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)
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)
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)
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)
Development of integration theory with introduction to Lebesgue measure and integral on the real line. Elementary theory of normed spaces, bounded linear operators and linear functionals with applications. Prerequisite:
MTH 532.
Credits
3(3-0)
A study of functional analysis. Consideration of Banach spaces, metric spaces, and compact spaces. General measure and integration theory. Prerequisite:
MTH 632.
Credits
3(3-0)
Study of Fourier Series, convergence, summability, Fourier Transforms, distributions. Applications of fast Fourier Transform to Heat and Wave Equation. Signal Processing, Fourier Optics. Prerequisites:
MTH 532.
Credits
3(3-0)
Complex numbers, analytic functions, elementary functions, Cauchy's theorem, Integral formula, Taylor and Laurent series, residue theorem and its applications, Rouche's theorem. Prerequisite:
MTH 532.
Credits
3(3-0)
Conformal mapping, Mobius transformations, harmonic functions, Dirichlet problem, entire and meromorphic functions, analytic continuation, Reimann surfaces, applications of complex analysis. Prerequisite:
MTH 636.
Credits
3(3-0)
Numerical linear algebra with applications in linear and nonlinear systems. Interpolation and approximation and their applications to numerical differentiation, numerical integration, and differential equations. Prerequisite:
MTH 532. Co-requisite:
MTH 533.
Credits
3(3-0)
Advanced topics in geometry, foundations, non-Euclidean geometry. Prerequisite:
MTH 341.
Credits
3(3-0)
Differential geometry of curves and surfaces. Curvature, maps between surfaces, vector fields and differential forms, Stokes' Theorem, Euler Characteristic, Gauss-Bonnet Theorem, manifolds, Riemannian metrics. Prerequisites:
MTH 532 or 545.
Credits
3(3-0)
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)
Mathematical concepts, fundamental processes, and mensuration formulas. Prerequisite: successful completion of the Elementary Teachers Proficiency Tests.
Credits
3(3-0)
The history, concepts, and learning of measurement systems. The metric system and laboratory activities are emphasized. Prerequisite: teaching experience.
Credits
3(3-0)
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)
Preparing materials and investigating methods for teaching mathematics in grades K-12. May be repeated, total credit not to exceed 6 hours. Prerequisite: permission of the instructor.
Credits
1-6(Spec)
Objectives of mathematics instruction in the middle school. Prerequisite: minor in mathematics or teaching experience in middle or senior high school mathematics.
Credits
3(3-0)
History of the development of modern mathematics from 1700 into the 20th century. Prerequisites:
MTH 525, 532.
Credits
3(3-0)
Rigorous study of graph theory, connectivity, coloring, flows, and Ramsey theory. Prerequisite:
MTH 578. Pre/Co-requisite:
MTH 525.
Credits
3(3-0)
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)
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)
Taken during last semester in the M.A. program. Introduces concepts of mathematical modeling using deterministic and probabilistic methods. When possible, supervised consulting work in industry. Prerequisites:
MTH 623 and permission of instructor.
Credits
3(3-0)
Consideration of subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed 6 hours. Prerequisite: permission of instructor.
Credits
1-6(Spec)
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)
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)
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)