Applied Mathematics Graduate Curriculum Guide

NORTH CAROLINA A&T STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS 

CURRICULUM GUIDE FOR M.S. DEGREE IN APPLIED MATHEMATICS

 

A student seeking the Master of Science in Applied Mathematics must complete the following:

  • 30 credit hours of graduate course work.
  • Three core courses (9 credit hours): MATH 603, 651, and 690.
  • A thesis or a project.
  • Master’s Comprehensive Examination (MATH 788: 0 credit hour)

 

Thesis option:

  • Take 9 credit hours of 700 level MATH courses with approval of advisor
  • Take 6 credit hours of additional graduate courses with approval of advisor
  • Master’s Thesis (MATH 797: 6 credit hours)
  • Pass Master’s Thesis defense

Project Option:

  • Take 9 credit hours of 700 level MATH courses with approval of advisor
  • Take 9 credit hours of additional graduate courses with approval of advisor
  • Graduate Design Project (MATH 796: 3 credit hours)
  • Pass Graduate Design Project oral examination

 

NORTH CAROLINA A&T STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS

APPLIED MATHEMATICS GRADUATE FACULTY

Shea D. Burns, Associate Professor
Education: B.S., North Carolina A&T State University; M.S., Ph.D., Howard University

Research Areas: Topological Groups, Semi-groups

Office: 128 Marteena Hall

Office Phone: 336-285-2069

E-mail: sburns@ncat.edu

 

Mingxiang Chen, Professor and Mathematics (Applied Mathematics) Program Coordinator
Education: B.S. and M.S., Huazhong Normal University; Ph.D., Georgia Institute of Technology

Research Areas: Dynamical Systems, Differential Equations

Office: 234 Marteena Hall

Office Phone: 336-285-2070

E-mail: chen@ncat.edu

 

Dominic P. Clemence, Professor
Education: B.S., North Carolina A&T State University; M.S., Ph.D., Virginia Polytechnic Institute and State University

Research Areas: Dynamical Systems, Differential Equations

Office: 110 Marteena Hall

Office Phone: 336-285-2076

E-mail: clemence@ncat.edu

 

Kathy M. Cousins-Cooper, Associate Professor and Secondary Education (Mathematics Education) Program Coordinator
Education: B.S., Virginia Polytechnic Institute and State University; M.S., North Carolina A&T State University; Ph.D., University of South Florida

Research Areas: Mathematics Education, Teacher Training

Office: 201A Marteena Hall

Office Phone: 336-285-2074

E-mail: cousinsk@ncat.edu

 

Ahmad A. Deeb, Adjunct Assistant Professor (Associate Graduate Faculty)
Education: B.S., Yarmouk University; M.S., Ohio University; Ph.D., Kent State University

Research Areas: Mathematical Education

Office: 228 Marteena Hall

Office Phone: 336-285-2075

E-mail: @ncat.edu

 

Zachary Denton, Assistant Professor
Education: B.S., Middle Tennessee State University; M.S. and Ph.D., University of Louisiana at Lafayette

Research Areas: Fractional Differential Equations

Office: 123A Hines Hall

Office Phone: 336-285-4756

E-mail: zdenton@ncat.edu

 

Kossi D. Edoh, Associate Professor
Education: B.S., University of Cape Coast; M.S. and Ph.D., Simon Fraser University

Research Areas: Information Security, Numerical Analysis.

Office: Marteena Hall

Office Phone: 336-285-2073

E-mail: kdedoh@ncat.edu

 

Gregory Gibson, Associate Professor
Education: B.A., State University of New York/College at Geneseo; M.S. and Ph.D., North Carolina State University

Research Areas: Group Theory, Lie Algebras

Office: 208 Marteena Hall

Office Phone: 336-285-2078

E-mail: gagibson@ncat.edu

 

Seong-Tae Kim, Assistant Professor

Education: B.A., Hanyang University; M.A., Korea University; M.S. and Ph.D., North Carolina State University

Research Areas: Time Series Analysis, Statistical Genetics

Office: 123B Hines Hall

Office Phone: 336-285-4758

E-mail: skim@ncat.edu

 

Alexandra Kurepa, Professor and Applied Mathematics Graduate Program Coordinator
Education: B.S. and M.S., University of Zagreb; Ph.D., University of North Texas

Research Areas: Ordinary & Partial Differential Equations

Office: 111 Marteena Hall

Office Phone: 336-285-2079

E-mail: kerupa@ncat.edu

 

Liping Liu, Associate Professor
Education: B.S., Huazhong University of Science and Technology; Ph.D, University of Alberta

Research Areas: Dynamical Systems, Mathematical Modeling

Office: A431 General Classroom Building

Office Phone: 336-285-3519

E-mail: lliu@ncat.edu

 

Nicholas Luke, Associate Professor and Student Success Coordinator
Education: B.S., North Carolina A&T State University; M.S. and Ph.D, North Carolina State University

Research Areas: Mathematical Modeling, Biomathematics

Office: 107 Marteena Hall

Office Phone: 336-285-3520

E-mail: luke@ncat.edu

 

Janis M. Oldham, Associate Professor and Mathematics Program Coordinator
Education: B.A., University of Chicago; M.S., Purdue University; Ph.D., University of California-Berkeley
Research Areas: Differential Geometry, Mathematical Education

Office: 202 Marteena Hall

Office Phone: 336-285-2084

E-mail: oldhamj@ncat.edu

 

Suzanne M. O’Regan, Assistant Professor
Education: B.S., University College Cork; Ph.D., University College Cork

Research Areas: Biomathematics, Mathematical Epidemiology

Office: A430 General Classroom Building

Office Phone: 336-285-3502

E-mail: smoregan@ncat.edu

 

Choongseok Park, Assistant Professor

Education: B.S., Yonsei University; Ph.D., Ohio State University

Research Areas: Mathematical Neuroscience, Ordinary Differential Equations

Office: 123C Hines Hall

Office Phone: 336-285-4973

E-mail: cpark@ncat.edu

 

Yevgeniy A. Rastigejev, Associate Professor
Education: M.S., Moscow Institute of Physics and Technology; M.S. and Ph.D., University of Notre Dame

Research Areas: Partial Differential Equations, Atmospheric Science, Combustion

Office: 308 Gibbs Hall

Office Phone: 336-285-2223

E-mail: yarastig@ncat.edu

 

Thomas C. Redd, Associate Professor & Associate Chairperson
Education: B.S., Fort Valley State University; M.S., University of Oklahoma; M.S. and Ph.D., Brown University

Research Areas: Lagrangian Dynamics, Mixing and Curve Matching

Office: A441 General Classroom Building

Office Phone: 336-285-3530

E-mail: tcredd@ncat.edu

 

John P. Roop, Associate Professor
Education: B.S., Roanoke College; M.S. and P.h.D., Clemson University

Research Areas: Numerical Analysis, Mathematical Modeling

Office: 233A Marteena Hall

Office Phone: 336-285-20

E-mail: jproop@ncat.edu

 

Guoqing Tang, Professor and Chairperson
Education: B.S., Anhui University; M.S., Nanjing University of Science and Technology; Ph.D., Rutgers University

Research Areas: Differential Geometric Optimal Control, Mathematical Modeling

Office: 102B Marteena Hall

Office Phone: 336-285-2089

E-mail: tang@ncat.edu

 

Barbara Tankersley, Associate Professor and Retention & Advisement Coordinator
Education: B.S., Paine College; M.S., North Carolina A&T State University; M.S. and Ph.D., Howard University

Research Areas: Combinatorics (Enumerative), Mathematical Education

Office: Marteena Hall

Office Phone: 336-285-2090

E-mail: tankers@ncat.edu

 

Paramanathan Varatharajah, Associate Professor
Education: B.S., University of Jaffna; M.S. and Ph.D., University of Arizona

Research Areas: Nonlinear Optics, Wave Propagation

Office: Marteena Hall

Office Phone: 336-285-2091

E-mail: rajah@ncat.edu

 

John Paul Ward, Assistant Professor

Education: B.S., University of Georgia; Ph.D., Texas A&M University

Research Areas: Applied Harmonic Analysis, Signal and Imaging Processing

Office: 323 Hines Hall

Office Phone: 336-285-2080

E-mail: jpward@ncat.edu

 

A. Giles Warrack, Associate Professor and Mathematics (Statistics) Program Coordinator
Education: B.S. and M.S., California State Polytechnic University; Ph.D., University of Iowa

Research Areas: Probability Theory, Statistical Inferences

Office: 230 Marteena Hall

Office Phone: 336-285-2092

E-mail: warrack@ncat.edu

 


 

NORTH CAROLINA A&T STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS

GRADUATE MATHEMATICS COURSES

MATH 600. Introduction to Modern Mathematics for Secondary School Teachers. Credit 3(3-0)

Elementary theory of sets, elementary logic and propositional systems, nature and methods of mathematical proofs, structure of the real number system will be studied. Evaluation of instructional software and use of computer integrated instruction to teach pertinent concepts in secondary school mathematics will also be included. Prerequisite: Consent of the instructor. (DEMAND)

MATH 601. Tech App Sec School Math. Credit 3(3-0)

 This course covers techniques of teaching algebra, advanced algebra, trigonometry, and other secondary mathematics using graphing calculators, software packages and other technology. Prerequisite: Consent of the instructor. (DEMAND)

MATH 602. Modern Algebra. Credit 3(3-0)

This course covers mappings, binary operations, groups, rings, integral domains, fields, and some applications to coding and cryptography. Prerequisite: MATH 211 or consent of the instructor. (DEMAND)

MATH 603. Introduction to Real Analysis. Credit 3(3-0)

The following topics will be covered in this course: elementary set theory, functions, axiomatic development of the real numbers, metric spaces, convergent sequences, completeness, compactness, connectedness, continuity, limits, sequences of functions, differentiation, the mean value theorem, Taylor’s theorem, Riemann integration, infinite series, the fixed point theorem, partial differentiation, and the implicit function theorem. Prerequisite: MATH 211 or consent of the instructor. (DEMAND)

MATH 604. Modern Geometry for Secondary School Teachers. Credit 3(3-0)

Re-examination of Euclidean geometry, axiomatic systems and the Hilbert axioms, introduction to projective geometry and other non-Euclidean geometries will be included. Prerequisite: MATH 600 or consent of instructor. (DEMAND)

MATH 607. Theory of Numbers. Credit 3(3-0)

Divisibility properties of the integers, the Euclidean algorithm, congruences, diophantine equations, number-theoretic functions and continued fractions will be studied. Prerequisite: Twenty hours of college mathematics. (DEMAND)

MATH 608. Methods of Applied Statistics. Credit 3(3-0)

This course introduces the SAS programming language, and uses it in the analysis of variance, both single and multifactor. It includes various methods of hypothesis testing and constructing confidence intervals. The course covers simple and multiple linear regression, including model building and variable selection techniques. Elements of time series and categorical data analysis are covered. Prerequisite: MATH 224. (DEMAND)

MATH 610. Complex Variables. Credit 3(3-0)

The following topics will be covered in this course: complex number systems, limits of complex sequences, complex functions, continuity, limits of functions, derivatives, elementary functions, Cauchy-Riemann equations, Prerequisite: Math 341 or consent of instructor. (DEMAND)

MATH 620. Elements of Set Theory and Topology. Credit 3(3-0)

Operations on sets, indexed families of sets, products of sets, relations, functions, metric spaces, general topological spaces, continuity, compactness and connectedness will be included. Prerequisites: MATH 231 and consent of the instructor. (DEMAND)

MATH 623. Probability Theory and Applications. Credit 3(3-0)

This course begins with an introduction to sample spaces and probability, including combinatorics. It covers continuous and discrete random variables, including multi-variate random variables and expectations; also marginal and conditional distributions are derived. The course introduces moment generating functions, and covers the central limit theorem and its applications. Prerequisite: MATH 231. (DEMAND)

MATH 624. Theory and Methods of Statistics. Credit 3(3-0)

This course introduces methods of statistical estimation and inference including the following topics: sufficient statistics, confidence sets, hypothesis tests, and maximum likelihood methods. The theory of uniformly most powerful tests and the Neyman-Pearson Lemma are covered. Other topics include least squares estimation, the linear model, and Bayesian methods. Prerequisite: MATH 623. (DEMAND)

MATH 625. Mathematics for Elementary Teachers, K-8. Credit 3(3-0)

This course is designed for in-service and prospective teachers who have as their goal to teach the basic skills and competencies of mathematics sought in today's world. The course emphasizes that the teacher first, must have the knowledge and skills in order to accomplish this goal. It stresses fundamentals of arithmetic, sets and operations, number systems, fractions, decimals, percents, estimation, consumer arithmetic, problem solving and traditional and metric geometry and measurement. (DEMAND)

 

MATH 631. Linear and Non-Linear Programming. Credit 3(3-0)

This course includes optimization subject to linear constraints; transportation problems, SIMPLEX algorithm; network flows; application of linear programming to industrial problems and economic theories; introduction to non-linear programming. Prerequisites: MATH 350 and a high level programming language. (DEMAND)

MATH 632. Games and Queue Theory. Credit 3(3-0)

This course is a general introduction to game theory; two-person-non-zerosum-non-cooperative games; two-person cooperative games; reasonable outcomes and values; the minimax theorem. Introduction to queuing theory; single server queuing processes; many serve queuing processes; applications to economics and business. Prerequisite: MATH 224, MATH 351, or consent of the instructor. (DEMAND)

MATH 633. Stochastic Processes. Credit 3(3-0)

This course begins with a review of Probability and Random Variables. Markov Processes, Poisson Processes, Waiting Times, Renewal Phenomena, Branching Processes, Queuing System, Service Times are covered. Prerequisite: MATH 623 or consent of the instructor. (DEMAND)

MATH 650. Ordinary Differential Equations. Credit 3(3-0)

This is an intermediate course in ordinary differential equations with emphasis on applications. Topics include linear systems and various phase plane techniques for non-linear ordinary differential equations. Prerequisite: MATH 341. (DEMAND)

MATH 651. Partial Differential Equations. Credit 3(3-0)

This course includes introduction to complex variables and residue calculus, transform calculus, higher order partial differential equations governing various physical phenomena, nonhomogeneous boundary value problems, orthogonal expressions, Green’s functions and variational principles. Prerequisites: MATH 341 and 432. (DEMAND)

MATH 652. Methods of Applied Mathematics. Credit 3(3-0)

This course covers matrix theory, systems of linear equations, vector spaces, eigenvalue problem and its applications to systems of linear ODEs and mechanical vibrations, the simplest problems of calculus of variations, Euler equations, boundary conditions, extensions of Euler equations, Hamilton's Principles, constraints and Lagrange multipliers, introduction to integral equations, and solutions in iterative and other methods. Prerequisites: MATH 341 and 432. (DEMAND)

 

 

MATH 665. Principles of Optimization. Credit 3(3-0)

Algebra, linear inequalities, duality, graph, transport network; linear programming; special algorithms; selected applications. An upper level course. Prerequisites: MATH 231 or equivalent and MATH 240 and 351. (DEMAND)

MATH 675. Graph Theory. Credit 3(3-0)

Varieties of graphs, graph theory algorithms, and applications of graph theory to other disciplines will be studied. Prerequisite: MATH 351. (DEMAND)

MATH 685. Special Topics in Applied Mathematics. Credit 3(3-0) (Formerly MATH 691)

Topics are selected from differential equations, numerical methods, operations research, applied mechanics and from other fields of applied mathematics. Prerequisites: Senior or graduate standing and consent of the instructor. (DEMAND)

MATH 690. Scientific Programming for Mathematical Scientists. Credit 3(1-4)

This course covers the implementation of the computer in the Mathematical sciences. MATLAB will be used to apply algorithms and solve problems in areas such as differential equations and linear algebra. Probability and statistical problems will be studied through the R language. Prerequisites: Senior or graduate standing or consent of instructor.

MATH 700. Theory of Functions of One Real Variable I. Credit 3(3-0)

 The focus of this course is a careful study of the fundamental theorems of Lebesgue theory, including Lebesgue measure, differentiation and integration on the real line. Topics from set theory and point set topology are also included in this course. Prerequisite: MATH 377 or equivalent.

MATH 701. Theory of Functions of One Real Variable II. Credit 3(3-0)

This course is a continuation of MATH-700. The following topics will be covered in this course: general measure and integration, measure and outer measure, and some basic topics from functional analysis. Prerequisite: MATH 700. (DEMAND)

MATH 705. Graduate Seminar. Credit 1(1-0)

The seminars will present current developments and ideas in applied mathematics and computational science. Topics explored may consist of material from various mathematics and computational science journals, including discussion of research by faculty and students. This course may be repeated for up to 3 credit hours. Prerequisite: Graduate Standing.

 

MATH 706. Categorical Data Analysis. Credit 3(3-0)

This course will include the following topics: Two-Way Contingency Table Inference for Two-Way Table, Models for Binary Response Variables, Log-linear Models, Testing in Loglinear Models, Multinomial Response Models and Estimation Theory for Parametric Models, and Computer Analysis of Categorical Data. Prerequisite: MATH 624. (DEMAND)

MATH 708. Nonparametric Statistics. Credit 3(3-0)

 

The following topics will be discussed in this course: Order Statistics, Run Test for Trend, Goodness of Fit Tests, Rank Tests for One and Two Populations, Linear Rank Statistics, One-Way and Two-Way Nonparametric Analysis of Variance, and applications to practical problems. Prerequisite: MATH 624. (DEMAND)

MATH 709. Discrete Mathematics. Credit 3(3-0)

This course covers topics in discrete mathematics that are taught at the secondary school level, Topics covered include a review of logic, proofs and set theory; functions and relations; recursive and non-recursive sequences; graphs and graph algorithms; directed graphs, trees and traversal algorithms, combinatorics; introduction to probability; and applications in political theory. Methods of teaching these topics will be discussed. (DEMAND)

MATH 710. Theory of Functions of One Complex Variable. Credit 3(3-0)

This course includes basic theory of analytic functions, including Cauchy's theorem, conformal mappings, Taylor and Laurent series, and residue theory. Prerequisite: MATH- 377 or equivalent. (DEMAND)

MATH 712. Numerical Linear Algebra. Credit 3(3-0)

Numerical analysis for solution of linear systems, approximation methods foreign values and eigenvectors, least squares solutions, ill-posed and ill-conditioned systems and error analysis are covered. Prerequisite: One programming language, MATH 351 or equivalent. (DEMAND)

MATH 713. Internship. Credit 6(6-0)

Internship for Master's of Arts in Teaching students. (DEMAND)

MATH 717. Special Topics in Algebra. Credit 3(3-0)

This course covers selected topics in algebra. Topics covered will be determined by the instructor. Prerequisites: Consent of the instructor and graduate standing. (DEMAND)

 

 

MATH 720. Special Topics in Analysis. Credit 3(3-0)

This course covers selected topics in analysis. Topics covered will be determined by the instructor. Prerequisites: Consent of the instructor and graduate standing. (DEMAND)

MATH 721. Multivariate Statistical Analysis. Credit 3(3-0)

Multivariate normal distribution, inference about a mean vector, comparison of several multivariate means, analysis of Covariance Structure, Analysis of Dispersion, classification and Clustering Techniques and Some Applications of Multivariate Tests will be discussed in this course. Also, practical examples of industrial use will be addressed. Prerequisites: MATH 608 and MATH 624. (DEMAND)

MATH 723. Advanced Topics in Applied Mathematics. Credit 3(3-0)

This course is designed to cover important topics in applied mathematics that may be desired from time to time for specific students in the graduate program. It may also be used as a vehicle for development of new courses for graduate program students. Prerequisite: consent of the instructor. (DEMAND)

MATH 731. Advanced Numerical Methods. Credit 3(3-0)

This course covers numerical methods for solution of parabolic, elliptic and hyperbolic boundary value problems. Problems are selected from engineering applications. Both finite difference and finite element methods are studied. Prerequisite: MATH 340 or 360 or equivalent. (DEMAND)

MATH 733. Advanced Probability & Stochastic Process. Credit 3(3-0)

The following topics will be discussed in this course: introduction to Lebesque integration. probability theory and random variables, laws of large numbers, central limit theorems, random walks, martingales, Markov processes and Markov chains, ergodic theorems and Brownian motion. Prerequisite: MATH 603 or permission of the instructor. (DEMAND)

MATH 752. Calculus Variations and Control Theory. Credit 3(3-0)

This course covers the following topics: functionals, Euler's equation, Lagrange multipliers. Kuhn-Tucker conditions, Pontryagin maximum principle, Weiserstrass- Edmann corner conditions. Euler-Legrange equations; first and second variational problems. Applications to engineering areas will also be included. Prerequisites: MATH 332 and MATH 432 or equivalent. (DEMAND)

MATH 761. Interdisciplinary Computational Science Project I. Credit 3(3-0)  (Formerly MATH 791)

This course continues development of skills required for independent research or problem-solving in the realm of computational science. The course requires completion of an agreed upon computational project, based upon a sound literature review, under the guidance of the instructor. Prerequisite: MATH 371 or equivalent. (DEMAND)

MATH 762. Interdisciplinary Computational Science Project II. Credit 3(3-0) (Formerly MATH 792)

This course continues development of skills required for independent research or problem-solving in the realm of computational science. The course requires completion of an agreed upon computational project, based upon a sound literature review, under the guidance of the instructor. Prerequisite: MATH 761. (DEMAND)

MATH 781. Mathematical & Computational Modeling. Credit 3(3-0)

This course explores the steps required to model and simulate a system, including discussion of generic governing equations, grid generation, basic numerical schemes, simulation strategies, and data analysis. Both discrete and continuous methods used in scientific applications will be examined. Representative applications include weather prediction, molecular dynamics, scheduling problems, and engine combustion modeling. Prerequisite: MATH 371 or equivalent. (DEMAND)

MATH 782. Scientific Visualization. Credit 3(3-0)

This course explores concepts and techniques for visualization and its implementation, with emphasis on the use of visualization tools in mathematical simulation modeling. The course will provide practical experience with visualization packages in both X-Windows and mainframe environments. Prerequisite: MATH 781. (DEMAND)

MATH 788. Master's Comprehensive Exam. Credit 0(0-0)

Examination. (DEMAND)

MATH 796. Graduate Design Project. Credit 3(3-0)  (Formerly MATH 725)

This course requires independent project work on an advanced mathematical topic of interest to the student and a faculty member acting as the student's advisor. The topic must be approved by the advisor. Prerequisite: Consent of the instructor. (DEMAND)

MATH 797. Thesis Research in Mathematics. Credit 3(3-0) (Formerly MATH 730)

Students who select the thesis option must do advanced research in an area of interest. The research topic must be approved by the thesis advisor. (DEMAND)

MATH 799. Continuation of Thesis for Mathematics. Credit 1(1-0) (Formerly MATH 799)

Continuation of MATH 797. (DEMAND)