 |
"The future mathematician ... should solve problems, choose the problems which are in his line, imeditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line." - G. Polya |
 |
Mathematics |
 |
Graduate Level Courses
| Math
6211. Optimization. (3) Prerequisite: Math 2215. |
Lagrange multipliers, gradient methods (steepest descent), search techniques, variational methods and control problems; other topics such as dynamic and nonlinear programming. (Formerly Math 611) |
| Math
6250. Complex Analysis. (3) Prerequisite: Math 3000. |
Complex numbers, analytic functions, complex series, Cauchy theory, residue calculus, conformal mapping.(Formerly Math 625) |
| Math
6253. Introduction to Operations Research. (3) Prerequisite: Math 3435 or 3030. |
Linear programming, the simplex method, network theory, game theory, Markov analysis, and other topics such as inventory analysis, queuing theory, integer programming. (Formerly Math 653) |
| Math
6258. Vector Calculus. (3) (Equivalent to Physics 6510) Prerequisite: Math 2215. |
Vector algebra, curvilinear motion, vector fields, gradient, divergence, Laplacian, line and surface integrals, integral theorems. (Formerly Math 658) |
| Math
6265. Partial Differential Equations. (3) (Equivalent to Physics 6520) Prerequisite: a course in ordinary differential equations. |
First-order
equations, classification of linear second-order equations, separation of variables,
Fourier series, orthogonal functions, Green's functions. (Formerly Math 665) |
| Math
6301. Transformational Geometry. (3) Prerequisite: Math 3000 |
For middle and secondary teachers, emphasizing an algebraic approach to geometry using vectors and transformations. (Formerly Math 601) |
| Math
6371. Modern Geometry. (3) Prerequisite: Math 3000. |
Euclidean
and non-Euclidean geometry, including incidence, order, and the parallel postulate.
(Formerly Math 671) |
| Math 6391. Introduction to Differential Geometry and its Applications. (3) (Same as Phys 6391) | The theory of curves and surfaces in parametric and implicit form. Curvature and torsion of a curve. The shape operator and the total and mean curvature of a surface. The Gauss-Weingarten equations. The Egregium Theorem. Surfaces of constant curvature and non-Euclidean geometry. Minimal surfaces. The Gauss Bonnet Theorem. Submanifolds in Euclidian spaces, vector fields, differential forms and the theorems of Frobenius and Stokes. Applications to Physics. |
| Math
6435. Linear Algebra. (3) Prerequisite: Math 3435 . |
Theory and applications of matrix algebra, vector spaces and linear transformations; topics include characteristic values, the spectral theorem, and orthogonality. (Formerly Math 635) |
| Math
6441. Modern Algebra I. (3) Prerequisite: Math 3000. |
Integers; rational, real and complex numbers; group theory. (Formerly Math 641) |
| Math
6442. Modern Algebra II. (3) Prerequisite: Math 4441/6441. |
Rings, integral domains, and fields; polynomials over a field, matrices over a field, algebraic numbers and ideals. (Formerly Math 642) |
| Math
6450. Theory of Numbers. (3) Prerequisite: Math 3000. |
Properties of integers, divisibility, congruence of numbers, Lagrange's theorem, residues, diophantine problems. (Formerly Math 650) |
| Math
6544. Biostatistics. (3) (Same as Bio 6744) Prerequisites: Bio 1410, 1420, and Math 2211. |
Principles and methods of statistics as applied to biology and medicine. (Formerly Math 644) |
| Math
6547. Introduction to Statistical Methods. (3) Prerequisite: a course in calculus. |
Data analysis, sampling, and probability; standard methods of statistical inference, including t-tests, chi-square tests, and nonparametric methods. Applications include use of a statistical computer package. (Formerly Math 647) |
| Math
6548. Methods of Regression and Analysis of Variance. (3) Prerequisites: a course in calculus and a course covering methods of statistical inference. |
Simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, design and analysis of experiments. applications include use of a statistical computer package. (Formerly Math 648) |
| Math
6610. Numerical Analysis I. (3) Prerequisites: Math 2215 and the ability to program in a high level language. Same as CSc 6610. |
Nature of error; iteration; techniques for nonlinear systems; zeros of functions; interpolation; numerical differentiation; Newton-Cotes formulae for definite integrals; computer implementation of algorithms. |
| Math
6620. Numerical Analysis II. (3) Prerequisites: Math/CSc 6610, Math 3435 or 3030. Same as CSc 6620 |
Gaussian elimination for linear systems; least squeares; Taylor, predictor-corrector and Runge-Kutta methods for solving ordinary differential equations; boundary value problems; partial differential equations. |
| Math
6661. Advanced Calculus I. (3) Prerequisite: Math 4435/6435 |
Functions of several variables; elements of point set theory, numerical sequences and series, limits, continuity, differentiation. (Formerly Math 661) |
| Math
6662. Advanced Calculus II. (3) Prerequisite: Math 4661/6661. |
Functions of several variables; sequences and series of functions; integration theory. (Formerly Math 662) |
| Math
6751. Mathematical Statistics I. (3) Prerequisite: Math 2215. |
Probability, random variables and their distributions, mathematical expectation, moment generating functions, sampling distributions. (Formerly Math 651) |
| Math
6752. Mathematical Statistics II. (3) Prerequisite: Math 4751/6751. |
Theory of estimation and hypothesis testing, applications of statistical inference, introduction to regression and correlation. (Formerly Math 652) |
| Math
6767. Statistical Computing. (3) Prerequisites: Math 4752/6752 or 4548/6548; Math 3435, and the ability to program in a high-level language. |
Computational implementation of statistical methods such as descriptive statistics, one and two sample t tests, regression, correlation, ANOVA methods of estimation, and Monte Carlo techniques. Standard statistical packages will be used as well as user-written programs. (Formerly Math 667) |
| ** Math
7120. Fundamental Concepts of Analysis. (3) Prerequisite: Math 2215. |
Designed to give a unified perspective to the concepts of function, limit, continuity, and derivative by studying them in various settings including vector valued functions, complex functions, and sequences of real valued functions of a real variable. (Formerly Math 712) |
| *Math 7800. Topics in Secondary Mathematics. (3) | |
| ** Math 7820. Historical and Cultural Development of Mathematics I. (3). | Exploration
of the historical and cultural development of mathematics between ~3000 B.C. and ~ A.D.
1600. Mathematics topics to include the development of arithmetic, geometry (practical,
deductive, and axiomatic), number theory, trigonometry, syncopated and symbolic algebra,
probability and statistics. |
| ** Math
7820. Historical and Cultural Development of Mathematics II. (3) Prerequisite: Math 2211. |
Exploration of the historical and cultural develoment of mathematics from ~A.D. 1600 to present. Mathematics topics to include the development of algebraic geometry, logarithms, calculus, non-Euclidean Geometry, abstract algebra, probability and analysis. |
| ** Math
7840. Mathematical Models. (3) Prerequisite: Math 3435. |
Use of
mathematical models to solve problem situations arising in the natural, social,
engineering, and business sciences. (Formerly Math 784) |
| Math
8110. Real Analysis I. (3) Prerequisite: Math 4661/6661. |
Topology of metric spaces, the RiemannStieltjes Integral, sequences and series of functions, analysis of functions from Rn to Rm and special functions. (Formerly Math 811) |
| Math
8120. Real Analysis II. (3). Prerequisite: Math 8110. |
Theory of measure and integration, and related topics. (Formerly Math 812) |
| Math
8200. Advanced Matrix Analysis. (3) Prerequisite: Math 4435/6435 . |
Topics oriented to applications of linear algebra; topics may include: Jordan canonical form, variational characterizations of eigenvalues of Hermitian matrices, congruence and simultaneous diagonalization, eigenvalue location and Gersgorin theory, positive definite matrices, nonnegative matrices, and the PersonFrobenius theorem. (Formerly Math 820) |
| Math
8220. Abstract Algebra. (3) Prerequisite: Math 4441/6441 . |
Advanced topics from groups, rings, modules, and fields including applications to combinatorics and coding theory. (Formerly Math 822) |
| * Math 8230. Topics in Algebra. (3) | (Formerly
Math 823) |
| Math
8310. Theory of Functions of a Complex Variable. (3) Prerequisite: Math 4662/6662 |
Basic theory of complex numbers and of analytic functions, conformal mapping, integration, power series, theory of residues, analytic continuation, theory of singularities, univalent functions, multiplevalued functions, Riemann surfaces. (Formerly Math 831) |
| Math
8510. Applied Mathematics. (3) Prerequisite: Math 4661/6661 . |
Topics in mathematics applicable to natural and social sciences, engineering, business, or the arts; differential and difference equations, integral equations, transform theory, numerical analysis, approximation theory, optimization and calculus of variations, and continuum mechanics. (Formerly Math 851) |
| Math
8520. Applied Combinatorics and Graph Theory. (3) Prerequisite: CSc 4520/6520. Same as CSc 8520. |
Development of combinatorial and graphical algorithms. Techniques for the study of complexity with application to algorithms in graph theory, sorting and searching. |
| * Math 8530. Topics in Applied Mathematics. (3) | (Formerly Math 853) |
| Math
8610. Advanced Numerical Analysis. (3) Prerequisite: Math 4435/6435, Math/CSc 4610/6610. Same as CSc 8610. |
Advanced topics in numerical analysis. Stability and conditioning, discretization error, convergence. Examples are drawn from linear algebra, differential and nonlinear equations. |
| Math 8620. Numerical Linear Algebra. (3) Prerequisite: Math 4435/6435, Math/CSc 4610/6610. Same as CSc 8620. | Computational aspects of linear algebra. Matrix factorization, least squares, orthogonal transformations, eigenvalues and methods for sparse matrices. |
| * Math 8800. Topics in Mathematics. (3) | (Formerly Math 880) |
| Math
8820. Research (3) Prerequisite: consent of instructor and chair of department. |
Independent investigation of topics of common interest to student and instructor. (Formerly Math 882) |
| Math
8999. Thesis Research. (19) Prerequisite: Thesis option |
(Formerly Math 899) |
| Stat
8090. Applied Multivariate Statistics. (3) Prerequisite: consent of instructor. |
Matrix algebra, multivariate normal distributions, discriminant analysis, canonical correlations, and multivariate analysis of variance. (Formerly Stat 809) |
| Stat
8440. Survival Analysis. (3) Prerequisite: Math 4752/6752. |
Topics included are survival function, hazard function, right censoring, nonparametric methods for comparing two survival distributions, parametric and nonparametric regression methods with survival data. |
| Stat
8540. Advanced Methods in Biostatistics. (3) Prerequisite: Math 4544/6544. |
Modern/Classical statistical/biostatistical methods like smoothing techniques and data summaries, linear models, generalized linear models, modern nonlinear regression techniques, multivariate statistics, survival analysis using S-PLUS. (Formerly Stat 854) |
| Stat
85618562 . Linear Statistical Analysis I and II. (3 each) Prerequisite: Math 4751/6751 for Stat 8561 and Math 4752/6752 for Stat 8562. |
Topics included are statistical inference, multivariate normal distribution, distribution of quadratic forms, linear models, regression models and experimental design models. (Formerly Stat 856 - 857) |
| Stat
85818582. Statistical Theory I and II. (3 each) Prerequisite: Math 4752/6752 for Stat 8581; Stat 8581 for Stat 8582. |
Classical and modern statistics, probability, decision theory, estimation theory, testing hypotheses, confidence intervals, large sample theory, sequential analysis. (Formerly Stat 858 - 859) |
| Stat
8600. Probability Theory. (3) Prerequisite: Math 4752/6752. |
Random variables and expectations, distribution and characteristic functions, laws of large numbers and central limit theorem, conditional probability and expectation. (Formerly Stat 860) |
| Stat
8610. Time Series Analysis. (3) Prerequisite: Math 4752/6752. |
Introduction to stationary stochastic processes, spectral representations; BoxJenkins time series models; forecasting methods. Applications include use of a statistical computer package. (Formerly Stat 861) |
| Stat
8630. Experimental Designs. (3) Prerequisite: Math 4752/6752. |
Analysis of randomized and incomplete block designs; factorial and nested designs using fixed, random, and mixed effects models. Applications include use of statistical computer package. (Formerly Stat 863) |
| Stat
8650. Multivariate Analysis. (3) Prerequisite: Math 4752/6752. |
Multivariate normal distribution and related distributions, multiple regression, canonical correlations, multivariate analysis of variance, discriminant functions, factor analysis. (Formerly Stat 865) |
| Stat
8660. Statistical Analysis of Directions, Shapes and Images. (3) Prerequisite: Consent of instructor. |
Methods of statistical analysis of digitized data with applications from natural images common in science and medicine. Distributions on shape spaces and projective shape spaces. High level image analysis using large sample, bootstrap, Bayesian and simulation methods. Scanning, landmarks and triangulations. Applications include use of imaging and statistical software. |
| Stat
8670. Computational Methods in Statistics. (3) Prerequisites: Math 4752/6752 and the ability to program in a high-level language. |
Numerical stability of statistical package program algorithms for general linear models; influential observations; principles of Monte Carlo methods; crossvalidation, jackknife, and bootstrap methods of data analysis with applications to regression and discriminant analysis; use of statistical software packages. (Formerly Stat 867) |
| * Stat 8690. Topics in Statistics. (3) | (Formerly Stat 869) |
| Stat 8700. Analysis of Qualitative Data. (3) Prerequisite: Math 4752/6752. | Analysis of multinomial data, contingency tables, single degrees of freedoms in chisquare analysis; RBAN estimation; quantitative methods in Bioassay. (Formerly Stat 870) |
| Stat
8760. Sample Surveys. (3) Prerequisite: Math 4752/6752. |
Sampling from finite populations; random, stratified, cluster, and systematic sampling; estimation of means and variances; ratio and regression sampling. (Formerly Stat 876) |
| Stat
8820. Research.(3) Prerequisite: consent of instructor and chair of department. |
Directed research leading to a research paper in statistics or analysis of a statistical problem. This course is intended to satisfy the requirement for a research paper or a written report of a laboratory experience for the nonthesis option. (Formerly Stat 882) |
| Stat
8999. Thesis Research. (19) Prerequisite: thesis option. |
(Formerly Stat 899) |
* May be taken more than once if topics are different.
** Math 7120, 7820 and 7840 are for high school mathematics teachers in the M.A.T. or
M.Ed. programs who have had a full sequence of calculus courses and a first course in
linear algebra.
| General Information | Courses | Schedules | Publications |
| Undergraduate Programs |
Graduate Programs | Faculty Pages | Careers and Employment |
Comments regarding the GSU Math & Stat Web Site should be referred to: web@mathstat.cs.gsu.edu