Prerequisite: Standard Teaching Certificate.

An exploration of both content and pedagogical topics for teachers of primary school mathematics. Topics may include new curriculum programs, materials and teaching strategies, calculators and computers, number systems, operations of arithmetic, and problem solving, as well as topics of current interest. A hands-on approach using manipulative and concrete models will be a focus for the course. May be repeated for up to a maximum of six credit hours. Cannot be used to satisfy requirements for certification or for a bachelor's or master's degree.

Prerequisite: MATH 4110.
Analytic and axiomatic projections, theory of conic sections, Pascal's and Branchon's theorems, linear transformations.

Prerequisite: MATH 4410.
Theory of curves and surfaces in Euclidean space, Frenet-Serret formulas, Gaussian curvature, and geodesics.

Prerequisite: Consent of the department.
Concept of topology, topological and metric spaces, continuity, connectedness, generalized limits, and separation concepts.

Prerequisite: MATH 4210 or equivalent.
Selected topics in classical, analytic, and algebraic number theory.

Prerequisite: MATH 4250.
Group theory: group action, Sylow theorems, and simple and solvable groups. Field theory: Galois correspondence, radical extensions, algebraic and transcendental extensions, and finite fields.

Prerequisite: MATH 5220.
Continuation of MATH 5220, Commutative algebra: integrality, Hilbert basis theorem, modules over PDI; non-commutative rings: Jacobson radical, Artin-Wedderburn theorem.

Prerequisite: Math 5220 and 5230.
An introduction to commutative rings and modules over commutative rings. Chain conditions, Noetherian and Artinian rings. Localization. Finitely generated algebras over a field and varieties. Further topics may include discrete valuation rings and Dedekind domains, completions,Nullstellensatz.

Prerequisite: MATH 4250.
Algebraic theory with applications to theoretical computing. Topics include finite state automata, Turing machines, computability, the theoretical limits of computers, and coding theory.

Prerequisite: Math 5220.
Geometry of curves/surfaces defined by polynomial equations. Emphasis on concrete computations with polynomials using computer packages, interplay between algebra and geometry, as well as algebra and biology. Algebra and topology presented as needed.

Prerequisite: MATH 4410.
Infinite series of real and complex terms, including the summability methods of Abel and Cesaro; tests for convergence of series of positive constants, including those of Cauchy, Maclaurin, Gauss; alternating series; conditional convergence and Riemann's theorem; absolute and uniform convergence; theorems of Weierstrass, Cauchy, Abel, Levi and Steinitz; introduction to the theory of divergent series.

Prerequisite: MATH 4410.
Functions of bounded variation, Riemann-Stieltjes integral, topology of the real line, measure theory, measurable functions, Lebesgue integral, other selected topics.

Prerequisite: MATH 5420.
Continuation of MATH 5420: Radon-Nikodym theorem, LP spaces, Riesz Representation theorem, functions of several variables, inverse and implicit function theorems, smooth manifolds, tangent and cotangent bundles, vector bundles, differential forms, pullback, wedge product, integration, Poincare lemma.

Prerequisite: MATH 4450 or 4410.
Complex numbers and polygenic and monogenic functions, theory of residues, Taylor and Laurent series, and Cauchy-Riemann and Laplace equations.

Prerequisite: Math 5440.
Harmonic functions and the Dirichlet problem. Introduction to Riemann surfaces. Negative curvature and Picard's Big Theorem. Further topics may include Hardy spaces, Corona theorem, a deeper study of Riemann surfaces, and the uniformization theorem.

Prerequisite: MATH 5420.
Hahn-Banach theorem, weak topologies; operators on Hilbert and Banach spaces, normal, self-adjoint, and compact operators; geometric and spectral analysis of linear operators; generalized functions. At instructor's discretion, applications to Fourier series, numerical analysis, probability, or differential equations will be discussed.

Prerequisite: MATH 2550 and 4410.
Boundary value problems, linear differential equations with periodic coefficients, nonlinear differential equations, perturbation theory, and Poincare's method.

Prerequisite: MATH 2550 and 4410.
Classical solutions of first and second order partial differential equations, Bessel and Legendre functions, orthogonal functions, solutions of boundary value problems by the separation of variables and integral transformations, Laplace's equation, and wave equation.

Prerequisite: MATH 5550, MATH 4410.
Difference equations, iteration, Aitken's delta square method, Steffensen's method, Bairstow's method, Bernoulli's method, and the quotient-difference algorithm. Additional topics may include Mesh-free methods, finite element methods, spectral methods, Galerkin type methods, and fast Fourier transform methods.

Prerequisite: MATH 5550.
Interpolation via polynomials, orthogonal families of polynomials, spline interpolation, least squares methods, and Fourier methods. Additional topics may include radial basis function methods and convolution kernel based methods.

Prerequisite: MATH 4600 or equivalent.
Random variables, conditional probability, multidimensional distributions, functions of random variables, central limit theorem, and limiting distributions.

Prerequisite: MATH 5610.
Test of hypothesis, point estimation, confidence intervals, sufficient statistics, Rao Blackwell theorem, and multivariate analysis.

Prerequisite: Consent of the Graduate Program Advisor.
The history of curriculum, content, and trends in mathematics of grades 7-12; study and analysis of major reports, recommendations, and theories in mathematics curricula and teaching and learning; issues and trends in assessment practices; study and analysis of reform movements and their effect in curricular designs, practices, and beliefs of mathematics and mathematics teaching and learning.

Prerequisite: Consent of the Graduate Program Advisor.
Survey and analysis of research in the field of mathematics education; issues, research, and practices in the teaching and learning of mathematics; critiques and conduct of research in the teaching and learning of mathematics.

Prerequisite: High school mathematics teaching experience and consent of the department.
Modern application of mathematics in such fields as economics, industrial management, psychology, political science, biology, ecology, and geography for high school classroom utilization.

Prerequisite: Twenty-one graduate level credit hours in mathematics and consent of the department.
Conducted by graduate faculty of department. The course may be repeated under a different topic with the permission of the department.

Prerequisite: Approval of the Graduate Program Advisor.
Research under the supervision of a regular faculty member leading to the completion of a master's project.

Prerequisite: Approval of the Graduate Program Advisor.
Research under the supervision of a regular faculty member leading to the completion of a master's thesis. (A thesis is a document with precise format prescribed by the Graduate School. Refer to the Graduate Students' Handbook for the thesis formalism.)