Number	Name	Credits	Term	Prerequisite	Other
M501	Combinatorics I	3(3-0-0)	Fa	M301 or M366
	Permutations and combinations, generating functions, recurrence relations, inclusion-exclusion, Polya counting, connectedness and traversability
M502	Combinatorics II	3(3-0-0)	Sp	M501
	Trees, circuits, cutsets, planarity, domination and coloring, networks, matchings, designs, geometries, schemes.
M505	Teaching Problem Solving in Mathematics K-12	3	Fa, Sp	Teacher licensure or written consent of instructor.  Offered as telecourse only.
	Problem-solving strategies, cooperative learning, and manipulatives for K-12 classroom.
M510	Linear Programming and Network Flows	3(3-0-0)	Fa,Sp,Su	M261 or M315	CNAB*:M510, EG510
	Optimization methods, linear programming, simplex algorithm, duality, sensitivity analysis, minimal cost network flows, transportation problem.
M517	Introduction to Mathematical Analysis I	3(3-0-0)	Fa	M417
	Euclidean spaces, metric spaces, sequences, series, limits, continuity, differentiability, Riemann-Stieltjes integral
M518	Introduction to Mathematical Analysis II	3(3-0-0)	Sp	M369 and M517
	Sequences and series of functions.  Differential and integral calculus of functions of several variables.
M519	Complex Variables I	3(3-0-0)	Fa	M317
	Analytic functions, complex integration theory, singularities, elementary functions, and mappings
M520	Nonlinear Programming	3(3-0-0)	Sp	M510 or EG510
	Theoretical, computational, practical aspects of nonlinear programming (NLP); unconstrained, constrained NLP; quadratic programming; large-scale NLP.
M531	Discrete Models of Physical Systems	3(3-0-0)	Fa	M340 or M345
	Discrete models for physical systems; systems of ordinary differential equations; applied linear algebra; introduction to finite elements.
M532	Continuous Models of Physical Systems	3(3-0-0)	Sp, Su	M340 or M345
	Continuous models for physical systems, integral transforms, and eigenfunction expansions for solving partial differential equations.
M540	Dynamical Systems	3(3-0-0)	Fa	M369 and M417
	Linear and nonlinear systems, orbits, phase space, flows of vector fields, stability, bifurcation theory, chaos, strange attractors and applications.
M545	Partial Differential Equations I	3(3-0-0)	Fa	M340 or M345
	Second order linear PDEs, elliptic and parabolic equations, equations of math physics, separation of variables, Fourier series.
M546	Partial Differential Equations II	3(3-0-0)	Sp	M545
	Laplace's equation, Green's functions, complex variable methods, eigenfunction expansions.
M550	Difference Methods - Partial Differential Equations	3(3-0-0)	Sp	M532 or M545	Knowledge of a programming language
	Explicit, implicit methods for second order equations, higher-dimensional problems, stability analysis, method of characteristics.
M560	Linear Algebra	3(3-0-0)	Fa	Written consent of instructor
	Finite dimensional vector spaces, inner products, dual spaces, transformations, projections, adjoints, norms, eigenvalues, eigenvectors.
M561	Numerical Analysis I	4(4-0-0)	Sp	M369	Knowledge of a programming language
	Numerical linear algebra, solving nonlinear systems, least squares, and minimization.
M566	Introduction to Abstract Algebra I	3(3-0-0)	Fa	M366
	Analysis of algebraic structures including groups, rings, fields, and vector spaces.
M567	Introduction to Abstract Algebra II	3(3-0-0)	Sp	M566
	Field theory, Galois theory, and advanced linear algebra.
M570	Topology I	3(3-0-0)	Fa	12 credits of upper-division Math.
	Point-set topology including basic set theory, continuity, product and quotient spaces, metrization, compactness, and connectedness
M571	Topology II	3(3-0-0)	Sp	M566 and M570
	Fundamental group, free groups and presentations, and manifolds
M584	Supervised College Teaching	1(1-0-0)	Fa, Sp
					CNAB: "Credit Not Allowed for Both"