Department of Mathematical Sciences

The Department of Mathematical Sciences offers programs of study for students interested in mathematics, mathematics education or statistics. The department is dedicated to providing students with excellent instruction that incorporates innovative instructional techniques and technologies. In their roles as teacher-scholars, the faculty maintains consistent and significant productivity, recognized at regional, national, and international levels, in basic research, applications, and pedagogy. The department is strengthened by the extensive service activities of the faculty on campus and in the community as well as through high-profile service to the profession. In addition, the department provides many areas for student involvement, including an active student organization and student competition teams.

Mathematical Sciences Degree

MATH   5090G   Selected Topics in Mathematics

1-3 Credit Hours.   1-3 Lecture Hours.   0 Lab Hours.

Specialized study in a selected area of Mathematics. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s):Permission of instructor required.

Cross Listing(s): MATH   5090.

MATH   5130G   Statistics and Probability for K-8 Teachers

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An in-depth study of topics in statistics, such as sampling and data analysis, and probability, such as counting methods, odds, and expected value. For Early Childhood and Middle Grade majors only.

Prerequisite(s): A minimum grade of "C" in MATH   3032.

Cross Listing(s): MATH   5130.

MATH   5135G   Algebraic Connections for K-8 Teachers

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The evolution of algebraic concepts through the curriculum will be followed by how algebra is related to other areas of mathematics and real-world applications. For Early Childhood and Middle Grade majors only.

Prerequisite(s): A minimum grade of "C" in MATH   3032.

Cross Listing(s): MATH   5135.

MATH   5136G   History of Mathematics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A survey of the historical development of mathematics. The emphasis will be on mathematical concepts, problem solving, and pedagogy from a historical perspective. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2242.

Cross Listing(s): MATH   5136.

MATH   5137G   Geometry for K-8 Teachers

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A continuation of the study of geometry from MATH   3032. Focus will be on two and three dimensional geometry. Motion geometry and tessellations will also be covered. For Early Childhood and Middle Grade majors only.

Prerequisite(s): A minimum grade of "C" in MATH   3032.

Cross Listing(s): MATH   5137.

MATH   5230G   Advanced Geometry

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Selected topics from Euclidean and Non-Euclidean Geometry. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   3130 or one year of teaching high school mathematics.

Cross Listing(s): MATH   5230.

MATH   5232G   Mathematical Applications Using Technology

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Selected mathematical topics used in research, problem solving, and demonstrations will be investigated with the use of current technologies. Intended for mathematics education majors. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2243 and 3 hours of mathematics at the junior level or above.

Cross Listing(s): MATH   5232.

MATH   5234G   Number Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Introduction to the principal ideas of elementary number theory: Divisibility, congruencies, linear Diophantine Equations, Fermat's Theorem, Euler's Theorem, Pythagorean triples and the distribution of primes. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2332.

Cross Listing(s): MATH   5234 and MATH   5234H.

MATH   5236G   Patterns of Problem Solving

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A study of patterns involved in solving problems. Particular attention is paid to Polya's heuristics and his characterization of the problem solving process. The student will also solve many problems. The application of these techniques by mathematics teachers will be stressed. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   1441 or permission of instructor.

Cross Listing(s): MATH   5236.

MATH   5330G   Operations Research

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Introduction to basic deterministic and probabilistic operations research models of decision problems. Mathematical methods of optimization for these models will be analyzed both analytically and numerically. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2331 and MATH   3337.

Cross Listing(s): MATH   5330.

MATH   5331G   Analysis I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Provides a transition from calculus to real analysis. Emphasis will be placed on understanding and constructing mathematical proofs. Rigorous development of fundamental concepts in analysis, including topics such as relations, functions, limits of functions, cardinality, topology of the reals, completeness axiom, compact sets, sequences, subsequence, continuity and differentiability. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2243 and MATH   2332.

Cross Listing(s):MATH   5331.

MATH   5332G   Analysis II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A continuation of Analysis I, including topics such as Riemann integration, infinite series, sequences and series of functions, metric spaces, and normed spaces. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   5331 or MATH   5331G.

Cross Listing(s): MATH   5332.

MATH   5333G   Modern Algebra I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This course is an introduction to the fundamental algebraic structures: groups, rings and fields. Topics covered include: binary operations, groups (permutation groups, subgroups, cyclic groups, group homomorphisms, factor groups), rings (integral domains, ring homomorphisms) and fields. The historical and mathematical connections to the secondary mathematics curriculum will be incorporated as appropriate. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2332.

Cross Listing(s): MATH   5333.

MATH   5334G   Modern Algebra II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A continuation of the study of the fundamental algebraic structures. Topics to be covered include: isomorphism of groups, rings, fields, a deeper study of quotient structures and the isomorphism theorems, field of quotients, factorization of polynomials over a field, arithmetic properties of rings of polynomials over fields, extension fields, algebraic extensions, geometric constructions and the classic problems. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" In MATH   5333 or MATH   5333G.

Cross Listing(s): MATH   5334.

MATH   5335G   Intermediate Linear Algebra

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

General vector spaces and bases, linear operators, least squares problems, eigenvalue problems, and applications of these concepts. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2331 and MATH   2332.

Cross Listing(s): MATH   5335.

MATH   5336G   Applied Numerical Methods

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Introduction to scientific computation. Solutions of linear and nonlinear equations, polynomial interpolation, numerical differentiation and integration, data fitting, and other numerical methods. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2331 and prior knowledge of a programming language.

Cross Listing(s): MATH   5336.

MATH   5337G   Difference Equations

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This course is an introduction to the theory and applications of difference equations. Topics include the difference calculus, first order linear difference equations, results and solutions of linear equations, applications, equations with variable coefficients and nonlinear equations that can be linearized. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2242 or MATH   2242H and MATH   2331.

Cross Listing(s): MATH   5337.

MATH   5338G   Methods of Applied Mathematics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Methods of applied mathematics concentrating on techniques for the analysis of differential and integral equations. Topics include: integral equations, differential operators, Fredholm alternative, distribution theory and Green's function methods. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2331 and MATH   3230.

Cross Listing(s): MATH   5338.

MATH   5339G   Partial Differential Equations

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of differential equations involving functions of more than one variable. Topics include: Laplace, heat and wave equations, boundary value problems, methods of separation of variables and eigenfunction expansions, Fourier series, Green's functions, maximum principle and computational methods. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2243 or MATH   2243H and MATH   3230.

Cross Listing(s): MATH   5339.

MATH   5430G   Introduction to Mathematical Biology

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introduction to applications of mathematics to various biological, ecological, physiological, and medical problems, which will be analyzed both analytically and numerically. Graduate students will be given additional assignments that will not be completed by undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   3230.

Cross Listing(s): MATH   5430.

MATH   5431G   Combinatorics and Graph Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The course covers basic theory and applications of combinatorics and graph theory. Combinatorics is a study of different enumeration techniques of finite but large sets. Topics that will be studied include principle of inclusion and exclusion, generating functions and methods to solve difference equations. Graph theory is a study of graphs, trees and networks. Topics that will be discussed include Euler formula, Hamilton paths, planar graphs and coloring problem; the use of trees in sorting and prefix codes; and useful algorithms on networks such as shortest path algorithm, minimal spanning tree algorithm and min-flow max-cut algorithm. Graduate students will be given extra assignments determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2332 and MATH   3337.

Cross Listing(s): MATH   5431.

MATH   5433G   Differential Geometry of Curves and Surfaces

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Differential geometry uses tools from calculus and linear algebra to study the geometric properties of smooth curves and surfaces in Euclidean spaces. Topics include: arc length surface area, geodesics, curvature, first and second fundamental forms, Gauss-Bonnett formula. Graduate students will be assigned additional assignments and/or project.

Prerequisite(s): A minimum grade of "C" in MATH   2243 or MATH   2243H and MATH   2331.

Cross Listing(s): MATH   5433.

MATH   5434G   Functions of a Complex Variable

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Topics in complex variables including functions, limits, derivatives, integrals, the Cauchy-Riemann conditions, series representation of functions, Cauchy Integral formula, and elementary conformal mappings. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   2332.

Cross Listing(s): MATH   5434.

MATH   5435G   Introduction to Topology

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introduction to metric spaces, topological spaces, connectedness and compactness of topological spaces, and continuous functions on topological spaces. Graduate students enrolled in this course will complete one or more assignments that the undergraduate students will not be required to complete.

Prerequisite(s): A minimum grade of "C" in MATH   2332.

Cross Listing(s): MATH   5435.

MATH   5436G   Introduction to Fractals

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Fractals as nonlinear systems involving feedback and iteration. Classical fractals, limits and self-similarity. Fractal dimensions. Encoding of fractals. Decoding of fractals. Iterated function systems. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   5331 or MATH   5331G.

Cross Listing(s): MATH   5436.

MATH   5437G   Mathematics and Computation of Curves and Surfaces

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This course is a study of the mathematical and computational techniques used for the computer generation of curves and surfaces. The primary representations for the curves and surfaces are univariate and multivariate polynomials and splines in the Bernstein/Bezier and B-spline bases. These curves and surfaces are used for data fitting (interpolation and smoothing) and approximation. Topics include: recursion, smoothness, surfaces over grids, surfaces over triangulations, simplex and box splines, variational curves and surfaces, transformations and projections. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2243 or MATH   2243H and MATH   2331.

Cross Listing(s): MATH   5437.

MATH   5530G   Mathematics for Scientists and Engineers

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A survey of mathematical topics useful in the study of areas of applied sciences such as physics, engineering and computer science. Topics include: linear algebra and matrices, ordinary differential equations, partial differential equations, Fourier series, vector calculus, complex variables, numerical methods, probability and graph theory. For non-math majors only. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2242 or MATH   2242H.

Cross Listing(s): MATH   5530.

MATH   5539G   Mathematical Models

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This course introduces students to a variety of mathematical tools used for solving real world problems, with the focus on identifying the problem, constructing an appropriate model, and finding the best available method to solve it. Graduate students will be given an extra assignment not required of undergraduate students.

Prerequisite(s): A minimum grade of "C" in MATH   2331 and MATH   3230.

Cross Listing(s): MATH   5539.

MATH   6130   Fundamental Concepts of Arithmetic and Geometry

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Emphasizes the mathematical content indicated, but time is also spent in exploring concepts in basic statistics and probability. There is also a field component for this course that teachers will complete by implementing course activities in their classrooms. This course is intended for teachers seeking a P-5 Mathematics Endorsement on their teaching certificate.

MATH   6131   Applications in Arithmetic and Algebra for K-5 Teachers

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

This is an online course intended for current K-5 teachers seeking a mathematics endorsement on their teaching certificate. The course will cover models for numbers and operations, patterns as a bridge from arithmetic to algebra, and applications of these topics to the K-5 classroom. This course cannot be taken for credit for students enrolled in a degree program outside the College of Education.

Prerequisite(s): Requires current Georgia Teacher Certification.

MATH   6132   Applications in Statistics for K-5 Teachers

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

This is an online course intended for current K-5 teachers seeking a mathematics endorsement on their teaching certificate. The course will cover graphical methods for categorical and numerical data, measures of descriptive statistics, probability, Venn diagrams, and applications of these topics to the K-5 classroom. This course cannot be taken for credit for students enrolled in a degree program outside the College of Education.

Prerequisite(s): Requires current Georgia Teacher Certification.

MATH   6133   Applications in Geometry for K-5 Teachers

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

This is an online course intended for current K-5 teachers seeking a mathematics endorsement on their teaching certificate. The course will cover two and three dimensional shapes and their properties, perimeter, area, volume, and measurement, and applications of these topics to the K-5 classroom. This course cannot be taken for credit for students enrolled in a degree program outside the College of Education.

Prerequisite(s): Requires currernt Georgia Teacher Certification.

MATH   6161   Mathematical Reasoning

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

MATH   6230   Fundamental Ideas of Calculus

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A review of the principal ideas of calculus, with emphases on concepts. Intended for Mathematics Education majors.

Prerequisite(s): A minimum grade of "C" in MATH   1441; permission of instructor.

MATH   6301   College Geometry

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

MATH   6435   Linear Algebra

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

MATH   6547   Intro to Statistical Methods

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Data analysis, sampling, and probability; standard methods of statistical inference, including tests, chi-square tests, and non parametric methods. Applications include use of a statistical computer package.

MATH   7090   Selected Topics in Mathematics

1-3 Credit Hours.   1-3 Lecture Hours.   0 Lab Hours.

Specialized study in a selected area of Applied Mathematics.

Prerequisite(s): Permission of instructor.

MATH   7130   Mathematical Optimization Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The course covers fundamentals of mathematical optimization theory. Topics include: elements of convex analysis, first and second order necessary and sufficient optimality conditions for unconstrained and constrained optimization problems, Lagrange multiplier theory, Lagrange duality theory, and an overview of important optimization techniques for convex, conic, semidefinite and complementarity problems.

Prerequisite(s): A minimum grade of "C" in MATH   5331.

MATH   7132   Methods of Optimization

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The first part of the course provides a brief introduction to the foundations of optimization, including optimality conditions. The second part concentrates on selected methods for unconstrained and constrained optimization problems. These include but are not limited to: line search methods, gradient methods, Newton-type methods, trust region methods, non-gradient methods, penalty and barrier methods, interior-point methods, methods of feasible directions and dual methods. Selected methods will be implemented on the computer. Prior completion of MATH   5330 is recommended.

Prerequisite(s): A minimum grade of "C" in MATH   5331.

MATH   7231   Advanced Numerical Analysis I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An in-depth study of computer arithmetic, the solution of non-linear equations, the solution of systems of linear equations, eigenvalue problems and interpolation. Algorithms and methods are developed and then implemented on a computer.

Prerequisite(s): A minimum grade of "C" in MATH   5336 or MATH   5336G.

MATH   7232   Advanced Numerical Analysis II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An in-depth study of orthogonal polynomials, numerical integration, and numerical solutions of ordinary and partial differential equations. Development and computer implementation of algorithms and methods.

Prerequisite(s): A minimum grade of "C" in MATH   7231.

MATH   7234   Advanced Linear Algebra

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of linear maps on finite dimensional vector spaces. Topics include: diagonalization (direct sums, invariant subspaces and Cayley-Hamilton theorem for linear operators), inner product spaces (self-adjoint, orthogonal operators, orthogonal projections and the spectral theorem, bilinear and quadratic forms), canonical forms (Jordan and rational forms, minimal polynomials), special matrices (non-negative matrices), and the exponential of a linear operator.

Prerequisite(s): A minimum grade of "C" in MATH   5335.

MATH   7235   Analytic Number Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

A study of topics from the classical analytic theory of numbers. Topics will be chosen from arithmetic functions, the distribution of primes, congruences, the Riemann-zeta functions, the prime number theorem, Eisenstein series, quadratic resides, Dirichlet series, Euler products, the Dedekind eta function, the Jacobi theta functions, integer partitions, and modular forms.

Prerequisite(s): A minimum grade of "C" in MATH   5234 and MATH   5434.

MATH   7236   Advanced Ordinary Differential Equations

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The theory of ordinary differential equations and dynamical systems. Topics include: Sturm-Liouville boundary value problems, eigenfunction expansions, Lyapunov stability, limit cycles, Poincare Bendixson theorem, Floquet's theory and Invariance theorems.

Prerequisite(s): A minimum grade of "C" in MATH   3230.

MATH   7237   Mathematical Control Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

State-space techniques from modern control system theory. Topics include realization theory for MIMO systems, state-space techniques for feedback control, closed loop observer design, and state-space techniques in optimal control.

Prerequisite(s): A minimum grade of "C" in MATH   3230 and MATH   5336G.

MATH   7330   Functional Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of normed linear spaces and linear operators. Topics include: Hilbert spaces (projection theorem, Riesz representation, Parseval relation); Banach spaces (convexity, duality, bounded and compact operators, theorems of Hahn-Banach, Banach-Steinhaus, open mapping, closed graph, Fredholm alternative); Stone-Weierstrass and Banach fixed point theorems.

Prerequisite(s): A minimum grade of "C" in MATH   5332 and MATH   5335.

MATH   7331   Real Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Theory of Lebesgue measure and integration, monotone convergence, the dominated convergence theorem, Fubini's Theorem, Radon-Nikodym theorem, Riesz representation theorem, Lp and lp spaces, functions of finite variation, Stieltjes integral, absolute continuity.

Prerequisite(s): A minimum grade of "C" in MATH   5331.

MATH   7332   Advanced Partial Differential Equations

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The theory of linear and nonlinear partial differential equations. Topics include: Classical theory of elliptic, parabolic and hyperbolic partial differential equations and their solutions, potential theory, maximum principle, existence of weak solutions, regularity of solutions, Duhamel's principle and Cauchy's problem.

Prerequisite(s): A minimum grade of "C" In MATH   5339 or MATH   5339G.

MATH   7333   Complex Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An in-depth study of functions of one complex variable. Topics include: properties of holomorphic, harmonic, meromorphic and entire functions (open mapping, maximum modulus, mean value, Poisson's, Rouche's, Liouville's, Picard's and Mittag-Leffler's theorems), residue theory (residue theorem, argument principle and applications), conformal mappings (Mobius and Christoffel-Schwarz canonical transformations, Riemann mapping theorem), analytic continuation (monodromy theorem, Schwarz reflection principle, Riemann surfaces and multi-valued functions).

Prerequisite(s): A minimum grade of "C" in MATH   5331 and MATH   5434.

MATH   7334   Approximation Theory

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of the approximation of functions in normed linear spaces. The course emphasizes the theory of interpolation and approximation by polynomials, rational functions and spline functions. Main topics include: best approximation, order of approximation, interpolation, existence and uniqueness of best approximants, theorems by Weierstrass, Haar, Chebyshev, Bernstein, Markov, Korovkin, Schoenberg, and applications.

Prerequisite(s): A minimum grade of "C" in MATH   5331 and MATH   5335.

MATH   7420   Applied Combinatorics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Counting principles including combinations, permutations, generating functions, recurrence relations, the principle of inclusion, exclusion and Polya's theory of counting. This course is for high school mathematics teachers in the MAT or MED programs, who have had a full sequence of calculus courses and a first course in linear algebra.

MATH   7430   Abstract Algebra I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This course provides a comprehensive study of group theory. The course begins with basic concepts of group theory (binary structures, subgroups, homomorphisms) and continues with the study of normal subgroups, quotient groups and the isomorphism theorems. Further topics to be studied include group actions, Sylow's theorem and the structure of finitely generated abelian groups.

Prerequisite(s): A minimum grade of "C" in MATH   5333 or MATH   5333G.

MATH   7431   Abstract Algebra II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The course provides a comprehensive study of rings and fields. The course begins with the basic concepts (rings, subrings, ideals, quotient rings, homomorphisms), continues with the arithmetic of rings, applications to rings of polynomials and field theory, and concludes with a chapter on Galois theory that links field theory and group theory.

Prerequisite(s): A minimum grade of "C" in MATH   7430.

MATH   7432   Differential Geometry of Manifolds

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study and applications of calculus on manifolds. Topics include: atlases, tangent spaces, differentiable maps; immersions and submanifolds, submersions and quotient manifolds; matrix groups and their Lie algebras; vector fields and flows; differential forms, exterior derivative, and Lie derivative.

Prerequisite(s): A minimum grade of "C" in MATH   3230 and MATH   5335.

MATH   7435   Elements of Algebraic Topology

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of the topology of geometric objects from the algebraic viewpoint, in particular using homotopy and homology groups. Main topics: Topological manifolds, homotopy, fundamental group, free groups, covering spaces, and homology.

Prerequisite(s): A minimum grade of "C" in MATH   5435.

MATH   7610   Graduate Seminar

1 Credit Hour.   1 Lecture Hour.   0 Lab Hours.

Under supervision of one or more faculty members, each student will choose topics related to his or her concentration, or topics of interest to the class, read and research on them, then make presentations in front of the class or a larger audience. Students will also attend presentations of internal and external speakers on mathematical sciences.

Prerequisite(s): A minimum grade of "C" in MATH   5332 or MATH   5335 or STAT   5531 or MATH   7231.

MATH   7820   Historical & Cult Dev of Math

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

MATH   7821   Hist & Cult Dev of Math II

3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

MATH   7890   Directed Study in Mathematics

1-3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

Directed study under faculty supervision.

Prerequisite(s): Permission of instructor and Department Chair required.

MATH   7895   Research

1-3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

Graduate students will conduct a program of independent research under the direction of a thesis advisor or an advisory committee on a topic in Mathematical Sciences. Results of the research will be presented as a thesis in partial fulfillment of the requirement of the Master of Science degree.

MATH   7999   Thesis

1-3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

Results of independent research conducted under the direction of a thesis advisor will be presented as a thesis in partial fulfillment of the Master of Science degree. The thesis will be defended before an advisory committee.

STAT   5130G   Sampling and Survey Methods

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introduction to the design and analysis of sample surveys suitable for students in business, social sciences, and biological sciences in addition to the mathematical sciences. Comparison of simple random sampling, stratified, systemic, cluster and multistage sampling. Emphasis on appropriate sample type and estimation of parameters. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Cross Listing(s): STAT   5130.

STAT   5330G   Introduction to Mathematical Statistics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introductory course intended to present a solid foundation in statistical theory, and, at the same time, to provide an indication of the relevance and importance of the theory in solving practical problems in the real world. Topics include, moments and moment-generating functions, point and interval estimation, test of statistical hypothesis, contingency tables and goodness-of-fit, nonparametric methods, and introduction to linear models. This course covers part of the material outlined in the Society of Actuaries' course 110. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   3337.

Cross Listing(s): STAT   5330.

STAT   5531G   Statistical Methods I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This is the first of a two course sequence in applied statistics. The material covered will provide an introduction to statistical concepts and terminology while focusing on descriptive and inferential methods of data analysis. Topics include descriptive statistics, parameter estimation, tests of significance, confidence intervals, analysis of variance, simple linear regression and correlation, and resampling methods including bootstrapping. Both parametric and nonparametric methods are presented for the analysis of central tendency, variability, proportions and categorical data. Graduate students will be required to complete advanced level assignments in an area beyond the scope of the undergraduate requirements that demonstrates a higher level of mastery in the subject matter with additional required deliverables representative of graduate level work, as determined by the instructor.

Prerequisite(s): A minimum grade of "C" in MATH   3337.

Cross Listing(s): STAT   5531.

STAT   5532G   Statistical Methods II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This is the second of a two course sequence in applied statistics. The material covered will provide an introduction to the ideas of linear models and experimental design while focusing on methods of data analysis using regression and analysis of variance. Topics include multiple regression analysis, analysis of variance with multiple classification, analysis of covariance, repeated measures analysis of variance, multiple comparison techniques, and diagnostic procedures and transformations. Suitable for students in business administration, economics, and the social, health and biological sciences. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Cross Listing(s): STAT   5532.

STAT   7090   Selected Topics in Statistics

1-3 Credit Hours.   1-3 Lecture Hours.   0-2 Lab Hours.

Selected study in a selected area of Statistics.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7130   Applied Multivariate Statistical Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Estimating and inference from the multivariate normal distribution, Hotelling's T 2, multivariate analysis of variance, multivariate regression, multivariate experimental design, principle component analysis, factor analysis, discriminate analysis and cluster analysis.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7132   Applied Nonparametric Statistics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Review of probability and statistical inference; binomial, quantile and sign tests; contingency tables; methods based on ranks.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7134   Applied Regression Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Simple and multiple linear regression, model selection, residual analysis, influence diagnostics, transformation of data to fit assumptions, multicollinearity and an introduction to nonlinear regression.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7135   Analysis of Discrete Data

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of discrete univariate and multivariate distributions and generating functions, two-way and higher dimensional contingency tables, chi-squared and other goodness-of-fit tests, Cochran-Mantel-Hanzel procedure, binary and multinomial response models, log-linear models, theoretical foundations for the generalized linear models, mixed generalized linear models, longitudinal and spatial data analysis.

Prerequisite(s): STAT   7331 and STAT   5531, with a minimum grade of "C".

STAT   7231   Design of Experiments I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Various statistically designed experiments are introduced including randomized blocks designs, Latin squares, incomplete block designs, factorial and fractional factorial designs with and without confounding and nested designs.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7232   Design of Experiments II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Response surface methodology is introduced. First- and second-order models and designs are studied which includes determining optimum conditions and methods of estimating response surfaces. Multiresponse experiments, nonlinear response surface models, and mixture designs are also studied.

Prerequisite(s): STAT   7231.

STAT   7234   Statistical Process Control

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Philosophy of statistical process control is studied along with SPC techniques of control charts, process-capability, designed experiments and acceptance sampling.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7331   Mathematical Statistics I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Random variables, density functions, mathematical expectation, discrete and continuous distributions, moments and moment-generating functions and limiting distributions.

Prerequisite(s): MATH   2242 and MATH   3337.

STAT   7332   Mathematical Statistics II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Rigorous introduction/development of interval estimation, test of significance, comparison of “k” means, randomized block design, multiple comparison procedures, nonparametric test and linear regression. The general linear model will be introduced.

Prerequisite(s): STAT   7331.

STAT   7430   Actuarial Mathematics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Survival distributions and life tables, life insurance, life annuities, net premiums, multiple life functions, multiple decrement models, valuation theory for pension plans, collective risk models, population theory and theory of pension funding.

Prerequisite(s): STAT   7331.

STAT   7432   Applied Stochastic Processes

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Poisson process, renewal theory, Markov chains, Brownian motion, random walks and Martingales and stochastic order relations.

Prerequisite(s): STAT   7331 with a minimum grade of "C".

STAT   7434   Applied Time Series Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Basic ideas of stochastic model building techniques with applications are discussed. Properties of the autocorrelation function and the spectrum of stationary processes are investigated. Models studied include the linear stationary ARMA and linear non-stationary ARIMA models along with forecasting models.

Prerequisite(s): STAT   7331.

STAT   7436   Reliability Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Probabilistic models for the reliability of coherent systems, statistical models for lifetimes of components and repairable systems, including the nonhomogeneous Poisson process, reliability estimation and prediction, MIL standards and accelerated life testing.

Prerequisite(s): STAT   7331.

STAT   7530   Statistical Computing I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Basic computer organization and computer arithmetic are investigated. Programming languages and statistical software packages are explored. Methods for approximating cumulative distribution function and percentage points of a probability distribution are studied including nonparametric procedures. Multiple comparison procedures are also examined. Random number generation and statistical tests for testing random number generators are explored.

Prerequisite(s): STAT   7331.

STAT   7532   Statistical Computing II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Various computational methods in linear algebra as applied to such statistical methods as multiple linear regression, designed experiments, multivariate analysis and the general linear model. Further topics include computational methods for unconstrained optimization, nonlinear regression and model fitting based on criteria other than least squares.

Prerequisite(s): STAT   5532 or STAT   5532G, and STAT   7331.

STAT   7610   Gradute Seminar

1 Credit Hour.   1 Lecture Hour.   0 Lab Hours.

Students will research topics related to their major/concentration, under supervision of one or more faculty members. Each student will present results on topics of interest to the class on new developments in mathematical sciences, or on his/her research project. Faculty members also may present lectures for the benefit of the students. Course may be repeated up to a maximum of 3 credit hours to be counted toward the M.S. in Mathematics.

Cross Listing(s): MATH   7610.

STAT   7890   Directed Study in Statistics

1-3 Credit Hours.   1-3 Lecture Hours.   0-2 Lab Hours.

Directed study under faculty supervision.

Prerequisite(s): Permission of instructor and Department Chair.

STAT   7895   Research

1-3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

Graduate students will conduct a program of independent research under the direction of a thesis advisor or an advisory committee on a topic in Statistics. Results of the research will be presented as a thesis in MATH   7999 for partial fulfillment of the requirement of the Master of Science Degree in Mathematics with an emphasis in Statistics.

STAT   7899   Research Project in Statistics

1-6 Credit Hours.   1-6 Lecture Hours.   0-4 Lab Hours.

Research project addressed toward a real world problem.

Prerequisite(s): Permission of project advisor and Department Chair required.