Course Requirements

Required Courses
Semester
Hours
MATH 6011: Real Analysis I Fall 3
MATH 6580: Computational Linear Algebra Fall 3
MATH 6200: Applied Partial Differential Equations Spring 3
MATH 6350: Numerical Analysis (3 Hours) Fall 3
MATH 6610: Mathematical Models Spring 3
MATH 6120: Statistical Theory I Fall 3
MATH 6960: Graduate Seminar Fall 3
MATH 6630: Topics in Mathematical Biology Spring 3
MATH 6965: Research Seminar
or
MATH 6990: Graduate Project
or
An approved interdisciplinary course from the list below:
MPHI 8001: Public Health Informatics
QUAN 6610: Operations Research
STAT 7010: Biostatistics I
STAT 7020: Biostatistics II
STAT 7070: Biomedical Statistics
STAT 6300: Introduction to Epidemiology and Biostatistics
STAT 7650: Introduction to Stochastic Processes
Spring


Spring/Fall



Variable
(Interdisciplinary elective)
3
Electives: 9 hours selected from the list below
Fall/Spring
9

MATH 6130: Statistical Theory (3 hours)
MATH 6220: Dynamical Systems (3 hours)
MATH 6400: Combinatorial Mathematics (3 hours)
MATH 6420: Graph Theory (3 hours)
MATH 6620: Mathematical Optimization (3 hours)
MATH 6980: Special Topics (3 hours)
MATH 6990: Graduate Project (3 hours)*

*MATH 6990 may be repeated a second time for an additional three hours if there is ongoing work which is likely to yield a peer-reviewed publication.

Total Semester Credit Hours
 
36


Sample Program of Study

Semester 1
Course Hours
MATH 6011 Real Analysis I 3
MATH 6580 Computational Linear Algebra 3
MATH 6350 Numerical Analysis 3
Subtotal 9
Semester 2
Course Hours
MATH 6200 Applied Partial Differential Equations 3
MATH 6610 Mathematical Models 3
Elective 3
Subtotal 9
Semester 3
Course Hours
MATH 6120 Statistical Theory I 3
Elective 3
MATH 6960 Graduate Seminar 3
Subtotal 9
Semester 4
Course Hours
MATH 6630 Topics in Mathematical Biology 3
Elective 3
MATH 6990 Graduate Project or MATH 6965: Research Seminar 3
Comprehensive Master's Exam** N/A
Subtotal 9
TOTAL HOURS In PROGRAM
36


Course Descriptions

MATH 6011 – Real Analysis I (3 hours) 3-0-0-3
A study of the real number system and functions. Topics include sequences, limits, continuity, differentiation and integration. Prerequisite(s): Permission of instructor.

MATH 6120 – Statistical Theory I (3 hours) 3-0-0-3
Fundamentals of random variables and probability theory, discrete, and continuous distributions, exponential families, joint, marginal, and conditional distributions, functions of random variables, transformation and change of variables, order statistics, convergence concepts, central limit theorem, sampling distributions.

MATH 6130 – Statistical Theory II (3 hours) 3-0-0-3
Point and interval estimation, hypothesis testing, maximum likelihood and moment estimators, Bayes estimators, unbiased estimators, sufficiency and completeness, Fisher information, uniformly most powerful tests, likelihood ratio tests, asymptotic inference, introduction to Bayesian inference Fundamentals of random variables and probability theory, discrete, and continuous distributions, exponential families, joint, marginal, and conditional distributions, functions of random variables, transformation and change of variables, order statistics, convergence concepts, central limit theorem, sampling distributions.Fundamentals of random variables and probability theory, discrete, and continuous distributions, exponential families, joint, marginal, and conditional distributions, functions of random variables, transformation and change of variables, order statistics, convergence concepts, central limit theorem, sampling distributions. 

MATH 6200 - Applied Partial Differential Equations (3 hours) 3-0-0-3
An advanced course in partial differential equations. First order conservation laws and general nonlinear and quasilinear first order partial differential equations are solved. Hyperbolic systems are solved by characteristic variables. Riemann's function, Green's function and similarity variable methods are introduced.

MATH 6220 - Dynamical Systems (3 hours) 3-0-0-3
A course in continuous dynamical systems.  Includes linear systems and the local, global and bifurcation theory of nonlinear systems.  Applications to systems arising in mechanics, biology, ecology, etc. will be discussed. 

MATH 6350 – Numerical Analysis (3 hours) 3-0-0-3
Further study of numerical approximations and algorithms, including the solution of non-linear equations and systems of equations, numerical differentiation and integration, interpolation and approximation, and the numerical solution of initial value problems. Prerequisite(s): Permission of instructor.

MATH 6400 - Combinatorial Mathematics (3 hours) 3-0-0-3
A course covering both elementary and advanced topics in combinatorial mathematics.  Basic concepts such as inclusion-exclusion, recurrence relations and generating functions will be covered and more advanced topics may include the calculus of finite differences, Mobius and binomial inversion, partially ordered sets, and algebraic combinatorics.

MATH 6420 – Graph Theory (3 hours) 3-0-0-3
A study of graphs, subgraphs, paths, arcs, trees, circuits, digraphs, colorability. Additional topics from topological and algebraic graph theory will also be presented.

MATH 6580 - Computational Linear Algebra (3 hours) 3-0-0-3
This course provides an introduction to computational linear algebra. Topics include direct and iterative methods for solving linear systems, error analysis, least squares problems, eigenvalue problems, Newton’s and Quasi-Newton methods for systems of nonlinear equations. 

MATH 6610 - Mathematical Models (3 hours) 3-0-0-3
Introduction to model development for physical and biological applications including analytical and numerical solution techniques and validation and verification techniques. Includes a study of examples of existing models chosen from physical, biological, social, and management sciences (e.g. conservation laws, heat transfer, fluid flow, population and disease models). Written and oral report is required for at least one of the models studied. Knowledge of a high-level programming language strongly recommended.

MATH 6620 - Optimization (3 hours) 3-0-0-3
Newton's method and Quasi-Newton methods for nonlinear equations and optimization problems, globally convergent extensions, applications to differential equations, integral equations and general minimization problems. The course may involve use of a high-level programming language.

MATH 6630 - Topics in Mathematical Biology (3 hours) 3-0-0-3 
Deterministic and stochastic models in biology and the health-related sciences.

MATH 6960 - Graduate Seminar (3 hours) 1-1-1-3
A series of seminars on topics in current mathematical research.

MATH 6965 - Research Seminar (3 hours) 0-1-2-3
A course in which students gain familiarity with current mathematical research.  This course will feature directed readings of topics selected from recent mathematical literature, culminating with each student giving multiple presentations for the Department’s regularly scheduled Applied Mathematics Seminar; attendance at the seminar talks throughout the semester will be required.

MATH 6980 - Special Topics
Catalog description: This course is designed to cover special topics in mathematics that are not covered in regular courses. The topics will depend on the research interests of the instructor and the students.

Prerequisite: Graduate status and permission of instructor.

MATH 6990 - Graduate Project
Catalog description: This course is an in-depth research experience, conducted under the direction of a faculty member, culminating in a written paper and seminar presentation.  This project may be expository in nature or may involve original research.   The course may be repeated when a project is likely to produce a peer-reviewed publication.

Prerequisite: At least 12 hours of MATH courses numbered 6000 or higher.

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