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Course Criteria
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3.00 Credits
Pr. grade of at least C in MAT 395 Vector-spaces: basis, dimension, Hilbert spaces; pre-Hilbert spaces, norms, metrics, orthogonality, infinite sums. Linear subspaces; annihilators, closed and complete subspaces, convex sets. Continuous linear mappings; normed spaces. Banach spaces, Banach algebras, dual spaces. Reisz-Frechet theorem. Completion. Bilinear and seaquilinear maps. Adjoints. Operators in Hilbert space: isometric, unitary, self-adjoint, projection, and normal operations. Invariant subspaces. Continuous operators. Special theorems for a normal co-operator.
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3.00 Credits
Pr. grade of at least C in 253 or 295 or 311 or 395, or permission of instructor The pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations.
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3.00 Credits
Pr. grade of at least C in 310 and any one of the courses 253, 295, 311, 395, 531 Basic concepts, graph coloring, trees, planar graphs, networks.
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3.00 Credits
Pr. grade of at least C in 293 The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.
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3.00 Credits
Pr. grade of at least C in MAT 394 and either MAT 353 or STA 351, or equivalents Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.
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3.00 Credits
Pr. grade of at least C in 293 and 390 or permission of instructor An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems.
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3.00 Credits
Pr. grade of at least C in 545 Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems.
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3.00 Credits
Pr. grade of at least C in 293 and 390 or permission of instructor May be repeated for credit with approval of the Department Head. Selected topics of current interest in applied mathematics.
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3.00 Credits
Pr. grade of at least C in 253 or permission of instructor Advanced topics in discrete mathematics and their uses in studying computer science.
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3.00 Credits
Pr. grade of at least C in 311 Set theory: sets, mappings, integers. Group theory: normal subgroups, quotient groups, permutation groups, Sylow theorems. Ring theory: homomorphisms, ideals, quotient rings, integral domains, fields, Euclidean rings, polynomial rings.
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