600
A non-credit course intended for students who have completed all program credits but still need to use university resources to complete their degree requirements.
Credits
1(1-0)
Prerequisites
None.
Corequisites
None.
Isomorphism theorems for groups, group actions, Sylow theorems, product of groups, structure theory of rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains. Prerequisite:
MTH 523, Recommended:
MTH 525.
Credits
3(3-0)
Prerequisites
MTH 525
Corequisites
None.
Modules, free modules, tensor products of modules, exact sequences of modules, modules over a principal ideal domain, field theory, and Galois theory. Prerequisites:
MTH 525, 623.
Credits
3(3-0)
Prerequisites
MTH 525, MTH 623
Corequisites
None.
Lie algebras, semisimplicity, representation of Lie algebras, weights and roots, universal enveloping algebras, character and dimension formulas. Prerequisite:
MTH 625. Recommended:
MTH 527.
Credits
3(3-0)
Prerequisites
MTH 625
Corequisites
None.
Development of Lebesgue Measure and Lebesgue Integration for Functions of Real Variables. Normed Linear Spaces, L^p Spaces, Inequalities of Holder and Minkowski. Prerequisite:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 532
Corequisites
None.
General measure and integration theory. Fundamental theorems on metric spaces, compact topological spaces, and Banach spaces. Prerequisite:
MTH 632.
Credits
3(3-0)
Prerequisites
MTH 632
Corequisites
None.
Study of Fourier Series, convergence, summability, Fourier Transforms, distributions and wavelet analysis. Applications of fast Fourier Transform to Heat and Wave Equation, Signal Processing. Prerequisites:
MTH 532 or graduate standing in Mathematics MA or PhD program.
Credits
3(3-0)
Prerequisites
MTH 532 or graduate standing in Mathematics MA or PhD program
Corequisites
None.
Complex numbers, holomorphic functions, elementary functions, Cauchy's theorem and Integral formula, Taylor and Laurent series, residue theorem and its applications, Rouché's theorem. Prerequisite:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 532
Corequisites
None.
Conformal mapping, Möbius transformations, harmonic functions, Dirichlet problem, entire and meromorphic functions, analytic continuation, Riemann surfaces, applications of complex analysis. Prerequisite:
MTH 636.
Credits
3(3-0)
Prerequisites
MTH 636
Corequisites
None.
Numerical solution of one-variable nonlinear equations, numerical linear algebra, approximation theory, eigenvalue-eigenvector computation, numerical differentiation and integration, initial value problems for ordinary differential equations. Prerequisite:
MTH 532. Pre/Co- requisite:
MTH 533.
Credits
3(3-0)
Prerequisites
MTH 532
Corequisites
None.
Topological and smooth manifolds, smooth maps, tangent bundles, vector fields, differential forms, submanifolds, Riemannian metrics, Lie groups, quotient manifolds, Stokes' theorem, de Rham cohomology. Prerequisites:
MTH 533 or 543;
MTH 623.
Credits
3(3-0)
Prerequisites
MTH 533 or MTH 543; MTH 623
Corequisites
None.
Homotopy and the fundamental group. Free products, van Kampen's theorem, covering spaces, universal covers, and deck transformations. Homology, cohomology, exact sequences, and higher homotopy groups. Prerequisites:
MTH 545, 623.
Credits
3(3-0)
Prerequisites
MTH 545, MTH 623
Corequisites
None.
The history, concepts, and learning of measurement systems. The metric system and laboratory activities are emphasized. Prerequisite: teaching experience.
Credits
3(3-0)
Prerequisites
teaching experience
Corequisites
None.
Use of instructional technology for teaching and learning mathematics and an introduction to related research literature in mathematics and mathematics education. Prerequisite: MTH 566.
Credits
3(3-0)
Prerequisites
MTH 566
Corequisites
None.
History of the development of modern mathematics from 1700 into the 20th century. Prerequisites:
MTH 525, 532.
Credits
3(3-0)
Prerequisites
MTH 525, MTH 532
Corequisites
None.
Rigorous study of graph theory, connectivity, coloring, flows, and Ramsey theory. Prerequisite:
MTH 578. Pre/Co-requisite:
MTH 525.
Credits
3(3-0)
Prerequisites
MTH 578
Corequisites
None.
Seminars focused on current issues in mathematics education. May be taken for credit more than once, total credit not to exceed four hours. Three credits needed before it counts as an elective on any graduate degree in mathematics. Prerequisite: Permission of an instructor.
Credits
1-4(Spec)
Prerequisites
Permission of an instructor
Corequisites
None.
One hour seminars in subfields of mathematics and its applications; 3 credits needed before it counts as elective on graduate degrees in mathematics. Prerequisites: Graduate standing in mathematics and permission of instructor.
Credits
1-4(Spec)
Prerequisites
Graduate standing in mathematics and permission of instructor
Corequisites
None.
Consideration of subject matter not included in regular courses. May be taken for credit more than once, total credit not to exceed 6 hours. Prerequisites: graduate standing; additional instructor prerequisites will be announced in the Course Search and Registration.
Credits
1-6(Spec)
Prerequisites
graduate standing; additional instructor prerequisites will be announced in the Course Search and Registration
Corequisites
None.
Consideration of subject matter not included in regular courses. May be taken for credit more than once; total credit not to exceed six hours. Pre/Co-requisites: See Course Search and Registration.
Credits
1-6(Spec)
Prerequisites
None.
Corequisites
None.
Open to graduate students in mathematics. May be taken for credit more than once; total credit not to exceed 9 hours. Prerequisite: permission of the instructor.
Credits
1-9(Spec)
Prerequisites
permission of the instructor
Corequisites
None.
Plan B paper is normally an expository paper or research project on an area or problem related to but in addition to material covered in a course, written under the direction of graduate faculty. Each Plan B project is 1 credit hour. May be taken for credit more than once. Total credit not to exceed 2 hours. CR/NC only. Prerequisites: permission of advisor.
Credits
1-2(Spec)
Prerequisites
permission of advisor
Corequisites
None.