Department of Mathematics
http://www.ncat.edu/~math/
Wilbur L. Smith, Chairperson

OBJECTIVES

The objectives of the Mathematics Department are as follows:

1. to prepare students for employment in government or industry as well as graduate studies;
2. to avail students of the opportunity to undertake independent investigations in mathematics;
3. to prepare students to teach and present mathematics in a modern, meaningful, and stimulating manner at secondary school level;
4. to provide courses which ensure acquisition of basic mathematical skills and concepts for all students at the university;
5. to encourage wide ranging professional growth and research by faculty;
6. to encourage faculty involvement in university, college, and departmental governance, as well as in community activities;
7. to understand and effectively respond to student retention and graduation rates.

DEGREES OFFERED

Applied Mathematics – Bachelor of Science
Mathematics – Bachelor of Science
Applied Mathematics – Master of Science*
Mathematics Education – Master of Science*

Computational Science and Engineering – Master of Science*

Energy and Environmental Studies – Doctor of Philosophy*
* See the Graduate School Bulletin

GENERAL PROGRAM REQUIREMENTS

Admission, retention and graduation requirements for students enrolled in degree programs in the Department of Mathematics are based upon the general admission, retention and graduation requirements of the University. However, two units of algebra, one unit of plane geometry and one-half unit of trigonometry are required of all students who elect to pursue any curriculum offered in the department.

SPECIFIC PROGRAM REQUIREMENTS

Applied Mathematics
The Applied Mathematics major must complete a minimum of 124 semester hours of University courses, including 48 hours in mathematics, 8 hours in physics and 24 hours of applications area electives.

Mathematics
The Mathematics major must complete a minimum of 126 semester hours of University courses. These include 48 hours in mathematics and 16 hours in science.

Mathematics, Secondary Education
The Mathematics Education major must complete a minimum of 124 semester hours of University courses. These include 43 hours in mathematics and 28 hours in education and/or psychology. Also, majors must earn a “C” or better grade in each mathematics course taken to fulfill the mathematics requirement. All Teacher Education admissions, retention and graduation standards apply.

CAREER OPPORTUNITIES

The Bureau of Labor Statistics of the U.S. Department of Labor in its “Occupational Outlook for College Graduates” continues to report that the employment opportunities in education, cost analysis, government service and public health are expected to be excellent for graduates in mathematics.

REQUIRED MAJOR COURSES FOR APPLIED MATHEMATICS

MATH 105 MATH 131 MATH 132 MATH 224

MATH 231 MATH 240 MATH 311 MATH 431

MATH 432 MATH 440 MATH 450 MATH 480

MATH 505 MATH 507 MATH 608 MATH Elective (one)

CURRICULUM GUIDE FOR APPLIED MATHEMATICS

FRESHMAN YEAR
First Semester	Credit	Second Semester	Credit
MATH 131 UNST 100/MATH 105 UNST 110 UNST 120 FOLA Elective1 GEEN 102	4 1 3 3 3 2 16	MATH 132 MATH 240 UNST 130 UNST 140 FOLA Elective1	4 3 3 3 3 16
SOPHOMORE YEAR
First Semester	Credit	Second Semester	Credit
MATH 231 UNST Cluster Theme    Elective2 PHYS 241/251 UNST Cluster Theme    Elective2 MATH 224	4   3 4   3 3 17	MATH 311 UNST Cluster Theme    Elective2 PHYS 242/252 Applications Area Elective3 UNST Cluster Theme    Elective2	4   3 4 3   3 17
JUNIOR YEAR
First Semester	Credit	Second Semester	Credit
MATH 431 MATH 450 Applications Area Elect.3 Applications Area Elect.3 SPCH 250	3 3 3 3 3 15	MATH 432 MATH 480 Applications Area Elective3 Applications Area Elective3 Elective	3 3 3 3 3 15
SENIOR YEAR
First Semester	Credit	Second Semester	Credit
MATH 507 MATH 440 or 465 Applications Area Elect.3 Applications Area Elect.3 Elective	3 3 3 3 3 15	MATH 608 MATH 505 Applications Area Elective3 UNST Capstone/    MATH 6924 Elective	3 1 3   3 3 13

Credit Hour Summary

Mathematics Physics and Computer Science Applications Area Elective General Education Free Elective Total Credit Hours:

48 16 24 35 6 125

¹ Two courses FOLA 100, 101; or FOLA 102, 103; or FOLA 104, 105: or FOLA 106, 107 taken in sequence.
² UNST Cluster Theme Elective:  must choose one cluster and take 12 hours in that cluster.
³ Must include a total of 24 credit hours taken in one of the applications areas, including but not limited to: Applied and Computational Mathematics, Physical Sciences, Engineering and Applied Sciences, Life Sciences, or Business and Economics, and approved by the Applied Mathematics Undergraduate Program Committee.  A list of suggested core courses for each of the applications areas is available from the Department of Mathematics.
⁴ MATH 692, Independent Study, is the Math Department capstone to fulfill the UNST capstone experience requirement.
 

REQUIRED MAJOR COURSES FOR MATHEMATICS

CURRICULUM GUIDE FOR MATHEMATICS
FRESHMAN YEAR

First Semester	Credit	Second Semester	Credit
MATH 131 Science Elective1 UNST 110 UNST 120 UNST 100/MATH 105	4 4 3 3 1 15	MATH 132 Science Elective1 UNST 130 UNST 140 HPED 200	4 4 3 3 2 16
SOPHOMORE YEAR
First Semester	Credit	Second Semester	Credit
MATH 231 UNST Cluster Theme    Elective2 PHYS 241/251 UNST Cluster Theme    Elective2 MATH 224	4   3 4   3 3 17	MATH 311 MATH 240 PHYS 242/252 UNST Cluster Theme    Elective2 UNST Cluster Theme    Elective2	4 3 4   3   3 17
JUNIOR YEAR
First Semester	Credit	Second Semester	Credit
MATH 431 MATH 507 Elective FOLA3 SPCH 250	3 3 3 3 3 15	MATH 508 MATH 432, 440 or 465 MATH 450 FOLA3 Elective	3 3 3 3 3 15
SENIOR YEAR
First Semester	Credit	Second Semester	Credit
MATH 511 MATH 505 MATH Elective4 Electives	3 1 3 9 16	MATH 512 MATH Elective4 UNST Capstone/MATH 692 Electives	3 3 3 6 15

Credit Hour Summary

Mathematics Physical and Computer Science General Education Free Elective Total Credit Hours:

50 24 39 12 125

¹ 8 hours: CHEM 100, 110 and BIOL 100; or CHEM 106,116 and CHEM 107, 117.
² UNST Cluster Theme Elective:  must choose one cluster and take 12 hours in that cluster.
³  A sequence of two courses in either French, German, Russian, or Spanish.
⁴ 6 hours: MATH 223, 420, 423, 440, 460, 607, 608, 610, 611, 612, 620, 623, 624, 631, 632, 633, 650, 651, 652, 665.

COURSE DESCRIPTIONS IN MATHEMATICS

This course covers elementary properties of real numbers and basic algebra through solving of quadratic equations by various means. It is required of students whose mathematics SAT scores are low and whose major curriculum includes either MATH 101 or MATH 111. (F;S;SS)

Numbers and their properties polynominals, rational expressions, rational exponents, radicals, equations and inequalities in one variable, relations and functions are studied. Prerequisite: A satisfactory score on the mathematics portion of the SAT or MATH 099. (F;S;SS)

This course is a continuation of MATH 101. Quadratic functions, systems of linear equations, exponential and logarithmic functions, circular functions, trigonometric functions, analytical trigonometry and the binomial theorem will be studied. Prerequisite: MATH 101. (F;S;SS)

This course will guide and encourage proper mathematics study habits, and develop an informed mathematics major who will be prepared to move through his or her curriculum. Seminar topics include: how to study mathematics; ethics-academic honesty, respect for property, civility; technology instruction; key information: special deadlines, required tests; and other related topics. (F;S)

Algebraic properties of the number system, fundamental operations, exponents and radicals, functions and graphs, solutions of equations and systems of equations, trigonometric functions and identities, inequalities, logarithms, progressions, mathematical induction, binomial theorem, permutations and combinations will be studied. Prerequisites: One unit of high school algebra and one unit of high school geometry. (F;S;SS)

This course is a review of basic algebra; first and second degree equations; polynomial and rational functions-systems of equations-inequalities, right triangle trigonometry; and trigonometric identities and equations. Prerequisites: Mathematics 099 or two units of high school algebra, one unit of high school geometry and a satisfactory score on the mathematical portion of the Scholastic Aptitude Test. (F;S;SS)

This course includes a brief treatment of basic concepts of differential and integral calculus with applications to business, economics, social and behavioral sciences; polynomial, rational, exponential and logarithmic functions. Prerequisite: MATH 102, 110, or 111. (F;S;SS)

This course includes a brief review of computing with whole numbers, decimals, fractions, percent, problem solving and the metric system. Simple interest, discount, partial payments, payroll wages and commission accounts, discounts and mark-ups, retailing, taxes, distribution of ownership, transactions in corporate securities, insurance, compound interest, annuities amortization and sinking funds will also be studied. Prerequisite: MATH 101, 110, or 111. (DEMAND)

This course is an introduction to applied discrete mathematics. Topics include set theory, introduction to logic, functions, recursion, relations, properties of integers, and elementary matrix algebra. Prerequisite: MATH 110 or equivalent. (F;S)

Limits and continuity of functions, the derivative, applications of the derivative, the definite integral and applications of the definite integral will be studied. Prerequisite: MATH 110 or appropriate approval. (F;S;SS)

Topics in analytic geometry, differentiation and integration of exponential, logarithmic, trigonometric, inverse trigonometric and hyperbolic functions, additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor’s Formula and infinite series will be studied. Prerequisite: MATH 131. (F;S;SS)

This course is a continuation of MATH 123. Topics include Boolean algebra and applications elementary graph theory, trees and applications, and mathematical techniques for algorithm analysis. Prerequisite: MATH 123 or 311. (F;S;SS)

This is a general course covering fundamentals of statistics, central tendencies, variabilities, graphic methods, frequency distributions, correlations, reliability of measures, theory and methods of sampling and descriptive and analytical measures of statistics. Prerequisite: MATH 111. (F;S;SS)

This course will cover plane curves and polar coordinates, vector and solid geometry, vector valued functions, partial differentiation, multiple integrals, applications of multiple integrals and vector analysis. Prerequisite: MATH 132. (F;S;SS)

This course teaches students problem-solving techniques and how to program in the FORTRAN language. Students are exposed to a variety of mathematical computer software, including Maple. Using the graphics calculator as a programming tool will be explored. Prerequisite: MATH 112 or 131. (DEMAND)

Postulational systems, Euclid’s Parallel Postulate, a brief study of non-Euclidean geometries, Euclidean geometry as a special case of other geometries and defects of Euclid’s system will be studied. Prerequisite: MATH 132. (DEMAND)

Emphasis is placed on development or writing skills and the ability to understand and develop proofs and logical arguments. Topics include quantifiers, rules of logic, and methods of mathematical proof, with applications to sets, integers, real numbers, functions, relations, and combinatorics. In the weekly 2-hour active learning lab, exercises and proofs are given to groups of two to four.  The students present solutions and the solutions are critiqued by the students and the instructor.  Prerequisite: MATH 132. (S)

This course is a supervised learning experience in a specified private or governmental facility. The student must be in industry full time for at least one summer or one semester and must perform supervised work that will enhance his/her educational background in an area related to mathematics and/or computer science. In addition to the supervisor’s evaluation on the field, the student’s performance will be evaluated by a departmental faculty committee, based upon reports, informal portfolios and forum and/or a seminar presented by the student upon his/her return to the University. (DEMAND)

The description of this course is the same as MATH 397 and is normally the second Co-op experience of the student related to mathematics and/or computer science. The maximum number of credit hours that may be earned by a student in the two courses MATH-397 and MATH 398 is six. (DEMAND)

This course is a survey of the development of mathematics by chronological periods with biographical references, illustrations of national and racial achievements and discussion of the evaluation of certain important topics of elementary mathematics. Prerequisite: MATH 231. (DEMAND)

Methods of solving cubics, quartics and other algebraic equations, methods of approximating roots-systems of equations, and elements of determinants and matrices will be studied. Prerequisite: MATH 132. (DEMAND)

This course covers the use of graphing calculators and mathematical software in doing and teaching of mathematics at the secondary and college levels.  It includes and introduction to a calculator based programming language with in-depth treatment of algorithms and control structures.  Application areas include algebra, geometry, trigonometry, precalculus, calculus, statistics, and elementary linear algebra.  Prerequisites: MATH 224, 132. (S)

This course will cover first order differential equations, higher order linear differential equations, matrices and determinants, systems of linear algebraic equations, systems of linear differential equations, and Laplace transforms. Prerequisite: MATH 132. (F;S;SS)

This course will cover Fourier series, partial differential equations, complex variables, Taylor and Laurent series and residue theory. Prerequisite: MATH 431. (F;S;SS)

Numerical methods as related to programming techniques, interpolation, extrapolation, approximate solutions of algebraic and transcendental equations, simultaneous linear equations, initial-value, characteristic-value and boundary-value problems, partial differential equations of the hyperbolic parabolic and elliptic types will be studied. Corequisite: MATH 240. (DEMAND)

This course is an introduction to linear algebra and matrix theory; the algebra of matrices and its application to the solutions of systems of linear equations, determinants, real and complex vector spaces, bases, dimension, linear transformations, eigenvalues and eigenvectors. Prerequisite: MATH 132. (F;S;SS)

This course is an introduction to principles and techniques of numerical mathematics. Topics in round-off error analysis, the approximation of functions, derivatives and integrals, and the numerical solutions of non-linear equations, ordinary differential equations and the systems of linear equations will be studied. Prerequisites: MATH 231, 240 and 450. (DEMAND)

This course will cover scientific computing fundamentals, and expose the student to high-performance programming languages and scientific computing tools. Topics include errors, approximations, floating point operations, polynomial interpolation, cubic splines, numerical integration, numerical linear algebra, solution of nonlinear equations, the initial value problems. The MATLAB or MAPLE computing environment is used. Prerequisites: MATH 431 and 450. (S)

This course explores the fundamentals of both discrete and continuous mathematical modeling of problems in various fields where mathematics is used.  The course will be project oriented and will emphasize multi-disciplinary problem solving.  Prerequisites: MATH 231, 431: Corequisites: MATH 432, 450. (F, S)

Methods of preparing and presenting seminars, presentation of seminars in current developments in mathematics and/or topics of interest which are not included in formal courses will be studied. Required for mathematics majors. Prerequisite: MATH 507 or 511. (DEMAND)

This course includes a rigorous treatment of the fundamental principles of analysis, limits, continuity, sequences, series, differentiability and integrability and functions of several variables. Prerequisites: MATH 231 and 311, or consent of instructor. (F)

This course is a continuation of MATH 507. Prerequisite: MATH 507. (S)

Elementary properties of integers, rings, integral domains, and fields, properties of groups, including abelian groups, permutations, homomorphisms, normal subgroups, and factor groups will be studied. Prerequisite: MATH 231, 311 or consent of instructor. (F)

This is a continuation of MATH 511, including topics in commutative ring theory, Galois field theory and module theory. Prerequisite: MATH 511. (S)

Vector and tensor calculus, covariant and contravariant components; integral theorems; applications to geometry, mechanics and electromagnetic theory will be studied. Prerequisite: MATH 431. (DEMAND)

Advanced Undergraduate and Graduate

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)

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)

This course covers mappings, binary operations, groups, rings, integral domains, fields, and some applications to coding and cryptography. Prerequisite: MATH 311 or consent of the instructor. (DEMAND)

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 311 or consent of the instructor. (DEMAND)

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 the Department of Mathematics. (DEMAND)

This course includes a review of those principles of mathematics which are involved in chemical computations and derivations from general chemistry through physical chemistry; topics covered include significant figures, methods of expressing large and small numbers, algebraic operations, trigonometric functions and an introduction to calculus. (DEMAND)

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)

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)

The following topics will be covered in this course: complex number system, limits of complex sequences, complex functions, continuity, limits of functions, derivatives, elementary functions, Cauchy-Riemann equations, antiderivatives harmonic functions, inverse functions, power series, analytic functions, analytic continuation, contour integrals, Cauchy’s theorem and Cauchy’s integral formula. Prerequisite: MATH 231. (DEMAND)

Mathematics 611 is a continuation of Mathematics 610. The following topics will be covered in this course: Liouville’s theorem, the fundamental theorem of algebra, the winding number, generalized Cauchy theorems, singularities, residue calculus, Laurent series, boundary value problems, harmonic functions, conformal mappings, Poisson’s formula, potential theory, physical applications and the Riemann mapping theorem. Prerequisite: MATH 610. (DEMAND)

This course covers vector spaces, linear transformations and matrices determinants and systems of linear equations, eigenvalues and eigenvectors, diagonalization, inner products, bilinear quadratic forms, canonical forms, and application to engineering, and applied sciences. Prerequisite: MATH 450 or consent of the instructor. (DEMAND)

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)

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)

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)

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. This course may not be used for degree credit. (DEMAND)

This is a continuation of MATH 625; provides no credit towards a degree in mathematics; is not open to secondary school teachers of mathematics. Credit on elementary education degree. Prerequisite: MATH 625. (DEMAND)

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 450 and a high level programming language. (DEMAND)

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 450, or consent of the instructor. (DEMAND)

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)

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 431. (DEMAND)

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 431 and 432. (DEMAND)

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 431 and 432. (DEMAND)

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 450. (DEMAND)

Varieties of graphs, graph theory algorithms, and applications of graph theory to other disciplines will be studied. Prerequisite: MATH 450. (DEMAND)

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)

This course offers guided independent undergraduate study under faculty supervision in an approved mathematical topic.  The course may be repeated for a maximum of six credit hours.  (F;S;SS)
* Students are required to purchase supplemental materials for this course. General Education course.

DIRECTORY OF FACULTY

B.S., Njala University College; M.S., North Carolina A&T State University, Ed.D., Louisiana State University

B.S., Gauhat University, India; M.S., Ph.D., Oregon State University

B.S., North Carolina A&T State University; M.S., Ph.D., Howard University

B.S., M.S., North Carolina A&T State University; Ph.D., Pennsylvania State University

B.S., M.S., Huazhong Normal University; Ph.D., Georgia Institute of Technology

B.S., M.S., Ph.D., Virginia Polytechnic Institute and State University

B.A., Hiram College; M.S., Purdue University; Ph.D., Kent State University

B.S., North Carolina A&T State University; M.S., Ph.D., Virginia Polytechnic Institute and State University

B.S., Virginia Polytechnic Institute and State University; M.S., North Carolina A&T State University; Ph.D., University of South Florida

B.S., Yarmouk University; M.S., Ohio University; Ph.D., Kent State University

B.S., Cap Coast University-Ghana; M.S., Ph.D., Simon Fraser University-Canada

B.S., West Virginia University; M.S., New Mexico Institute of Technology; Ph.D., North Carolina A&T State University

B.A., State University of New York/College at Geneseo; M.S., Ph.D., North Carolina State University

B.S., M.S., University of Zagreb; Ph.D., University of North Texas

B.S., M.S., North Carolina A&T State University; M.S., University of Illinois

B.S., Elizabeth City State University; M.S., North Carolina A&T State University

A.B., University of Texas; M.S., University of Illinois; Ph.D., University of Colorado

B.A., University of Chicago; M.S., Purdue University; Ph.D., University of California-Berkeley

B.S., Virginia Union University; M.S., University of North Carolina at Chapel Hill

B.S., M.S., North Carolina A&T State University

B.S., North Carolina A&T State University, M.S., Ph.D., Pennsylvania State University

B.S., Anhui University; M.S., Nanjing University of Science and Technology; Ph.D., Rutgers University

B.S., Paine College; M.S., North Carolina A&T State University; M.S., Ph.D., Howard University

B.S., University of Jaffna; M.S., Ph.D., University of Arizona

B.S., M.S., California State Polytechnic University; Ph.D., University of Iowa

M.S., Ph.D., Moscow Institute of Physics and Technology

Departments in the College of Arts & Sciences

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