Department of Mathematics and Computer Science Georgia State University

CSc 615. Design and Analysis of Algorithms.(5)
   Prerequisite: CSc 231.
   Techniques for designing efficient algorithms; analysis
of algorithms; lower bound arguments; algorithms for sorting, 
selection, graphs, and string matching.

CSc 631. Organization of Programming Language. (5)
   Prerequisite: CSc 231, CIS 303, or CIS305.
   Comparative study of several programming languages
including compilers and interpreters, run time behavior, 
and formal language concepts.

CSc 633. Software Engineering. (5)
   Prerequisite: CSc 631.
   Techniques used in large-scal scientific or
technical software development, including requirements
analysis, specification, systems design, implementation,
testing, validation, verification, and maintenance.

CSc 634. Human-Computer Interaction. (5)
   Extra Information
   Prerequisite: CSc 231.
   Tehniques and methodologies for development of user 
interfaces in software systems; topics of user interaction
styles, interaction devices, user documentation, and 
interface assessment.

CSc 637. Introduction to Compilers. (5)
   Prerequisite: CSc 631.
   Topics related to compiler design, including parsing, 
table processing, code generation, and optimization.

CSc 639. Operating Systems. (5)
   Prerequisite: CSc 631.
   Introduction to operating system concepts. Topics
may include multiprogramming, resources allocation and
management, and their implementation.

CSc 643. Computer Architecture. (5)
   Prerequisite: CSc 343 and Math 220.
   Logic design, combinatorial and sequential circuits,
input-output devices, memory, processors, controllers,
parallel architectures, bit-slicing, reduced instruction
sets.

CSc 655. Numerical Approximation. (5)
   Prerequisite: Math 215, Math 216, 335, and ability to 
program.
   Nature of error, Gauss elimination for linear systems;
iteration, Newton's method, steepest descent for nonlinear 
systems; zeros of polynomials, interpolation.

CSc 656. Numerical Calculus. (5)
   Prerequisite: Math 215, 216, and
ability to program.
   Least squares, Newton-Cotes formula for definite integrals,
difference formulas for numerical differentiation; Taylor,
predicator corrector, and Runge-Kutta methods for ordinary
differential equations; boundary value problems; partial
differential equations.

CSc 659. System Simulation. (5)
   Prerequisites: CSc 221 or CSc 226, and
Math 652.
   Concepts and methods for developing simulation
models of discrete systems, including development
of algorithms for program execution for statistical
analyses of sample event sequences, for random
number generation, and computer sampling. Translation
of models into high level language and a simulation
language.

CSc 670. Computer Graphics Algorithms. (5)
   Algorithms used for computer graphics programming.
Windows, viewports, modeling transformations in two
and three dimensions, viewing transformations, and
hidden surface elimination. Graphics standards for 
hardware and software systems.

CSc 675. Mathematical Computing. (5)
   Prerequiste: CSc 456 and 226 or
equivalent.
   Performance evaluation of algorithms taken from
the mathematical sciences. Comparisons of complexity
versus accuracy. Software design, testing, documentation,
and maintenance.

CSc 681. Automata. (5)
   Prerequisite: CSc 631.
   Theory of computing devices and the languages they
represent.

CSc 750/751. Computer Science I and II. (5 each)
   An introduction to a high level programming
language and basic data structures with a structured
approach to problem solving, slgorithmic analysis,
and program development.

CSc 815. Advanced Numerical Analysis. (5)
   Prerequisite: Math 635 and CSc 655 or 656.
   Advanced topics in numerical analysis. Stability and
conditioning, discretization error, convergence. Examples 
are drawn from linear algebra, differential and nonlinear 
equations.

CSc 816. Numerical Linear Algebra. (5)
   Prerequisite: Math 635 and CSc 655.
   Computational aspects of linear algebra. Matrix
factorizations, least squares, orthogonal transformations,
eigenvalues and methods for sparse matrices.

CSc 821. Principles of Programming Languages. (5)
   Prerequisite: CSc 631.
   Formal treatment of programming language.
Topics may include grammars, scanners, parsers,
translation, data abstractions, and language 
transformations. 

CSc 829. Applied Combinatories and Graph Theory. (5)
   Prerequisite: CSc 615.
   Development of combinatorial and graphical
algorithms. Techniques for the study of complexity
with application to algorithms in graph theory,
sorting and searching.

CSc 830. Theory of Computation. (5)
   Prerequisite: CSc 681.
   Finite automata and Turing machines as formal
models for computation. Topics may include recursion,
program verification, program schemes, and complexity.

CSc 834. Advanced Human-Computer Interaction. (5).
   Extra Information
   Prerequisite: CSc 633, 634.
   Current trends in user interface technology;
topics include alternative interaction devices,
user interface tools, and interface modeling techniques.

CSc 836. Mathematical Models and Simulation. (5).
   Prerequiste: Math 856 and knowledge
of FORTRAN or Pascal.
   Construction of mathematical models for simulating 
real systems. Emphasis is on the probabilistic and
statistical properties of the models. Models are applied
with computational algorithms using a standard simulation
language.

CSc 870. Advanced Graphics Algorithms. (5)
   Prerequiste: CSc 670.
   Advanced topics in computer graphics, primarily
for raster graphics systems, including raster scan
conversion, three dimensional clipping, removal of
hidden lines and surfaces, solid modeling, shading,
texturing, and use of fractals.

CSc 872. Advanced Software Engineering. (5)
   Prerequisite: CSc 433/633.
   Advanced concepts in software engineering. Topics
may include new lifecycle paradigms, code reusability
issues, formal specifications, new design methodologies, 
and others.

CSc 899. Thesis Research. (1-15)

Math 601. College Geometry. (5)
   Prerequiste: Math 335.
   For secondary teachers, emphasizing an algebraic
approach to geometry using vectors and transformations.

Math 611. Optimization. (5)
   Lagrange multipliers, gradient methods
(steepest descent), search techniques, 
varational methods and control problems;
other topics such as dynamic programming,
nonlinear programming.

Math 625. Complex Analysis. (5)
   Complex numbers, analytic functions, complex
series, Cauchy theory, residue calculus, conformal
mapping.

Math 635. Intermediate Linear Algebra. (5)
   Prerequisite: Math 335.
   Vector spaces and linear transformations;
topics include linear equations, matricies,
determininants, characterisitc values, the
spectral theorem, linear functionals, and dual 
spaces.

Math 641-642. Modern Algebra I and II. (5 each)
   Prerequisite: Math 635.
   Integers; rational, real and complex numbers;
group theory, rings, integral domains, and fields;
polynomials over a field, matrices over a field,
algebraic numbers, and ideals.

Math 644. Biostatistics. (5)
   (Same as Bio 644.)
   Prerequisite: Bio 141, 142, and Math 211.
   Principles and methods of statistics as applied
to biology and medicine.

Math 647. Introduction to Statistical Methods. (5)
   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.

Math 648. Methods of Regression and Analysis
   of Variance. (5)
   Prerequisite: a course in calculus and a
course covering methods of statistical inference.
   Simple and multiple regression, model 
selection procedures, analysis of cariance,
simultaneous inference, design, and analysis of 
experiments. Applications include use of a statistical
computer package.

Math 650. Theory of Numbers. (5).
   Properties of integers, divisibility,
congruence of numbers. Applications include
use of a statistical computer package.

Math 651-652. Mathematical Statistics  I and II. (5 each)
   Introduction to probability; distribution
functions and moment generating functions;
correlation and regressions; development and
applications of the binomial, normal, students't, 
chi-square, and F distributions.

Math 653. Introduction to Operations Research. (5)
   Linear programming, the simplex method, 
network theory, game theory, Markov analysis;
other topics such as inventory analysis,
queueing theory, integer programming.

Math 658. Vector Calculus. (5)
   Prerequiste: Math 215.
   Vector algebra, curvilinear motion, vector
firlds, gradient, divergence, Laplacian,
line and surface integrals, integral theorems.

Math 661-662. Advanced Calculus I and II. (5)
   Prerequisite: Math 635.
   Functions of several variables; elements of
point set theory, sequences, series, continuity, 
limits, differation, and integration.

Math 665. Partial Differential Equations. (5)
   Prerequisite: a course in ordinary 
differential equations.
   First-order equations, classification of
linear second-order equations, separation of
variables, Fourier series, othogonal functions, 
Green's functions.

Math 667. Statistical Computing. (5)
   Prerequisite: Math 652 or 648, and
Math 335; knowledge of FORTRAN.
   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.
 
Math 671. Modern Geometry. (5)
   Prerquisite: Math 335 or 365.
   Euclidean and non-Eucludean geometry, including
incidence, orderm and the parallel postulate.

** Math 703. Geometry for Teachers. (5)
   Points, lines, planes, parallel and
perpendicular lines, congruence, similarity,
measurement, constructions, space figures,
analytical geometry, and non-Euclidean
geometries.

** Math 704. Algebraic Structures for Teachers. (5)
   Elementary study of the properties of groups,
integral domains, and fields.

** Math 705. Probability and Statistics for Teachers. (5)
   Probability, gathering and recording data,
construction and use of tables, tabulating
and graphing percentiles, mean and standard
deviation, frequency distribution, normal
distribution, statistical inference, and correlation.

** Math 708. Computer Mathematics for Teachers. (5)
   Introduction to flow diagrams and BASIC; 
the use and application of computers in grades
4 through 9.

** Math 711. The Real Number System. (5).
   A careful construction of the real
number system followed by a study of the 
important properties of the system.

*** Math 712. Fundamental Conepts of Analysis. (5)
   Designedf to give a unified perspective
to the concepts of function, limit, continutity,
and derivatice by studying them in various
settings including vecotr valued functions, complex
functions, and sequences of real valued functions of 
a real variable.

*** Math 751. Mathematical Problem Solving with
   Computers. (5)
   Prerequisite: CSc 750.
   Computer applications in solving problems
drawn from calculus, probability and statistics,
number theory, numerical analysis, geometry, and 
algebra.

*** Math 782. History of Mathematics. (5)
   Designed to acquaint the student with the
growth and development of the discipline of
mathemtics from antiquity to modern times.
Special emphasis will be given to the 
evolutionary character of the principal ideas
of modern mathematics.

*** Math 784. Mathematical Models. (5)
   Use of mathematical models to solve problem
situations arising in the natural, social,
engineering, and business sciences.

**** Math 791-792. Fundamental Concepts of
   Calculus I and II. (5 each)
   Basic concepts and applications of
calculus including the derivative, the 
integral, and multivariable calculus.

Math 809. Applied Multivariate Statistics. (5)
   (Same as Psy 902.)
   Prerequisite: consent of instructor(s)
   Matrix alegbra, multivariate normal distributions,
discriminant analysis, canonical correlations,
and multivariate analysis of variance.

Math 811. Real Analysis I. (5)
   Prerequisite: Math 661.
   Topology of metric spaces, the
Riemann-Stieltjes Integral, sequences and
series of functions, analysis of functions
from R^n to R^m and special functions.

Math 812. Real Analysis II. (5).
   Prerequisite: Math 811.
   Theory of measure and integration, 
and related topics.

Math 820. Advanced Matrix Analysis. (5)
   Prerequisite: Math 635.
   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 matricies, nonnegative matrices, and
the Perron-Frobenius theorem.

Math 822. Abstract Algebra. (5)
   Prerequisite: Math 642.
   Advanced topics from groups, rings, modules,
and fields including applications to 
combinatories and coding theory.

* Math 823. Topics in Alegbra. (5)

Math 831. Theory of Functions of a Complex
   Variable. (5)
   Prerequisite: Math 662.
   Basic theory of complex numbers and of
analytic functions, conformal mapping, 
integration, power series, theory of residues,
analytic continuation, theory of singularities,
univalent functions, multiple-valued functions,
Riemann surfaces.

Math 841. General Topology. (5)
   Prerequisite: Math 661.
   Topological spaces and subspaces,
connected sets, metrics and metrizability,
compactness, separability, countability
and second countability, function spaces, 
arcs and curves, other topological concepts.

Math 851. Applied Mathematics. (5)
   Prerequisite: Math 661.
   Topics in mathematics applicable to
natural and social sciences, engineering,
business, or the arts; differential and
difference equations, integral equations,
transform theory, optimization and
calculus of variations, and continuum 
mechanics.

* Math 853. Topics in Applied Mathematics. (5)
   
Math 854. Multivariable Methods in Biostatistics. (5)
   Prerequisite: Math 644 or
equivalent.
   Statistical techniques involving several
variables, including analysis of variance and
multiple regression, applied to problems
in the biological sciences. Computer
package programs are used.

Math 856-857. Linear Statistical Analysis I
   and II. (5 each)
   Prerequisite: Math 651 for Math 856 and
Math 652 for Math 857.
   Topics included are statistical inference,
multivaiate normal distribution, distribution 
of quadratic forms, linear models, regression 
models and experimental models.

Math 858-859. Statistical Theory I and II. (5 each)
   Prerequisite: Math 652.
   Classical and modern statistics, probability,
decision theory, estimation theory, testing
hypotheses, confidence intervals, large sample
theory, sequential analysis.

Math 860. Probability Theory. (5)
   Prerequisite: Math 652.
   Random variables and expectations,
distribution and characteristic functions,
laws of large numbers and central limit
theorem, conditional probability and
expectation.

Math 861. Time Series Analysis. (5)
   Prerequisite: Math 652.
   Introduction to stationary stochastic
processes, spectral representations; Box-
Jenkins time series models; forecasting
methods. Applications include use of a 
statistical computer package.

Math 863. Experimental Designs. (5)
   Prerequisite: Math 652.
   Analyis of randomized and incomplete
block designs; factorial and nested designs
using fixed, random, and mixed effects models.
Applocations include use of statistical 
computer package.

Math 865. Multivariate Analysis. (5)
   Prerequisite: Math 652.
   Multivariate normal distribution and
related distributions, multiple regression, 
canonical correlations, multivariate analysis
of variance, discriminant functions, factor
analysis.

Math 867. Computational Methods in Statistics. (5)
   Prerequisite: Math 652.
   Numerical stability of statistical
package program algorithms for general
linear models; influential observations;
principles of Monte Carlo methods; cross-
calidation, jackknife, and bootstrap
methods of data analysis with applications
to regression and discriminant analysis;
use of statistical package programs.

* Math 869. Topics in Statisitics. (5)

Math 870. Analysis of Qualitative Data. (5)
   Prerequisite: Math 652.
   Analysis of multinomial data,
contingency tables, single degrees of
freedoms in chi-square analysis;
RBAN estimation; quantal methods in
Bioessay.

Math 876. Sample Surveys. (5)
   Prerequisite: Math 652.
   Sampling from finite populations;
random, stratified, cluster, and
systematic sampling; estimation of
means and variances; ratio and regression
sampling.

* Math 880. Topics in Mathematics. (5)
  
Math 899. Thesis Research. (1-15)



*    May be taken more than once
     if topics are different.

**   Math 703 through 708 are for students
     in the M.Ed. programs in the College of Education. 
     They may not be applied for degree credit for the 
     M.A.T., M.A., or M.S. in mathematics.

***  Math 711 through 784 are for high school
     mathematics teachers in the M.A.T. or M.Ed. programs
     who ahve had a full sequence of calculus courses and
     a first course in linear algebra.

**** Mathematics courses numbered 791 and 792 
     are special courses for graduate students in majors
     other than mathematics. They may not be applied toward
     degree credit for the M.A.T., M.A., or M.S. in
     mathematics.