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Mathematics |
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MATH 6203 - Stochastic Calculus for Finance I
This course starts with the probability theory in discrete probability space, discrete-time stochastic processes, and derivatives pricing in the Binomial model. The second part covers probability theory in general probability space and continuous-time martingale and Markov processes. Topics include: the It’o integral, Black-Scholes model, It’o-Doeblin formula, Girsanovs theorem, and Martingale Representation theorem. Applications to pricing of exotic derivatives and American options are discussed.
Credit Hours: (3)
Restriction(s): Admission to the graduate program and permission of Program Director.
Schedule of Classes
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MATH 6204 - Numerical Methods for Financial Derivatives
This course will introduce students to numerical and computational techniques for solving both European- and American-style financial derivatives. The approach will be the finite difference method and the basic theoretical concepts will be introduced. Final projects will involve implementing the techniques on computers. Some spectral and Monte Carlo methods will also be discussed.
Credit Hours: (3)
Schedule of Classes
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MATH 6205 - Financial Computing
This laboriented course introduces the numerical methods needed for quantitative work in finance, focusing on derivative pricing and fixed income applications. Topics include: binomial and trinomial methods, Crank-Nicholson methods for various exotic options, treatment of discrete dividends, numerical methods for stochastic differential equations, random number generators, Monte-Carlo methods for European and American options. The computing course teaches theory and practice of numerical finance as well as the programming skills needed to build software systems in C/C++, Java, Javascript, and Mathematica/Matlab.
Credit Hours: (3)
Schedule of Classes
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MATH 6206 - Stochastic Calculus for Finance II
The applications of stochastic calculus techniques to advanced financial modeling. Topics include: pricing of European, American, and fixedincome derivatives in the Black-Scholes and stochastic volatility models. The Jump-diffusion model is also introduced.
Credit Hours: (3)
Prerequisite(s): MATH 6203 or permission of department.
Cross-listed Course(s): MATH 8206
Schedule of Classes
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MATH 6609 - Seminar in Mathematics
A series of regularly scheduled meetings in which each student presents one or more topics selected by the instructor.
Credit Hours: (1 to 3)
Restriction(s): Permission of department.
Cross-listed Course(s): EDCI 8609 .
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 6690 - Graduate Teaching Assistant Training
Discusses techniques used in the teaching of mathematics and statistics. This course is required as a condition of employment for new graduate teaching and instructional assistants in the department.
Credit Hours: (1)
Restriction(s): Permission of department
Schedule of Classes
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MATH 7028 - Topics in Probability
Topics of current interest in probability and advanced topics in probability.
Credit Hours: (3)
Prerequisite(s): MATH 7120 and MATH 7121 , or permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 7050 - Topics in Mathematics
Topics chosen from such fields as algebra, topology, analysis, applied mathematics, differential geometry, mathematical physics, graph theory, probability, statistics.
Credit Hours: (2 to 3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with change of topic and with the approval of the department.
Schedule of Classes
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MATH 7065 - Topics in Applied Algebra and Algebraic Structures
Current topics in Applied Algebra and Algebraic Structure.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 7070 - Topics in Numerical Analysis
Topics of current interest in numerical analysis.
Credit Hours: (3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 7071 - Topics in Differential Equations
Topics of current interest in ODE, PDE, dynamical systems, inverse problems and related subjects.
Credit Hours: (3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 7120 - Probability Theory I
Topics include: probability spaces, probability measures, sigma-algebras, characteristic functions, sequences of random variables, law of large numbers, general forms of the Central Limit Theorem.
Credit Hours: (3)
Prerequisite(s): MATH 7143 and MATH/STAT 3122 or permission of department.
Schedule of Classes
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MATH 7125 - Stochastic Processes I
Basic ideas in the study of stochastic processes, selected from: discrete and continuous time Markov processes, stationary and renewal processes, applications to queuing theory, reliability theory, stochastic differential equations, time-series analysis, filtering and stochastic control theory.
Credit Hours: (3)
Prerequisite(s): MATH 3122, MATH 7120 , and MATH 7143 , or permission of department.
Schedule of Classes
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MATH 7141 - Complex Analysis I
Holomorphic functions, complex integration, residues, entire and meromorphic functions, conformal mapping, harmonic functions.
Credit Hours: (3)
Prerequisite(s): MATH 5143 or permission of department.
Schedule of Classes
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MATH 7143 - Real Analysis I
Lebesgue integration on the real line, Lp spaces, introduction to general measure and integration theory.
Credit Hours: (3)
Prerequisite(s): MATH 5144 or permission of department.
Schedule of Classes
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MATH 7147 - Applied Functional Analysis
Introduction to functional analysis and its applications to such areas as linear and nonlinear differential equations, integral equations, and control theory. Topics chosen from Banach spaces, operators, the Hahn-Banach, open mapping and closed graph theorems, Sobolev spaces, spectral theory, operators in Hilbert space.
Credit Hours: (3)
Prerequisite(s): MATH 5144 .
Schedule of Classes
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MATH 7148 - Functional Analysis
Material selected from: spectral theory, spectral theory of differential operators, groups and semigroups of operators, nonlinear functional analysis, asymptotic analysis, integral equations, Fourier analysis, distributions, and Sobolev spaces.
Credit Hours: (3)
Prerequisite(s): MATH 7144 or permission of department.
Schedule of Classes
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MATH 7163 - Modern Algebra I
Topics include: Galois theory, commutative algebra, modules, ring theory, homological algebra.
Credit Hours: (3)
Prerequisite(s): MATH 4163 and MATH 4164, or permission of department.
Schedule of Classes
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MATH 7172 - Partial Differential Equations
Harmonic functions, mean-value theorem, maximum principle, Green’s representation for the solution of the Dirichlet problem for Laplace’s equation; Poisson’s equations and the Poisson formula; statement and proof of the existence theorem for general second-order elliptic operators, generalized maximum principles; Sobolev spaces. Evolution equations involving elliptic operators, such as the heat or wave equations, may also be introduced.
Credit Hours: (3)
Prerequisite(s): MATH 5174 and MATH 7144 , or permission of department.
Schedule of Classes
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MATH 7173 - Evolution Equations
Semigroups of operators and their generators, examples of semigroups. The heat equation, examples of elliptic operators that generate semigroups, Hille-Yosida theory, analytic semigroups; examples, fractional powers of operators.
Credit Hours: (3)
Prerequisite(s): MATH 7144 and MATH 7172 or permission of department.
Schedule of Classes
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MATH 7174 - Linear and Nonlinear Waves
Hyperbolic waves, characteristics, Riemann invariants, conservation laws, weak solutions, shock structure. Burger’s equation, gas dynamics, dispersive waves, group velocity, water waves, nonlinear optics.
Credit Hours: (3)
Prerequisite(s): MATH 5124 and MATH 7144 or permission of department.
Schedule of Classes
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MATH 7175 - Inverse Problems
Ill-posed problems and numerical methods for them. Applications of inverse problems to real processes. One dimensional inverse problems. Multi-dimensional inverse problems: uniqueness and numerical methods. Inverse scattering problems.
Credit Hours: (3)
Prerequisite(s): MATH 5174 and MATH 7144 , or permission of department.
Schedule of Classes
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MATH 7176 - Advanced Numerical Analysis
A selection of topics from such areas as iterative methods of solving linear and nonlinear systems of equations, approximation theory, splines, and finite element methods for partial differential equations.
Credit Hours: (3)
Prerequisite(s): MATH 2164, MATH 2171 and MATH 5176 , or permission of department.
Schedule of Classes
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MATH 7177 - Applied Optimal Control
Examples of control systems and optimization problems, optimal control of discretetime systems, solutions of the general discrete-time optimization problem, optimal control of continuoustime systems, the calculus of variations, solution of the general continuous optimization problem, applications of the Pontryagin Maximum Principle, Dynamic programming, and Bang-bang control. Controllability and differential games may also be introduced.
Credit Hours: (3)
Prerequisite(s): MATH 5143 or permission of department.
Schedule of Classes
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MATH 7178 - Computational Methods for Fluid Dynamics
Topics on various numerical techniques for the solution of incompressible and compressible flows. Finite difference, finite element and spectral methods, and shock capturing and fitting methods. Multi-grid method and acceleration techniques.
Credit Hours: (3)
Prerequisite(s): MATH 2242, MATH 2171, MATH 5174 , and MATH 5176 , or permission of department.
Schedule of Classes
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MATH 7179 - Advanced Finite Difference Methods
Accuracy analysis and design of high order schemes, stability theory of schemes with variable coefficients, stability theory of schemes for initial-boundary value problems, convergence theory for nonlinear cases.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 7180 - Advanced Numerical Methods in Scientific Computing
Introduces advanced numerical methods in scientific computing. Topics include: Particle-Mesh Ewald and the Fast multipole methods, boundary element methods, absorbing and perfectly matched layered boundary conditions, Yee’s finite difference and discontinuous Galerkin methods, surface integral equation methods, Nedelec edge elements for Maxwell equations, Bloch theory and periodic structures and photonics, Boltzmann and Wigner kinetic methods, high resolution Godunov methods and WENO methods for hydrodynamic equations, particle-in-cell and constrained transport methods for magnetohydrodynamics.
Credit Hours: (3)
Prerequisite(s): MATH 5172 and MATH 5176 , or permission of the department.
Schedule of Classes
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MATH 7181 - Topology I
Topological spaces, continuous functions, connectedness, compactness, and metrizability, and further topics from point-set, geometric or algebraic topology.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 7184 - Differential Geometry I
Manifolds, differential structures, tangent bundles, embeddings, immersions, inverse function theorem, Morse-Sard theorem, transversality, Borsuk-Ulam theorem, vector bundles, Euler characteristics, Morse theory, Stokes theorem, Gauss-Bonnet theorem, Whitney embedding theorem.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 7185 - Differential Geometry II
Differentiable manifolds, differential forms, critical points, local and global theory of curves, local and global theory of surfaces, connections, geodesics, curvature, spaces of constant curvature, Lie groups and Lie algebras.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 7273 - Advanced Finite Element Analysis
Selection of topics from such areas of finite element analysis as convergence theorems (Ciarlet), hierarchical basis functions, the hp method, adaptive grid techniques and solution methods for nonlinear equations.
Credit Hours: (3)
Prerequisite(s): MATH 5172 and MATH 5174 , or permission of department.
Schedule of Classes
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MATH 7275 - Dynamical Systems I
Cycles and separatrix cycles, Poincaré first-return map: diffeomorphisms, Poincaré-Bendixson Theory, flows on the two-torus; structural stability, genericity, Peixoto’s theorem; singularities of planar systems. Degenerate singularities, Hopf bifurcation, saddle-node bifurcation, center bifurcation.
Credit Hours: (3)
Prerequisite(s): MATH 5143 and MATH 5173 , or permission of department.
Schedule of Classes
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MATH 7276 - Dynamical Systems II
Method of averaging, Melnikov functions, hyperbolic structure, symbolic dynamics, homoclinic and heteroclinic orbits, global bifurcations, infinite dimensional dynamical systems, inertial manifolds, Lyapunov exponents and dimension of attractors, codimensiontwo bifurcations, Duffing’s equation, Lorenz equations, finite dimensional systems of dimension at least three.
Credit Hours: (3)
Prerequisite(s): MATH 7275 or permission of department.
Schedule of Classes
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MATH 7490 - Industrial Internship
Full- or part-time academic year or summer internship in mathematics and/or statistics complementary to the student’s major course of study and designed to allow theoretical and course-based practical learning to be applied in a supervised industrial experience. Each student’s program must be approved by the department’s Graduate Program Director. Requires a mid-term report and final report to be graded by the supervising faculty. Credit hours gained from the internship may not be counted toward the courses leading to advancement to candidacy.
Credit Hours: (0 to 6)
Restriction(s): Completion of 6 credit hours of MATH/STAT/OPRS graduate courses and permission of department.
Grading Method: Graded on a Pass/Unsatisfactory basis.
Repeatability: May be repeated for credit up to 6 credit hours.
Schedule of Classes
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MATH 7891 - Independent Study in Mathematics
Faculty-directed independent study of topics not provided by other course offerings and/or to examine, extend, and enrich extant knowledge in mathematics through supervised individual study.
Credit Hours: (1 to 3)
Restriction(s): Permission of department
Repeatability: May be repeated for credit with change of topic.
Schedule of Classes
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MATH 7892 - Directed Project in Mathematics
The directed independent project may be original work, work of an expository nature, or the mathematical formulation and solution of a particular problem of mathematical significance. The project may also involve a specific application of techniques identified in the literature or studied in other courses. The project must be defended in an oral presentation.
Credit Hours: (1 to 3)
Restriction(s): Permission of department
Repeatability: May be repeated for credit up to 6 credit hours.
Schedule of Classes
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MATH 7994 - Master’s Thesis Research
Subject to the approval of the department Graduate Committee, the thesis may be original work, work of an expository nature, or the mathematical formulation and solution of a particular industrial or business problem suggested by the career interests of the student. The thesis must be defended in an oral presentation.
Credit Hours: (3)
Restriction(s): Permission of department
Grading Method: Graded on a Satisfactory Progress/Unsatisfactory Progress or Standard Letter Grade basis each term.
Repeatability: May be repeated for credit up to 6 credit hours.
Schedule of Classes
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MATH 8028 - Topics in Probability
Topics of current interest in probability and advanced topics in probability.
Credit Hours: (3)
Prerequisite(s): MATH 8120 and MATH 8121 , or permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 8050 - Topics in Mathematics
Topics chosen from such fields as algebra, topology, analysis, applied mathematics, differential geometry, mathematical physics, graph theory, probability, statistics.
Credit Hours: (2 to 3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with change of topic and with the approval of the department.
Schedule of Classes
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MATH 8065 - Topics in Applied Algebra and Algebraic Structures
Current topics in Applied Algebra and Algebraic Structure.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 8070 - Topics in Numerical Analysis
Topics of current interest in numerical analysis.
Credit Hours: (3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 8071 - Topics in Differential Equations
Topics of current interest in ODE, PDE, dynamical systems, inverse problems and related subjects.
Credit Hours: (3)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with permission of department.
Schedule of Classes
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MATH 8120 - Probability Theory I
Topics include: probability spaces, probability measures, sigma-algebras, characteristic functions, sequences of random variables, law of large numbers, general forms of the Central Limit Theorem.
Credit Hours: (3)
Prerequisite(s): MATH 8143 ; and MATH 3122 or STAT 3122, or permission of department.
Schedule of Classes
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MATH 8125 - Stochastic Processes I
Basic ideas in the study of stochastic processes, selected from: discrete and continuous time Markov processes, stationary and renewal processes, applications to queuing theory, reliability theory, stochastic differential equations, time-series analysis, filtering and stochastic control theory.
Credit Hours: (3)
Prerequisite(s): MATH 3122, MATH 8120 , and MATH 8143 , or permission of department.
Schedule of Classes
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MATH 8141 - Complex Analysis I
Holomorphic functions, complex integration, residues, entire and meromorphic functions, conformal mapping, harmonic functions.
Credit Hours: (3)
Prerequisite(s): MATH 5143 or permission of department.
Schedule of Classes
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MATH 8143 - Real Analysis I
Lebesgue integration on the real line, Lp spaces, introduction to general measure and integration theory.
Credit Hours: (3)
Prerequisite(s): MATH 5144 or permission of department.
Schedule of Classes
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MATH 8144 - Real Analysis II
An introduction to linear functional analysis. Topics include: normed linear spaces, bounded linear operators, Banach spaces, duality for normed linear spaces, weak convergence, Hilbert spaces, and compact self-adjoint operators.
Credit Hours: (3)
Prerequisite(s): MATH 7143 , MATH 8143 , or permission of department
Cross-listed Course(s): MATH 7144
Schedule of Classes
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MATH 8147 - Applied Functional Analysis
Introduction to functional analysis and its applications to such areas as linear and nonlinear differential equations, integral equations, and control theory. Topics chosen from Banach spaces, operators, the Hahn-Banach, open mapping and closed graph theorems, Sobolev spaces, spectral theory, operators in Hilbert space.
Credit Hours: (3)
Prerequisite(s): MATH 5144
Schedule of Classes
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MATH 8148 - Functional Analysis
Material selected from: spectral theory, spectral theory of differential operators, groups and semigroups of operators, nonlinear functional analysis, asymptotic analysis, integral equations, Fourier analysis, distributions, and Sobolev spaces.
Credit Hours: (3)
Prerequisite(s): MATH 8144 or permission of department.
Schedule of Classes
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MATH 8163 - Modern Algebra I
Topics selected from Galois theory, commutative algebra, modules, ring theory, homological algebra.
Credit Hours: (3)
Prerequisite(s): MATH 4163 and MATH 4164 or permission of department.
Schedule of Classes
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MATH 8172 - Partial Differential Equations
Harmonic functions, mean-value theorem, maximum principle, Green’s representation for the solution of the Dirichlet problem for Laplace’s equation; Poisson’s equations and the Poisson formula; statement and proof of the existence theorem for general second-order elliptic operators, generalized maximum principles; Sobolev spaces. Evolution equations involving elliptic operators, such as the heat or wave equations, may also be introduced.
Credit Hours: (3)
Prerequisite(s): MATH 5174 and MATH 8144 , or permission of department.
Schedule of Classes
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MATH 8173 - Evolution Equations
Semigroups of operators and their generators, examples of semigroups. The heat equation, examples of elliptic operators that generate semigroups, Hille-Yosida theory, analytic semigroups; examples, fractional powers of operators.
Credit Hours: (3)
Prerequisite(s): MATH 8144 and MATH 8172 , or permission of department.
Schedule of Classes
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MATH 8174 - Linear and Nonlinear Waves
Hyperbolic waves, characteristics, Riemann invariants, conservation laws, weak solutions, shock structure. Burger’s equation, gas dynamics, dispersive waves, group velocity, water waves, nonlinear optics.
Credit Hours: (3)
Prerequisite(s): MATH 5144 and MATH 8144 , or permission of department.
Schedule of Classes
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MATH 8175 - Inverse Problems
Ill-posed problems and numerical methods for them. Applications of inverse problems to real processes. One dimensional inverse problems. Multi-dimensional inverse problems: uniqueness and numerical methods. Inverse scattering problems.
Credit Hours: (3)
Prerequisite(s): MATH 5174 and MATH 8144 , or permission of department.
Schedule of Classes
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MATH 8176 - Advanced Numerical Analysis
A selection of topics from such areas as iterative methods of solving linear and nonlinear systems of equations, approximation theory, splines, and finite element methods for partial differential equations.
Credit Hours: (3)
Prerequisite(s): MATH 2164, MATH 2171, and MATH 5176 , or permission of department.
Schedule of Classes
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MATH 8177 - Applied Optimal Control
Examples of control systems and optimization problems, optimal control of discrete-time systems, solutions of the general discrete-time optimization problem, optimal control of continuous-time systems, the calculus of variations, solution of the general continuous optimization problem, applications of the Pontryagin Maximum Principle, Dynamic programming, and Bang-bang control. Controllability and differential games may also be introduced.
Credit Hours: (3)
Prerequisite(s): MATH 5143 or permission of department.
Schedule of Classes
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MATH 8178 - Computational Methods for Fluid Dynamics
Topics on various numerical techniques for the solution of incompressible and compressible flows. Finite difference, finite element and spectral methods, and shock capturing and fitting methods. Multi-grid method and acceleration techniques.
Credit Hours: (3)
Prerequisite(s): MATH 2242, MATH 2171, MATH 5174 , and MATH 5176 , or permission of department.
Schedule of Classes
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MATH 8180 - Advanced Numerical Methods in Scientific Computing
Introduces advanced numerical methods in scientific computing. Topics include: Particle-Mesh Ewald and the Fast multipole methods, boundary element methods, absorbing and perfectly matched layered boundary conditions, Yee’s finite difference and discontinuous Galerkin methods, surface integral equation methods, Nedelec edge elements for Maxwell equations, Bloch theory and periodic structures and photonics, Boltzmann and Wigner kinetic methods, high resolution Godunov methods and WENO methods for hydrodynamic equations, particle-in-cell and constrained transport methods for magnetohydrodynamics.
Credit Hours: (3)
Prerequisite(s): MATH 5172 and MATH 5176 , or permission of the department.
Schedule of Classes
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MATH 8181 - Topology I
Topological spaces, continuous functions, connectedness, compactness, and metrizability, and further topics from point-set, geometric or algebraic topology.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 8184 - Differential Geometry I
Manifolds, differential structures, tangent bundles, embeddings, immersions, inverse function theorem, Morse-Sard theorem, transversality, Borsuk-Ulam theorem, vector bundles, Euler characteristics, Morse theory, Stokes theorem, Gauss-Bonnet theorem, Whitney embedding theorem.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 8185 - Differential Geometry II
Differentiable manifolds, differential forms, critical points, local and global theory of curves, local and global theory of surfaces, connections, geodesics, curvature, spaces of constant curvature, Lie groups and Lie algebras.
Credit Hours: (3)
Restriction(s): Permission of department.
Schedule of Classes
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MATH 8202 - Partial Differential Equations for Finance
This course deals with those partial differential equations which are associated with financial derivatives based on factors such as equities and spot interest rates.
Credit Hours: (3)
Cross-listed Course(s): MATH 6202 .
Schedule of Classes
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MATH 8203 - Stochastic Calculus for Finance
An introduction to those aspects of partial differential equations and diffusion processes most relevant to finance, Random walk and first-step analysis, Markov property, martingales and semi-martingales, Brownian motion. Stochastic differential equations: Ito’s lemma, backward and forward Kolmogorov equations, the Feynman-Kac formula, stopping times, Hull and White Models, Cox-Ingersoll-Ross Model. Applications to finance including portfolio optimization and option pricing.
Credit Hours: (3)
Cross-listed Course(s): MATH 6203 .
Schedule of Classes
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MATH 8204 - Numerical Methods for Financial Derivatives
Introduction to numerical and computational techniques for solving both European- and American-style financial derivatives. The approach is the finite difference method and the basic theoretical concepts are introduced. Final projects involve implementing the techniques on computers. Some spectral and Monte Carlo methods are also be discussed.
Credit Hours: (3)
Cross-listed Course(s): MATH 6204 .
Schedule of Classes
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MATH 8206 - Stochastic Calculus for Finance II
The applications of stochastic calculus techniques to advanced financial modeling. Topics include: pricing of European, American, and fixed-income derivatives in the Black-Scholes and stochastic volatility models. The Jump-diffusion model is also introduced.
Credit Hours: (3)
Prerequisite(s): MATH 8203 or permission of department.
Cross-listed Course(s): MATH 6206
Schedule of Classes
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MATH 8273 - Advanced Finite Element Analysis
Selection of topics from such areas of finite element analysis as convergence theorems (Ciarlet), hierarchical basis functions, the h-p method, adaptive grid techniques and solution methods for nonlinear equations.
Credit Hours: (3)
Prerequisite(s): MATH 5172 and MATH 5174 , or permission of department.
Schedule of Classes
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MATH 8275 - Dynamical Systems I
Cycles and separatrix cycles, Poincaré first-return map: diffeomorphisms, Poincaré-Bendixson Theory, flows on the two-torus; structural stability, genericity, Peixoto’s theorem; singularities of planar systems. Degenerate singularities, Hopf bifurcation, saddle-node bifurcation, center bifurcation.
Credit Hours: (3)
Prerequisite(s): MATH 5143 and MATH 5173 , or permission of department.
Schedule of Classes
|
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-
MATH 8276 - Dynamical Systems II
Method of averaging, Melnikov functions, hyperbolic structure, symbolic dynamics, homoclinic and heteroclinic orbits, global bifurcations, infinite dimensional dynamical systems, inertial manifolds, Lyapunov exponents and dimension of attractors, codimension-two bifurcations, Duffing’s equation, Lorenz equations, finite dimensional systems of dimension at least three.
Credit Hours: (3)
Prerequisite(s): MATH 8275 or permission of department.
Schedule of Classes
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MATH 8490 - Industrial Internship
Full- or part-time academic year or summer internship in mathematics and/or statistics complementary to the student’s major course of study and designed to allow theoretical and course-based practical learning to be applied in a supervised industrial experience. Each student’s program must be approved by the department’s Graduate Program Director. Requires a mid-term report and final report to be graded by the supervising faculty. Credit hours gained from the internship may not be counted toward the courses leading to advancement to candidacy.
Credit Hours: (0 to 6)
Restriction(s): Completion of 6 credit hours of MATH/STAT/OPRS graduate courses and permission of department.
Grading Method: Graded on a Pass/Unsatisfactory basis.
Repeatability: May be repeated for credit up to 6 credit hours.
Schedule of Classes
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MATH 8891 - Independent Study in Mathematics
Faculty-directed independent study of topics not provided by other course offerings and/or to examine, extend, and enrich extant knowledge in mathematics through supervised individual study.
Credit Hours: (1 to 3)
Restriction(s): Permission of department
Repeatability: May be repeated for credit with change of topic.
Schedule of Classes
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MATH 8892 - Directed Project in Mathematics
The directed independent project may be original work, work of an expository nature, or the mathematical formulation and solution of a particular problem of mathematical significance. The project may also involve a specific application of techniques identified in the literature or studied in other courses. The project must be defended in an oral presentation.
Credit Hours: (1 to 3)
Restriction(s): Permission of department
Repeatability: May be repeated for credit up to 9 credit hours.
Schedule of Classes
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MATH 8994 - Doctoral Research and Reading
Investigation of a topic in mathematics culminating in a research paper.
Credit Hours: (0 to 9)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit.
Schedule of Classes
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MATH 8999 - Doctoral Dissertation Research
Individual investigation and research leading to the preparation of a doctoral dissertation.
Credit Hours: (1)
Restriction(s): Advancement to Candidacy.
Repeatability: May be repeated for credit.
Schedule of Classes
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Mathematics Education |
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MAED 5000 - Topics in Mathematics Education, Early Childhood
Major topics in early childhood mathematics education.
Credit Hours: (1 to 6)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with change of topic.
Schedule of Classes
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MAED 5040 - Topics in Mathematics Education, Intermediate
Major topics in mathematics education involving intermediate grades.
Credit Hours: (1 to 6)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with change of topic.
Schedule of Classes
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MAED 5070 - Topics in Mathematics Education, Secondary
Major topics in mathematics education involving secondary education.
Credit Hours: (1 to 6)
Restriction(s): Permission of department.
Repeatability: May be repeated for credit with change of topic.
Schedule of Classes
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MAED 5101 - Arithmetic in the School
A study of the number systems with emphasis placed upon the basic concepts and meanings, properties of addition, multiplication, inverses, systems of numeration and number line appropriate for each grade. (Does not count toward a major in mathematics. Open only to transfer students who have completed six credit hours of mathematics at another university.)
Credit Hours: (3)
Prerequisite(s): MATH 1100 or equivalent.
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MAED 5104 - Micro-computing for Teachers
Introduction to basic computer concepts, to microcomputer systems, to the design and development of programs to assist instruction in mathematics and computer sciences. A programming language such as BASIC or LOGO will be used. Students integrate skills learned by selecting, designing and developing a specific project. (No prior experience with computer programming required.)
Credit Hours: (3)
Restriction(s): Working knowledge of college algebra and trigonometry, and permission of department.
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MAED 5105 - Geometry for Teachers
A study of the foundations of Euclidean geometry and a brief treatment of non-Euclidean geometry. Emphasis on learning activities and teaching techniques for teachers of mathematics K-12.
Credit Hours: (3)
Prerequisite(s): MATH 2102, MAED 5101 , or permission of department.
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MAED 5141 - Mathematics for the Intermediate School Teacher
A study of the algebraic properties of the real numbers; functions, equations, inequalities and their graphs, activities and applications related to upper elementary and intermediate grades.
Credit Hours: (3)
Prerequisite(s): MATH 2102 or permission of department.
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MAED 5232 - Teaching Mathematics to Middle School Learners
Initial teaching methods course for middle school mathematics teachers. Focuses on secondary school mathematics and its relation to the K-12 curriculum. Topics include: the development of teaching strategies and activities in middle school mathematics with an emphasis on problem solving, mathematical connections, communication and assessment, including schoolbased field experiences.
Credit Hours: (3)
Restriction(s): Admission to the MAT Program (Middle Grades mathematics emphasis) or permission of department.
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MAED 5252 - Teaching Mathematics to Secondary School Learners
The initial teaching methods course for secondary school mathematics teachers. Focuses on secondary school mathematics and its relation to the K-12 curriculum. Topics include: the planning and implementation of high quality mathematics lessons with an emphasis on problem solving, mathematical connections, and communication, including school-based field experiences.
Credit Hours: (3)
Prerequisite(s): MDSK 5204 , MDSK 6162 , and MDSK 6162L
Corequisite(s): MDSK 5100L
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MAED 6122 - Theoretical Foundations of Learning Mathematics
Introduction to theories of learning that have influenced the teaching of mathematics in K-12. An overview of theories that have guided reforms in mathematics teaching; contemporary constructivist theories of mathematics learning.
Credit Hours: (3)
Restriction(s): Admission into the M.S. in Mathematics with Concentration in Mathematics Education program.
Cross-listed Course(s): EDCI 8112
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MAED 6123 - Research in Mathematics Education
An introduction and overview of research in the teaching and learning of mathematics in K-12. Overview of contemporary research perspectives and paradigms; interpreting and synthesizing the research literature; survey of contemporary research problems in mathematics teaching and learning; development of classroombased research studies.
Credit Hours: (3)
Restriction(s): Admission into the M.S. in Mathematics with Concentration in Mathematics Education program.
Cross-listed Course(s): EDCI 8113
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MAED 6124 - Issues in the Teaching of Secondary School Mathematics
Study of major issues affecting secondary mathematics education: analysis of the impact of learning theories on methods of teaching; assessment methods for improving mathematics learning; analysis of the historical and programmatic development of the secondary school mathematics curriculum leading to current trends, issues, and problems; and analysis of the role of technology in the secondary mathematics classroom.
Credit Hours: (3)
Restriction(s): Admission into the M.S. in Mathematics with Concentration in Mathematics Education program.
Cross-listed Course(s): EDCI 8115
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MAED 6252 - Advanced Methods in Middle and Secondary Mathematics Education
Examination of current research and scholarship on the teaching of mathematics in middle and secondary schools. Particular emphasis on the development of advanced instructional expertise and leadership.
Credit Hours: (3)
Restriction(s): Enrollment in the MAT or M.Ed. program.
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MAED 8124 - Advanced Topics in Mathematics Education
Advanced research topics in the teaching and learning of mathematics. Includes a survey, interpretation, and synthesis of contemporary research problems in mathematics teaching and learning.
Credit Hours: (3)
Restriction(s): Enrollment in the Mathematics Education specialization of the Ph.D. in Curriculum and Instruction program.
Repeatability: May be repeated for credit with change of topic.
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MAED 8160 - Readings in Mathematics Education
Readings in the teaching and learning of mathematics K-16; analysis of the historical development of the K-16 mathematics curriculum leading to current trends, issues, and problems; theory, methods, and techniques for assessment; and analysis of contemporary issues impacting the teaching of mathematics.
Credit Hours: (3)
Restriction(s): Enrollment in the Mathematics Education specialization of the Ph.D. in Curriculum and Instruction program.
Schedule of Classes
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