and symmetric matrices and quadratic forms. Prerequisite: MTH 3020 or 3030. (MTH 3006 or 3010 are acceptable with departmental permission.)
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3.00 Credits
3 hours; 3 credits Topics to be included are existence and uniqueness of solutions, first-order equations, linear equations, series solutions of second-order linear equations, Laplace transforms, linear systems, boundary value problems, and numerical methods. Prerequisite: MTH 3020 or 3030.
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4.00 Credits
4 hours; 4 credits This course is an introduction to the theory of probability. Topics to be included are basic theorems of probability, permutations and combinations, binomial and multinomial theorems, random variables with densities, sequences of independent identically distributed random variables, method of moments, the moment-generating function, Markov chains, expectation, conditional expectation, central limit theorem, and standard-type probability distributions. (Not open to students who have completed MTH 3120.) Prerequisite: MTH 3020 or 3030 or departmental permission.
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4.00 Credits
4 hours; 4 credits This course is designed to introduce the undergraduate to the fundamental ideas of stochastic (or random) processes. Such processes are used in the study of mathematical models where there are elements of uncertainty and hence probabilistic quantities are introduced into the model. These models are found in fields such as the analysis of algorithms, the theory of queues, the pricing of stock options, financial mathematics, econometrics, linear programming, and biomathematics. The course will cover the topics of Markov chains (discrete and continuous time), renewal theory, queueing theory, Brownian motion, and stationary processes. Applications of the various topics will also be discussed. Prerequisite: MTH 4120 or departmental permission.
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4.00 Credits
4 hours; 4 credits This course is an introduction to the inferential aspects of mathematical statistics. Topics to be included are Bayes estimators, maximum likelihood estimators, sufficient statistics, sampling distributions of estimators such as the Chi-square distribution and the t-distribution, confidence intervals, unbiased estimators, testing hypotheses, Neyman-Pearson lemma, the t-test, the F-distribution, and introduction to linear models. Prerequisite: MTH 4120.
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4.00 Credits
4 hours; 3 credits This course will introduce the student to the basic tech - niques of simulating randomized systems via computer. Topics include generating discrete and continuous random variables, simulating general Markov chains, variance reduction techniques, and statistical analysis of simulation output. Applications will be drawn from finance, actuarial science, natural sciences, and queuing theory. Prerequisites: MTH 3300 and 4120, or departmental permission.
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3.00 Credits
3 hours; 3 credits This course covers basic topics in graph theory, including connectivity, Eulerian graphs, planarity, genus, Hamiltonicity, isomorphism, chromatic number, Ramsey numbers, and enumeration. These are followed by an introduction to networks with graph algorithms, including algorithms for a maximum matching in a graph and algorithms for maximum flow in a network. Prerequisite: MTH 3006 or 3010.
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3.00 Credits
3 hours; 3 credits Students will define and offer solutions to real-world problems and give both a written and oral presentation of their solutions. Examples of problems to be studied are scheduling, portfolio investment, and reliability of machinery. Some of the following mathematical techniques will be used in the formation of the solution to the problems: these include but are not limited to stochastic processes, linear algebra, differential equations, dynamical systems, and probability theory. The entire class will be expected to offer written critiques of the work presented by each of the students. Students may take this class either as part of a proposed major in operations research or as part of their major in mathematics. Prerequisites: MTH 4100, MTH 4110, and knowledge of a programming language, or departmental permission. Corequisite: MTH 4120.
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