Xu Zhang

Directed reading on advanced topics in mathematics.Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours.Prerequisite(s): Consent of instructor and student's advisory committee.

A continuation of MATH 2144, including techniques of integration, series and their applications, parametric equations, and polar coordinates. Previously offered as MATH 2155, MATH 2163, and MATH 2365.Prerequisite(s): MATH 2144 with grade of 'C' or better.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Directed reading and research culminating in preliminary doctoral research project.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

A guided program of independent reading and research under the direction of a faculty member. The project culminates in an oral presentation, and a written report also approved by a second faculty reader. Required for graduation with Departmental honors in mathematics.Prerequisite(s): Consent of instructor, senior standing, and Honors Program participation.

Introduction to derivative pricing and market derivatives. Introduction to the Ito-Doeblin calculus and martingales; the martingale properties of Brownian motion, the Black-Scholes-Merton theory as a simple, special case of martingale pricing, market models of modern fixed income pricing. Insurance, hedging, and options.Prerequisite(s): MATH 4143 or MATH 5043, STAT 4203 or consent of instructor.

Advanced machine computing, algorithms, analysis of truncation and rounding errors, convergence and stability applied to discrete variables, finite elements, and spectral methods in ordinary and partial differential equations.Prerequisite(s): MATH 4233, MATH 4513 or CS 4513.

A guided program of independent reading and research under the direction of a faculty member. This course may serve as the first part of a two-semester senior thesis or senior honors thesis experience.Prerequisite(s): Consent of instructor, junior or senior standing.

Directed reading on advanced topics in mathematics.Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours.Prerequisite(s): Consent of instructor and student's advisory committee.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Theory and practice of finite element methods, including elliptic boundary value problems, weak formulations, the Ritz-Galerkin method, conforming and non-conforming finite elements, error estimates, and numerical experiments.Prerequisite(s): MATH 4023; MATH 4263; and MATH 4513 or CS 4513 or equivalent. MATH 4143 or MATH 5043 preferred.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Selected mathematical problems from industry. Independent problem-solving, oral presentation of solutions, and technical report writing. Seminar-style format.Offered for variable credit, 1-3 credit hours, maximum of 6 credit hours.Prerequisite(s): MATH 2233, MATH 4013, and knowledge of computer programming.

Introduction to derivative pricing and market derivatives. Introduction to the Ito-Doeblin calculus and martingales; the martingale properties of Brownian motion, the Black-Scholes-Merton theory as a simple, special case of martingale pricing, market models of modern fixed income pricing. Insurance, hedging, and options.Prerequisite(s): MATH 4143 or MATH 5043, STAT 4203 or consent of instructor.

Computer arithmetic and round-off errors, numerical solution to nonlinear equations, interpolation, numerical differentiation and integration, numerical solutions to ordinary differential equations, error analysis for numerical solutions and approximations. Additional topics may include direct and iterative solutions for linear systems for equations. Same course as CS 4513. May not be used for degree credit with MATH 5513.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better and knowledge of programming, or consent of instructor.

Computer arithmetic and round-off errors, numerical solution to nonlinear equations, interpolation, numerical differentiation and integration, numerical solutions to ordinary differential equations, error analysis for numerical solutions and approximations. Additional topics may include direct and iterative solutions for linear systems of equations. Same course as MATH 4513. May not be used for degree credit with MATH 5513.Prerequisite(s): MATH 2233 and MATH 3013, each with a grade of 'C' or better, knowledge of programming or consent of instructor.

Computer arithmetic and round-off errors, numerical solution to nonlinear equations, interpolation, numerical differentiation and integration, numerical solutions to ordinary differential equations, error analysis for numerical solutions and approximations. Additional topics may include direct and iterative solutions for linear systems of equations. May not be used for degree credit with MATH 4513 or CS 4513.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better and knowledge of programming, or consent of instructor.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Selected mathematical problems from industry. Independent problem-solving, oral presentation of solutions, and technical report writing. Seminar-style format.Offered for variable credit, 1-3 credit hours, maximum of 6 credit hours.Prerequisite(s): MATH 2233, MATH 4013, and knowledge of computer programming.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.