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Course Criteria
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3.00 Credits
Ring homomorphisms; factorization and reducibility in polynomial rings; integral domains; vector spaces; fields and their extensions. As time permits, application to one or more of the following: Frieze and crystallographic groups, Caley digraphs, and coding theory. 3. 000 Credit Hours 3. 000 Lecture hours 0. 000 Lab hours Levels: Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Introduction to both theoretical and algorithmic aspects of linear optimization: geometry of linear programs, simplex method, anticycling, duality theory and dual simplex method, sensitivity analysis, large scale optimization via Dantzig-Wolfe decomposition and Benders decomposition, interior point methods, network flow problems, integer programming. Credit may not be granted for both MATH 435 and MATH 535. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Permutations and combinations; pigeonhole principle; inclusion-exclusion principle; recurrence relations and generating functions; enumeration under group action. 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
Graph theory is the study of systems of points with some of the pairs of points joined by lines. Sample topics include: paths, cycles and trees; adjacency and connectivity; directed graphs; Hamiltonian and Eulerian graphs and digraphs; intersection graphs. Applications to the sciences (computer, life, physical, social) and engineering will be introduced throughout the course. Credit will not be granted for both MATH 454 and MATH 553 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
Fourier series and integrals. The Laplace, heat, and wave equations: Solutions by separation of variables. D'Alembert's solution of the wave equation. Boundary-value problems. 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
Elementary probability theory including discrete and continuous distributions, sampling, estimation, confidence intervals, hypothesis testing, and linear regression. Credit not granted for both MATH 474 and MATH 475. 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
Elementary probability theory; combinatorics; random variables; discrete and continuous distributions; joint distributions and moments; transformations and convolution; basic theorems; simulation. Credit not granted for both MATH 474 and MATH 475. 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
Estimation theory; hypothesis tests; confidence intervals; goodness-of-fit tests; correlation and linear regression; analysis of variance; nonparametric methods. 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
Fundamentals of matrix theory; least squares problems; computer arithmetic; conditioning and stability; direct and iterative methods for linear systems; eigenvalue problems. Credit may not be granted for both MATH 477 and MATH 473. 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
Polynomial interpolation; numerical integration; numerical solution of initial value problems for ordinary differential equations by single and multi-step methods, Runge-Kutta, Predictor-Corrector; numerical solution of boundary value problems for ordinary differential equations by shooting method, finite differences and spectral methods. Credit may not be granted for both MATH 478 and MATH 472. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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