DEPARTMENT OF MATHEMATICS

Paul Dowell, Acting Chairperson, 129 Austin

John P. Daughtry, Director of Graduate Studies, 331 Austin

The Department of Mathematics requires that the applicant meet the admission requirements of the Graduate School, have an undergraduate major in mathematics or its near equivalent or (in the case of the MAEd pre-secondary concentration) a concentration in mathematics, and submit satisfactory scores on the Graduate Record Examinations or the Miller Analogy Test.  Each applicant’s credentials will be reviewed by the director of graduate studies, who will determine if undergraduate deficiencies are present and, if so, will prescribe the method of their removal and determine a precondition for admission.

MA IN MATHEMATICS

The department currently offers seven areas of concentration at the graduate level: algebra, analysis, applied mathematics, differential equations, geometry, number theory, and topology.  All students are required to complete successfully MATH 5101, 5102, Advanced Calculus I and II, if they have not previously completed equivalent courses. Applicants to a graduate program should normally have completed an undergraduate major, or its equivalent, in mathematics.

A student enrolled in the MA program who wishes to write a thesis and to receive the 6 s.h. credit for thesis work must register for and successfully complete MATH 7000.

The research skills requirement for students enrolled in the MA program is satisfied by demonstrating sufficient competency in an appropriate foreign language or by having earned a minimum grade of C in CSCI 2510 or 2600 and either MATH 5031 or CSCI 5774, provided that these courses were completed no more than five years from the date of acceptance to graduate studies at East Carolina University.

Additional requirements are given below:

1. Students must satisfy the research skills requirement in a foreign language or computer science.
2. Students must score satisfactorily on a comprehensive examination.
3. Students must write a thesis (6 s.h.) or take 9 s.h. of course work prefixed MATH and numbered above 5000. Students electing to take the 9 s.h. of course work are required to complete a research project under the direction of a member of the graduate faculty. 
4. Students must complete an additional 24 s.h. of course work prefixed MATH to include each of the following: MATH 5102, 6011, 6111, 6121; 6651; 5311 or 5801 or 6401 or 6411.
5. Students must successfully complete at least one two-course sequence from among the following: MATH 5801, 6802; 6121, 6122; 6011, 6012; 6111, 6112; 6651; or 5601, 6601.

MAEd IN MATHEMATICS

The MAEd in mathematics is designed for a teacher whose primary teaching assignment has been in the area of pre-secondary or secondary mathematics. Prior teaching experience is not necessary for admission to this program, but certification to teach is required for admission.   

Students holding the equivalent of an undergraduate mathematics major and certified to teach at the secondary level will complete the secondary level concentration.  Students who earned the equivalent of an undergraduate concentration in mathematics and are certified to teach at the pre-secondary level will complete the pre-secondary-level concentration.  In addition to the general requirements for admission to graduate studies in the Department of Mathematics, admissions materials must include a letter of recommendation from someone aware of the applicant’s performance or potential as a classroom teacher.

Degree Requirements

Minimum degree requirement is 39 s.h. of credit. 

STATISTICS MINOR

Twelve s.h. of graduate course work for the statistics minor is required as follows: MATH 5031, 5801, 6802; one additional graduate-level statistics course.

CERTIFICATE IN STATISTICS

The statistics certification requires a minimum of 9-15 s.h. credit as follows:

Students who have successfully completed MATH 3307, 3308 must complete 9 s.h. as follows: CSCI 5774; MATH 5000, 5031.

Students who have successfully completed MATH 3307 must complete 12 s.h. as follows: CSCI 5774; MATH 5000, 5031, 6802.

Students who have not successfully completed MATH 3307 must complete 15 s.h. as follows: CSCI 5774;  MATH 5000, 5031, 5801, 6802.

MATH: Mathematics

5000. Introduction to Sampling Design (3) (F) P: MATH 3308 or 3229 or consent of instructor. Fundamental principles of survey sampling. Data sources and types, questionnaire design, various sampling schemes, sampling and nonsampling errors, and statistical analysis.

5002. Logic for Mathematics and Computer Science (3) (S) Same as CSCI 5002 P: CSCI 3510 or MATH 2427 or 2775 or 3223 or 3256 or PHIL 3580 or equivalent. Methods of mathematical logic that have important applications in mathematics and computer science.

5021. Theory of Numbers I (3) P: MATH 3263 or consent of instructor. Topics in elementary and algebraic number theory such as properties of integers, Diophantine equations, congruences, quadratic and other residues, and algebraic integers.

5031. Applied Statistical Analysis (3) (WI) May not count toward mathematics hours required for mathematics MA. P: MATH 2228, 3584; or equivalent; or consent of instructor. Topics include analysis of variance and covariance, experimental design, multiple and partial regression and correlation, nonparametric statistics, and use of computer statistical package.

5064. Introduction to Modern Algebra II (3) May not be taken for credit by those having completed MATH 6011. P: MATH 3263 or consent of instructor. Continuation of development of topics begun in MATH 3263. Normal subgroups, factor groups, homomorphism, rings, ideals, quotient rings, and fields.

5101. Advanced Calculus I (3) P: MATH 2173 or consent of instructor. Axioms of real number system, completeness, sequences, infinite series, power series, continuity, uniform continuity, differentiation, Riemann integral, Fundamental Theorem of Calculus.

5102. Advanced Calculus II (3) P: MATH 3256, 5101; or consent of instructor. Mathematical analysis of functions of several real variables. Includes limits, continuity, differentiation, and integration of multivariable functions.

5110. Elementary Complex Variables (3) May not be taken for credit by those having completed MATH 6111. P: MATH 2173. Complex numbers, analytic functions, mapping by elementary functions, integrals, residues, and poles.

5121. Numerical Analysis in One Variable (3) P: MATH 2173. Numerical analysis of problems with one independent variable.  Solution of nonlinear equations in one unknown, interpolation and approximation of functions of one variable, numerical integration, and numerical differentiation and optimization.

5122. Numerical Analysis in Several Variables (3) P: MATH 2173, 3256, 4331. Numerical analysis of problems with several independent variables.  Numerical solution of ordinary differential equations, systems of linear equations, numerical linear algebra and matrix algebra, systems of nonlinear equations, and systems of ordinary differential equations.

5131. Deterministic Methods in Operations Research (3) P: MATH 2173; 3307 or 5801. Mathematical models; linear programming; simplex method, with applications to optimization; duality theorem; project planning and control problems; and elementary game theory.

5132. Probabilistic Methods in Operations Research (3) P: MATH 2173, 3256; 3307 or 5801. Introduction to stochastic processes. Queuing theory with applications to inventory theory and forecasting, Poisson and Markov processes, reliability simulation, decision analysis, integer programming, and nonlinear programming.

5251. Modern Mathematics for Elementary Teachers I (3) Not open to undergraduate or graduate mathematics majors or minors. A teacher taking this course would receive certificate renewal credit and/or 3 s.h. of graduate elective credit in elementary education. P for undergraduate students: MATH 3223 or consent of instructor; P for graduate students:  MATH 2127, 2129; 3219 or 3221; or equivalent; or consent of instructor. Numeration systems and real numbers from axiomatic approach. Topics in geometry, algebra, probability theory, and number theory. Emphasis on relationship between these topics and school mathematics.

5263, 5264. Modern Mathematics for Junior High School Teachers I, II (3,3) May not count toward MATH or CSCI major or minor. P for 5263: Consent of instructor; P for 5264: MATH 5263 or consent of instructor. Set theory, mathematical systems and proofs, number systems, elementary number theory, applications of mathematics in business, science, and other areas. Basic concepts of geometry, algebra, probability, and statistics.

5265, 5266. Microcomputers in Secondary Education (3,0) 2 lecture and 2 lab hours per week. May not count toward a MATH or CSCI major or minor. P: MATH 1075 or 1085 or 3166; consent of instructor. Operation and programming of microcomputers in secondary school system.

5267, 5268. LOGO: A Computer Language for Educators (3,0) 2 lecture and 2 lab hours per week. May not count toward MATH major or minor. P: MATH 3166 or consent of instructor. LOGO and its uses with students K-12.

5270. Pascal Using the Microcomputer (3) May not be taken by students who have successfully completed CSCI 2610. May not count toward MATH or CSCI major or minor. P: MATH 1065 or equivalent. Pascal language and use in problem solving utilizing a microcomputer.

5311. Mathematical Physics (3) Same as PHYS 5311 P: MATH 4331; PHYS 2360; or consent of instructor. Mathematical methods important in physics. Emphasis on application. Functions of complex variables, ordinary and partial differential equations, integrals and integral transforms, and special functions.

5322. Foundations of Mathematics (3) (WI) P: MATH 3233, 3263; or equivalent. Fundamental concepts and structural development of mathematics. Non-Euclidean geometries, logic, Boolean algebra, and set theory. Construction of complex number systems. Transfinite cardinal numbers and study of relations and functions. Topics developed as postulational systems.

5521. Readings and Lectures in Mathematics (3) Individual work with student.

5551. The Historical Development of Mathematics (3) P: MATH 3233; C: MATH 2172 or consent of instructor. History of mathematics from antiquity to present. Emphasis on study of significant problems which prompted development of new mathematics. Uses computer resources and library for research of topics and solutions.

5581. Theory of Equations (3) P: MATH 2173 or consent of instructor. Topics include operations with complex numbers, De Moivre's Theorem, properties of polynomial functions, roots of general cubic and quartic equations, methods of determining roots of equations of higher degree, and methods of approximating roots.

5601. Non-Euclidean Geometry (3) P: MATH 3233 or consent of instructor. Non-Euclidean geometries, finite geometries, and analysis of other geometries from point of view of properties which remain invariant under certain transformations.

5774. Programming for Research (3) Same as CSCI 5774 For graduate student who wishes to use computer science to meet required research skills of his or her dept. May not count toward MATH major or minor. P: General statistics course or consent of instructor. Emphasis on minimum-level programming skill and use of statistical packages.

5801. Probability Theory (3) P: MATH 2173 or 3307. Axioms of probability, random variables and expectations, discrete and continuous distributions, moment generating functions, functions of random variables, Central Limit Theorem, and applications.

6000. Introduction to Graduate Mathematics (3) May not be taken for credit after MATH 5101 or 6011. P: Consent of the director of graduate studies or adviser. Introduction to advanced mathematics for beginning graduate students. Covers various proof methods and provides rigorous introduction to topics in logic, number theory, abstract algebra, and analysis.

6001. Matrix Algebra (3) P: MATH 3256 or consent of instructor. Properties of vectors and matrices and their applications.

6011, 6012. Modern Algebra I, II (3,3) P for 6011: MATH 3263 or equivalent; P for 6012: MATH 6011. Basic algebraic structures. Groups, rings, modules, integral domains, and fields.

6022. Theory of Numbers II (3) P: MATH 5021. Advanced topics in algebraic and analytic number theory.

6111, 6112. Introduction to Complex Variables I, II (3,3) P for 6111: MATH 5102; P for 6112: MATH 6111. I. Analytic functions, mapping of functions, differentiation and integration, power series, and residues.  II. Integral functions, infinite products, Mittag-Leffler expansion, maximum modulus theorem, convex functions, the Schwarz-Christoffel transformation, analytic continuation, Riemann surfaces, and selected topics in functions of a complex variable.

6121, 6122. Real Variables I, II (3,3) P for 6121: MATH 5101 or consent of instructor; P for 6122: MATH 6121 or consent of instructor. I. Study of functions of one real variable and convergence of sequences and series of functions: functions of bounded variation, measures, measurable sets, measurable functions, convergence almost everywhere, absolutely continuous functions, Lebesque integration, differentiation, and the Fundamental Theorem of the Calculus. II. Lebesque spaces and associated inequalities, measures in Rⁿ, measure spaces and the associated theory of integration and differentiation; the Radon-Nikodym Theorem with applications to probability and statistics.

6200. Mathematics Assessment for the Classroom Teacher (3) P: Consent of instructor. Theory, methods, and techniques of assessment for improving mathematics learning. Requires assessment and intervention project adapted to local classroom setting.

6206. Leadership in Mathematics Education (3) P: Admission to MAEd program; consent of instructor. Mathematics content and information necessary for service as leader in public school mathematics education.

6211. Research in Mathematics Education (3) Readings, reports, and syntheses of research literature on teaching and learning K-12 mathematics. Projects based on this literature.

6221, 6222, 6223. Current Topics in Mathematics Education (1,2,3) May be repeated once with change of topic. May not count toward mathematics hours required in the MATH MA or MAEd. P: Consent of instructor. Exhaustive study of current topic in mathematics education.

6226, 6227, 6228. Leadership in Mathematics (1,2,3) Each course may be repeated once with change of topic. May not count toward mathematics hours for MATH MA or MAEd. P: Consent of instructor. Mathematics content and information necessary for service as leader in public school mathematics education.

6229. Leadership in Mathematics Education (4) May not count toward mathematics hours for MATH MA or MAEd. P: Consent of instructor. Mathematics content and information necessary for service as leader in public school mathematics education.

6251, 6252. Advanced Placement Mathematics for Secondary Teachers I, II (3,3) May count toward certificate renewal or certification in teaching gifted and talented students. May not count toward mathematics hours for any graduate mathematics degree. Intensive study of topics covered in Calculus AB and Calculus BC of advanced placement mathematics.

6261. Diagnostic Approach to Teaching Elementary Mathematics I (3) May not count toward mathematics hours for MATH MA.  May count as elective in other programs. P: MATH 5251 or 5263 or consent of instructor. Methods of diagnosing and prescribing for individual difficulties in mathematics at elementary and secondary school levels. Application of principles and techniques during clinical work.

6271. Teaching Collegiate Mathematics (2) P: MATH 4323. Curricula and methods of teaching mathematics to adults in colleges and technical schools.

6320. Advanced Elementary Mathematics Methods (3) May not count toward mathematics requirement for MATH MA or MAEd. P: Certification in elementary education at undergraduate level. Current research, materials, methods, and curricula for teaching and learning elementary school mathematics.

6321. Advanced Middle-Level Mathematics Methods (3) May not count toward mathematics requirement for MATH MA or MAEd. P: Certification in mathematics at middle grades undergraduate level. Current research, materials, methods, and curricula for teaching and learning middle-level mathematics.

6323. Issues and Trends in Mathematics Education (3) May not count toward mathematics requirement for MATH MA or MAEd. P: Graduate standing and certification in secondary mathematics. Current research, materials, methods, and curricula for teaching and learning high school mathematics.

6401, 6402. Introduction to Partial Differential Equations I, II (3,3) P for 6401: MATH 4331 or consent of instructor; P for 6402: MATH 6401 or consent of instructor. I. Study of linear and nonlinear partial differential equations of the first order with emphasis on the formal aspects of these equations. Also, use of partial differential equations in analysis, geometry, and physical sciences is considered where appropriate. II. Continuation of MATH 6401 to include nonlinear partial differential equations of the second order and higher orders. Certain theoretical aspects of partial differential equations and a limited amount of Fourier Series, Fourier transforms, Laplace transforms, and boundary value problems are included.

6411, 6412. Ordinary Differential Equations I, II (3,3) P for 6411: MATH 4331 or consent of instructor; P for 6412: MATH 6411 or consent of instructor. I. Existence, uniqueness, and technique of solutions to first and second order differential equations are considered. Bases for linear equations, stability, and series solutions about an ordinary point are considered. II. Autonomous systems, series solutions about a regular singular point, and Sturm-Liouville Systems are examined.

6561. Properties of Infinite Series (3) P: Consent of instructor. Infinite series beyond advanced calculus level.

6571. Elements of Probability (3) May not count toward mathematics requirement for MATH MA. P: Consent of instructor. Axiomatic development of probability from set operations viewpoint. Use of probability measures.

6601. An Introduction to Differential Geometry (3) P: MATH 2173, 3256. Basic ideas of differential geometry through study of curves and surfaces in three-dimensional space. Regular curves, regular surfaces, Gauss Map, and intrinsic and global differential geometry of surfaces.

6611, 6612. Introduction to Higher Geometry I, II (3,3) P for 6611: MATH 3233 or consent of instructor; P for 6612: 6611. I. Homogeneous linear equations and linear dependence; projections and rigid motions, homogeneous Cartesian coordinates; linear dependence of points and lines; point geometry and line geometry; harmonic division and cross ratio; one- and two-dimensional projective transformations. II. Continuation of the study of projective coordinates in the plane; an introduction to various types of geometries; a study of point curves and line curves with intensive study of point conics and line conics.

6651. Introduction to Topology (3) P: MATH 5101. Metric spaces and basic point-set topology, open sets, closed sets, connectedness, compactness, and limit points.

6802. Statistical Inference (3) P: MATH 3307 or 5801; consent of instructor. Estimation and hypothesis testing from both classical and Bayesian points of view. Use of t, F, and chi-squared distributions. Least squares procedures.

6803. The Linear Model (3) P: MATH 3256, 5801. Topics include general linear model, regression models, design models, estimation of parameters, theory of least squares, and testing general linear hypotheses.

6804. Stochastic Processes (3) P: MATH 3256, 5801. Most widely used models for random phenomena which vary with time. Topics include Markov, Poisson, birth and death, and stationary processes.

6805. Topics in Mathematical Statistics (3) P: MATH 3256, 5801. Mathematical theory of certain topics in statistics outside range of MATH 6802. Topics vary by faculty and student interests.

7000. Thesis (3) May be repeated. May count maximum of 6 s.h.

MATH Banked Courses

5252. Modern Mathematics for Elementary Teachers II (3)
5261, 5262. Modern Mathematics for Secondary Teachers I, II (3,3)
5301, 5302. Analytical Mechanics I, II (3,3)
5321, 6322. Applied Mathematics I, II (3,3)
5331. Introduction to Celestial Mechanics (3)
5610. Applied Analysis (3)
6652. Introduction to Topology II (3)

MEDIEVAL AND RENAISSANCE STUDIES

Bodo Nischan, Director, A-315 Brewster

MRST: Medieval and Renaissance

5000. Medieval and Renaissance Studies Seminar (3) P: 9 s.h. in MRST or consent of director. Interdisciplinary seminar.