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Course Criteria
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4.00 Credits
Introduction to combinatorics. Topics include techniques of enumeration, fundamental concepts of graph theory, applications to transport networks, matching theory and block design. Offered every fall. Prerequisites: MTH 275 with a grade of 2.0 or higher (or MTH 256 with a grade of 2.0 or higher) and APM 263 with a grade of 2.0 or higher.
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4.00 Credits
The mathematics and algorithms for symbolic computation. Includes theory of algebraic extensions, modular and p-adic methods, Groebner bases, factorization and zeros of polynomials, solutions to systems of polynomial equations, applications to automatic geometric theorem proving and closed form solutions to differential equations. Prerequisites: MTH 275 with a grdeof 2.0 or higher (MTH 256 with a grade of 2.0 or higher) and knowledge of a scientific comuter programming language, or permission of instructor.
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2.00 - 4.00 Credits
Reading or research on some topic in applied mathematics. May be repeated for additional credit. Prerequisite: permission of department.
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4.00 Credits
Approximations and interpolations, propagation of errors, numerical differentiation and integration, solutions of equations, Newton's method, solutions of differential equations and initial value problems, Runge-Kutta and predictor-corrector methods. Credit will not be granted for both APM 533 and CSE 517. Required background includes courses in linear algebra and differential equations.
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4.00 Credits
Laplace transforms; linear algebra; matrices, vectors, determinants, linear systems of equations, matrix eigenvalue problems; vector differential calculus; vector integral calculus, integral theorems; Fourier series, integrals and transforms. Required background includes courses in multivariable calculus, linear algebra and differential equations.
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4.00 Credits
Elementary graph theory (trees, cycles, planar graphs and flows) and elementary enumeration (generating function, 0-1 strings, planted plane trees, cycle decomposition and Lagrange's inversion formula). Required background includes courses in linear algebra and discrete methods.
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4.00 Credits
A study of the mathematics and algorithms which are used in symbolic algebraic manipulation packages. Topics include computer representation of symbolic mathematics, polynomial ring theory, field theory and algebraic extensions, modular and p-adic methods, subresultant algorithm for polynomial GCD's, Groebner bases for polynomial ideals and Buchberger's algorithm, factorization and zeros of polynomials. Required background includes a course in abstract algebra and knowledge of a scientific programming language.
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2.00 - 4.00 Credits
Reading and independent research activities under faculty supervision. Student must have permission of the graduate coordinator.
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4.00 Credits
Mathematical modeling, using P.D.E., for industrial problems. Topics will vary, depending on instructor and industry contacts, but some possibilities are: contact and friction problems, electropainting and electrochemistry, solid-liquid transitions and Stefan problems, wave phenomena, fluid flows, granular materials, heat conduction and diffusion. Required background includes courses in PDEs and Functional Analysis.
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1.00 Credits
Applied problems and solutions using advanced mathematical methods presented by students and faculty. Each Ph.D. student is required to earn at least three credits. Student must have permission of the graduate coordinator.
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