MATH 462 Partial Differential Equations (3 credits) - UMCP
Prerequisite: MATH 241 and MATH 246.
Linear spaces and operators, orthogonality, Sturm-Liouville problems and eigenfunction expansions for ordinary differential equations. Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation. Boundary value problems, initial value problems, and initial-boundary value problems. 

MATH 463 Complex Variables for Scientists and Engineers (3 credits) - UMCP
Prerequisite: MATH 241 or equivalent with permission of department.
The algebra of complex numbers, analytic functions, mapping properties of the elementary functions. Cauchy integral formula. Theory of residues and application to evaluation of integrals. Conformal mapping. 

MATH 620 Algebraic Number Theory I (3 credits) - UMCP
Prerequisite: MATH 601.
Algebraic numbers and algebraic integers, algebraic number fields of finite degree, ideals and units, fundamental theorem of algebraic number theory, theory of residue classes, Minkowski's theorem on linear forms, class numbers, Dirichlet's theorem on units, relative algebraic number fields, decomposition group, inertia group and ramification group of prime ideals with respect to a relatively Galois extension. 

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