MTH - Mathematics
An introduction to the theory, practical applications, and algorithms of linear programming and nonlinear programming. Prerequisites:
MTH 233 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233 or graduate standing
Corequisites
None.
Properties of integers, divisibility, the Euclidean algorithm, distribution of primes, congruences, arithmetic functions, quadratic reciprocity. MTH 321 and MTH 521 cannot be taken in the same semester. Prerequisite: MTH 523 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 523 or graduate standing.
Corequisites
None.
Groups, rings, integral domains, fields, and fundamental homomorphism theorems. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate status
Corequisites
None.
Vector spaces, subspaces, bases and dimensions; linear transformations, their algebra, their representation by matrices, and linear functionals; eigenvalues, triangularizable and diagonalizable transformations; inner product spaces. Prerequisite:
MTH 523 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 523 or graduate status
Corequisites
None.
Representation theory of finite groups, Specht modules, combinatorics of Young tableaux, and symmetric functions. Prerequisite:
MTH 525.
Credits
3(3-0)
Prerequisites
MTH 525
Corequisites
None.
Rigorous development of calculus for functions of one variable. The real number system, sequences, limits, continuity, differentiation, integration, exponential and logarithmic functions, series, uniform convergence. Credits will not count towards MA or Ph.D. degree requirements in mathematics. Prerequisites:
MTH 233, 332; or graduate status.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 332; or graduate status
Corequisites
None.
Continuation of
MTH 532. Rigorous development of calculus of several variables. Limits, continuity, differentiation, integration, implicit and inverse function theorems, differential forms. Prerequisite:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 532
Corequisites
None.
High order equations, series solutions, Bessel functions, nonlinear differential equations, stability, introduction to partial differential equations, boundary value problems, SturmLiouville theory, applications to physical/engineering sciences. Prerequisites:
MTH 233, 334; or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 334; or graduate standing
Corequisites
None.
Differential geometry of curves and surfaces. Curvature, maps between surfaces, vector fields and differential forms, Stokes' theorem, Euler characteristic, Gauss-Bonnet theorem. Prerequisites:
MTH 233, 332; or admission to graduate program in Mathematics. Recommended:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 332; or admission to graduate program in Mathematics
Corequisites
None.
Sets, functions, metric spaces, topological spaces, homeomorphisms, compactness and connectedness, quotient spaces. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate status
Corequisites
None.
This course explores how popular culture (such as television, comics, movies, music and books) portrays mathematicians and mathematics as a discipline. Prerequisite: 45 credit hours completed or graduate status.
Credits
3(3-0)
Prerequisites
45 credit hours completed or graduate status.
Corequisites
None.
Survey of the history of mathematics, focusing on topics taught in secondary schools and undergraduate courses. Emphasis on representing diverse mathematics traditions and legacies. Prerequisite:
MTH 332 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate standing
Corequisites
None.
Introduction to enumerative combinatorics and graph theory. Topics include the graphs, networks and flows, partially ordered sets, principle of inclusion-exclusion, generating functions, and partitions. Prerequisites:
MTH 523.
Credits
3(3-0)
Prerequisites
MTH 523
Corequisites
None.
Theory and application of linear programming and mathematical programming. Simplex method, duality theory and sensitivity analysis, interior point algorithm, and mathematical programming problems. Prerequisite:
MTH 233 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233 or graduate standing
Corequisites
None.
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)
Prerequisites
Permission of instuctor.
Corequisites
None.
The in-depth study of a topic in mathematics under the direction of a faculty member. Prerequisite: Permission of instructor.
Credits
1-6(Spec)
Prerequisites
Permission of instructor
Corequisites
None.
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, MTH 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.
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. Prerequisites: Permission of instructor.
Credits
1-6(Spec)
Prerequisites
Permission of instructor.
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.
Advanced topics in the area of algebra that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisite: MTH 623; permission of instructor. Recommended: MTH 525, MTH 625.
Credits
3-9(Spec)
Prerequisites
MTH 623; permission of instructor
Corequisites
None.
Advanced topics in the area of applied mathematics that are not covered in the regularly offered courses. Specific topics are determined by the instructor. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites:
MTH 534 or 632 or 634; permission of instructor. Recommended:
MTH 534, 632, 634, 638.
Credits
3-9(Spec)
Prerequisites
MTH 534 or MTH 632 or MTH 634; permission of instructor
Corequisites
None.
Fundamentals of topological vector spaces, normed spaces, Banach and Hilbert spaces, functionals on such spaces, operators on Banach and Hilbert spaces, spectral theorems, Banach algebras. Prerequisites:
MTH 632, 636.
Credits
3(3-0)
Prerequisites
MTH 632, MTH 636
Corequisites
None.
Solutions of partial differential equations by analytic and numerical techniques using standard methods, including Fourier series and Laplace transforms, perturbation, finite elements and finite differences. Prerequisites: MTH 534, MTH 636.
Credits
3(3-0)
Prerequisites
MTH 534, MTH 636.
Corequisites
None.
Topics in the area of analysis that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites:
MTH 632 or 636; permission of instructor. Recommended:
MTH 533, 632, 636, 732.
Credits
3-9(Spec)
Prerequisites
MTH 632 or MTH 636; permission of instructor
Corequisites
None.
Advanced topics in the area of geometry that are not covered in the regularly offered courses. To be taken as a three-credit course and may be repeated for a maximum of nine credit hours. Prerequisites: MTH 543 or 643; permission of instructor. Recommended: MTH 533, 645.
Credits
3-9(Spec)
Prerequisites
MTH 543 or MTH 643; permission of instructor
Corequisites
None.
Methods in teaching undergraduate mathematics including technology use, cooperative learning, inquiry, and guided discovery. Students will create activities and discuss best practices of undergraduate instruction. Prerequisite: Admission to the MA or Ph.D. program in the Department of Mathematics or the Department of Statistics, Actuarial and Data Sciences.
Credits
3(3-0)
Prerequisites
Admission to the MA or Ph.D. program in the Department of Mathematics or the Department of Statistics, Actuarial and Data Sciences.
Corequisites
None.
Introduction to understanding and interpreting mathematics education research at the undergraduate level. Prerequisite:
MTH 761.
Credits
3(3-0)
Prerequisites
MTH 761
Corequisites
None.
Advanced perspectives in collegiate mathematics education as it relates to the areas of teaching, learning, and curriculum. Prerequisites: MTH 762 and EDU 614.
Credits
3(3-0)
Prerequisites
MTH 762 and EDU 614
Corequisites
None.
Introduction to the methods of qualitative research in mathematics education including research design, development of protocols, fieldwork, collecting and analyzing data, and techniques of interviewing. Prerequisite:
MTH 763.
Credits
3(3-0)
Prerequisites
MTH 763
Corequisites
None.
Teaching of approved undergraduate mathematics courses. Students will conduct their teaching internship under the supervision of a graduate faculty member. CR/NC only. Prerequisites: MTH 761; successful completion of all qualifying examinations.
Credits
3-6(Spec)
Prerequisites
MTH 761; successful completion of all qualifying examinations
Corequisites
None.
Use of a review of literature to focus research questions and to develop a research proposal. Each student develops a proposal for his/her dissertation research. Prerequisites:
MTH 764.
Credits
3(3-0)
Prerequisites
MTH 764
Corequisites
None.
Students will conduct the pilot study they designed in MTH 767. They will collect and analyze data and develop conclusions based on their data. Prerequisites: MTH 767. Pre/Co-requisite: PSY 611.
Credits
3(3-0)
Prerequisites
MTH 767
Corequisites
None.
In-depth doctoral practicum project supervised by a faculty member or internship experience in an external agency supervised by a faculty member and a professional supervisor. CR/NR only. Prerequisites: Successful completion of all required Ph.D. qualifying examinations; permission of the faculty supervisor.
Credits
3-6(Spec)
Prerequisites
Successful completion of all required PhDqualifying examinations; permission of the faculty supervisor
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. Prerequisite: completion of 30 hours of coursework required for the Doctoral program.
Credits
1-6(Spec)
Prerequisites
Prerequisite: completion of 30 hours of coursework required for the Doctoral program
Corequisites
None.
Open to doctoral students in mathematics. May be taken for credit more than once; total credit not to exceed 9 hours. Prerequisites: 30 hours of coursework toward the doctoral program; permission of the instructor.
Credits
1-9(Spec)
Prerequisites
30 hours of coursework toward the doctoral program; permission of the instructor.
Corequisites
None.
Master's thesis research. CR/NC only. Prerequisites: Graduate status and permission of thesis advisor.
Credits
1-6(Spec)
Prerequisites
Graduate status and permission of thesis advisor
Corequisites
None.
Doctoral dissertation research. CR/NC only. Prerequisites: Completion of all Ph.D. qualifying exam requirements; permission of dissertation advisor.
Credits
1-30(Spec)
Prerequisites
Completion of all PhDqualifying exam requirements; permission of dissertation advisor
Corequisites
None.