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Course Criteria
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3.00 Credits
Continuation of MATH 420. Homomorphisms and factor groups; introduction to commutative rings, with emphasis on polynomial rings; and fields, and algebraic extensions. Applications to classical geometric problems. Prerequisites & Notes PRQ: MATH 420. Credits: 3
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3.00 Credits
General theory of vector spaces, linear transformations, and matrices. Topics selected from determinants, tensor products, canonical forms, and bilinear and quadratic forms. Prerequisites & Notes PRQ: MATH 240 and MATH 420, or consent of department. Credits: 3
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3.00 Credits
Re-examination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral. Prerequisites & Notes PRQ: MATH 232 and MATH 240, or MATH 334. Credits: 3
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3.00 Credits
Further study of sequences and series of functions; functions of several variables. Prerequisites & Notes PRQ: MATH 430. Credits: 3
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3.00 Credits
Line and surface integrals, the Riemann-Stieltjes integral, gamma and beta functions, and Fourier series and integrals. Applications to probability theory and mathematical physics. Prerequisites & Notes PRQ: MATH 431 or both MATH 334 and PHYS 385. Credits: 3
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3.00 Credits
Roundoff errors and computer arithmetic. Direct and iterative methods for solving linear systems; norms and condition numbers, iterative refinement. Linear least squares problems: the normal equations and QR approach for overdetermined systems. Numerical methods for eigenvalues: an introduction to the QR iteration. Extensive use of computers. Prerequisites & Notes PRQ: MATH 232, MATH 240, and CSCI 230, CSCI 240, or approved equivalent. Credits: 3
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3.00 Credits
Polynomial interpolation, numerical solutions of nonlinear equations, least squares approximation by polynomials, orthogonal polynomials, economization of power series. Numerical integration including quadrature formulae, adaptive quadrature, composite quadrature formulae, and Romberg integration. Numerical methods for initial value problems including Taylor series methods, Runge-Kutta methods, and multistep methods. Extensive use of computers. Prerequisites & Notes PRQ: MATH 232, MATH 240, and CSCI 230, CSCI 240, or approved equivalent. Credits: 3
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3.00 Credits
Topics include linear systems, existence and uniqueness of solutions, nonlinear equations, and stability. Prerequisites & Notes PRQ: MATH 232, MATH 240, and either MATH 334 or MATH 336, or consent of department. Credits: 3
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3.00 Credits
Green's functions and integral transform solutions of partial differential equations. Coordinate transformations and tensor analysis. Gamma, beta and error functions. Elliptic functions. Asymptotic series. Series solutions of ordinary and partial differential equations. Orthogonal expansions. Probability. Numerical methods. Prerequisites & Notes PRQ: MATH 339 with a grade of C or better. Credits: 3
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3.00 Credits
Beginning course in complex analysis emphasizing the applications of complex function theory. Prerequisites & Notes PRQ: MATH 232 and MATH 240, or MATH 334, or equivalent. Credits: 3
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