MATH 624 Applicable Algebra (3) Topics from partially ordered sets and applications, Polya's theory of counting, matroids and optimization, coding, semigroups and automata. Prerequisite: MATH 520.

MATH 630 Applied Analysis (3) Study of the basic concepts of analysis and their applications. Metric spaces, topology, differentiation and integration, operators, orthogonal functions, Fourier series, special functions, calculus of variations, differential equations. Prerequisites: MATH 360 and 374.

MATH 632 Ordinary Differential Equations (3) Theory and applications of ordinary differential equations. Existence and uniqueness of solutions, methods for solving equations, linear differential equations, singularities, qualitative analysis of solutions, systems of equations. Homework assignments may require use of differential equations software packages. Prerequisites: MATH 630 and 626, or consent of instructor.

MATH 634 Partial Differential Equations (3) Theory and applications of partial differential equations. Cauchy problems, the Cauchy-Kovalevsky Theorem, elliptic equations, hyperbolic equations. Homework assignments may require use of differential equations software packages. Prerequisites: MATH 630 and 626, or consent of instructor.

MATH 636 Complex Analysis (3) The study of functions of a complex variable, including analytic functions, the Cauchy-Riemann equations, Cauchy's Theorem, Liouville's Theorem, Laurent Series, the Residue Theorem. Prerequisite: MATH 360 or 630.

MATH 644 Applied Combinatorics (3) Matching theory, network flows, location of facilities on networks, social choice, optimization problems on graphs, experimental designs, combinatorial optimization. Prerequisite: MATH 520 or 540 or consent of instructor.

MATH 655 Differential Geometry (3) Covers the basic material of the differential geometry of manifolds building upon the intuition of curves and surfaces. Concentration in Riemannian geometry with special emphasis on geodesics and metric space properties. Use of differential geometric software. Combines theoretical ideas with hands-on laboratory experience. Prerequisite: MATH 550.

MATH 699 Thesis (3) Preparation of a thesis for the master's degree. Prerequisites: An officially appointed thesis committee and advancement to candidacy.

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