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Course Criteria
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3.00 Credits
This is an introductory course in stochastic processes. Its purpose is to introduce students to a range of stochastic processes which are used as modeling tools in diverse fields of applications, especially in the business applications. The course introduces the most fundamental ideas in the area of modeling and analysis of real World phenomena in terms of stochastic processes. The course covers different classes of Markov processes: discrete and continuous-time Markov chains, Brownian motion and diffusion processes. It also presents some aspects of stochastic calculus with emphasis on the application to financial modeling and financial engineering. Credit will not be granted for MATH 481 and 542. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Principles of estimation; hypothesis-tests, confidence intervals. Contingency tables; goodness-of-fit. Analysis of variance; linear regression. Hierarchical and split-plot designs; analysis of covariance. Multiple regression. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This is an introductory course in mathematical finance. Technical difficulty of the subject is kept at a minimum by considering a discrete time framework.Nevertheless, the major ideas and concepts underlying modern mathematical finance and financial engineering will be explained and illustrated. Credit may not be granted for MATH 485 and MATH 548. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
A general introduction to optimization problems. Linear programming: the simplex method. Elements of graphs and networks. Introduction to game theory. Applications. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department Course Attributes: Communications Requirement
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3.00 Credits
The formulation of mathematical models, solution of mathematical equations, interpretation of results. Selected topics from queuing theory and financial derivatives. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department Course Attributes: Communications Requirement
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3.00 Credits
Boundary-value problems and Sturm-Liouville theory; linear system theory via eigenvalues and eigenvectors; Floquet theory; nonlinear systems: critical points, linearization, stability concepts, index theory, phase portrait analysis, limit cycles, and stable and unstable manifolds; bifurcation; and chaotic dynamics. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
First-order equations, characteristics. Classification of second-order equations. Laplace's equation; potential theory. Green's function, maximum principles. The wave equation: characteristics, general solution. The heat equation: use of integral transforms. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Independent reading and research. (Credit: Variable) Prerequisite: Instructor permission required. 1. 000 TO 6.000 Credit Hours 1. 000 TO 6.000 Other hours Levels: Undergraduate Schedule Types: Independent Study/Research College of Science & Letters College Applied Mathematics Department Course Attributes: Communications Requirement
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3.00 Credits
Prerequisite: Instructor permission required. 1. 000 TO 20.000 Credit Hours 1. 000 TO 20.000 Other hours Levels: Undergraduate Schedule Types: Independent Study/Research College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Metric and Normed Spaces; Continuous Functions; Contraction Mapping Theorem; Topological Spaces; Banach Spaces; Hilbert Spaces; eigenfunction expansion. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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