Math 5110 Discrete Mathematical Structures 3
Selected topics from sets and relations, algebraic
structures, logic, combinatorics, graphs, trees, recursion
and generating functions, analysis of algorithms,
formal languages and finite state machines.
Prerequisite: Two semesters of calculus
Math 5115 Logic 3 Truth functions, Post's theorem, sentence and predicate
logic, decidability, completeness, recursive functions,
formal arithmetic, Go del's theorem, applications
to automata theory. Prerequisite: An undergraduate course in logic or
modern algebra, geometry or analysis
ALGEBRA
Math 5200 Linear Algebra 3
Systems of linear equations, vector spaces, matrices,
linear transformations, linear programming, and applications.
Prerequisite: One year of calculus
Math 5220 Modern Algebra 3
Topics are selected from boolean algebras, monoids
and groups, lattices and posets, rings and ideals,
modules, vector spaces and fields.
Prerequisite: Six credits of undergraduate mathematics
at the junior-senior level, or permission of the instructor.
GEOMETRY
Math 5300 Geometry 3
Affine and Euclidean geometry of 3-space and complex
metric spaces. Applications to crystallography, tessellations,
fractals.
Prerequisite: On year of calculus and one semester
of linear algebra.
Math 5310 Topological Structures 3
The topology of the real line and plane along with
abstract topological spaces are considered. Topics
include compactness, connectedness, homeomorphism,
nets, filters, separation axioms and cardinality,
introduction ot uniform and proximity spaces and elementary
homotopy and homology theory.
Prerequisite:Four semesters of calculus or the equivalent.
ANALYSIS
Math 5400 Principles of Mathematical Analysis
3
A methematically rigorous study of the real number
system, topology of Euclidean space, continuity, differentiation,
Riemann - Stieljes integra, Lebesque measure and integration,
sequences of functions.
Prerequisite: Math 3452 or equivalent.
Math 5410 Partial Differential Equations 3
Physical sources of partial differential equations,
separation of variables, eigen function expansions,
transforms, Green's functions, operational methods,
numerical and analog methods, applications to problems
of physical science.
Prerequisite: Math 3451 Calculus III or permission
of instructor.
Math 5420 Applied Complex Variables 3
A mathematically rigorous study of the complex number
system, topology of the complex plane, analytic functions,
complex integration, conformal mappings, power series,
applications to physics and engineering.
Prerequisite: Math 3452 or equivalent.
PROBABILITY AND STATISTICS
Math 5500 Statistical Methods for Analyzing Data
3
Designed to give graduate students with some mathematical
maturity basic skills in research. Includes use of
the computer to do statistical analyses, review of
descriptive statistics, correlation and regression,
hypothesis testing for different types of data, distribution
of data, estimators. For general elective credit only.
Prerequisite: Undergraduate course in statistics.
Math 5505 Applied Statistical Analysis 3
Presents fundamental concepts of statistical methodology.
Topics include sampling distributions, statistical
inference, analysis of variance for designed experiments
with applications, analysis of categorical data, correlation
and regression analysis, applications to statistical
model building, and analysis of covariance. Computer
software will be utilized.
Prerequisite: An undergraduate course in statistics
and Calculus II.
Math 5510 Multiple Regression Analysis 3
Least squares estimators as applied to multiple independent
variables and the single dependent variable. Application
to ANOVA and ANCOVA designs including coded variables,
disproportionate cell frequencies, dicriminant and
path analysis. Computer facilities utilized.
Prerequisite: A course in statistics or linear algebra
or permission of the instructor.
Math 5515 Design and Analysis of Experiments
3
Introduction to the principles of the design and analysis
of experiments with emphasis on applications. Topics
include randomized blocks, Latin squares, factorial
experiments, nested designs, split-plot designs and
response surface methods. Statistical software packages
will be utilized.
Prerequisite: Math 5505.
Math 5520 Probability 3
Formal structure of a probability model. Combinatorial
analysis. Discrete and continuous random variables.
Law of large numbers. Conditional probability, stochastic
independence. Bernoulli, binomial, Poisson, uniform,
exponential and normal distributions and their applications.
Multivariate distributons. Stochastice processes and
Markov chains. Applications.
Prerequisite: Six hours of calculus or permission
of the instructor.
Math 5525 Statistical Quality Control 3
Shewhart's control charts, exponentially weighted
moving average charts, statistical process-control
techniques, process-capability analysis, economic
design of control charts, process improvement with
designed experiments, cmparison of different types
of control cahrts, control charts of autocorrelated
data, multivariate quality control charts, acceptance
sampling, differences between theory and practice
in quality control. Computer will be utilized.
Prerequisite: A course in statistics and one year
of calculus.
Math 5530 Applied Multivariable Analysis 3
Varieties of analytic models including principal discriminant
analysis. Computer applications. Correlated random
variables and their applications in econometrics,
sociometrics, psychometrics and education.
Prerequisite: Math 5500 or permission of the instructor.
Math 5540 Actuarial Mathematics 3
Survial distributions and Life Tables, Introduction
to Risk Theory, Short-Term insurance, Life Insurance,
Pensions, Life Annuities, Net Premiums, Net Premium
Reserves, Multiple Life Functions, Multiple Decrement
Models, Collective Risk Models for single and extended
periods, Applications of Risk Theory.
Prerequisite: Math 5520 and Multivariate Calculus.
APPLICATIONS
Math 5600 Special Topics in Mathematics 3
A study of several classical as well as recent results
in various areas of mathematics. Topics may be chosen
from (but not be limited to) analysis, topology, geometry,
algebra, logic, statistics and discrete mathematics.
Prerequisite: Calculus IV or equivalent or permission
of the instructor.
Math 5610 Project/Research Seminar in Computing,
Statistics and Mathematics 3
A seminar course to integrate ideas, concepts, and
methods from the various areas of applied mathematics.
The student will select a research paper topic or
an industry related problems, write a paper, present
the paper and lead discussion. The topic or project
must be approved by the instructor.
Prerequisite: Completion of the core requirements
and 24 graduate credits.
Math 5620 Mathematics, Randomness, and Linguistics
3
The notion of randomness is explored by simple applications
to the field of linguistics and information theory.
Topics include: analysis and reconstruction of "dead"
languages, language statistics in the design of computer
text processing applications, determination of document
authorship, and extraterrestrial communication.
EDUCATION
Math 5700 Current Issues in Mathematics Education
3
Critical study of secondary mathematics curriculum:
courses of study, instructional methods, evaluative
procedures and reform initiatives. Investigation of
issues affecting the above, such as attitudes, anxiety,
sexism, the use of calculators and computers.
Math 5710 Supervision of Mathematics Programs
3
The role of the mathematics supervisor in the administration
and supervision of a K-12 program; mathematics laboratories;
computer facilities; media; remedial programs; advanced
placement programs; curriculum revision; budget.
Math 5798 - 5799 Advanced Seminar: Research in
Mathematics Education I & II (3,3)
Study of recent reaserch in mathematics education
reported in the professional literature. Guidance
in preparing a research proposal and carrying it out.
Examination of current problems in the field.
HISTORY
Math 5800 The Contemporary Mathematical Scene
3
An exploration of some creative mathematical ideas
primarily form the nineteenth century that have had
important applications in the twentieth century.
COMPUTER SCIENCE COURSES
CPS 5900 Numerical Analysis 3
Development and analysis of numerical algorithmic
solutions. Recognition of propagated errors. Applications
via computer programming.
Prerequisite: Math 3451 Calculus III and knowledge
of a high level programming language.
CPS 5910 Computer Simulations of Models 3
Design, programming and analysis of discrete and continuous
computer simulation languages applied to modeling
techniques.
Prerequisite: Knowledge of computer programming, Math
3544 Probalility or permission of the instructor.
MIS Prerequisite: MIS 5104.
CPS 5911 - 5912 Computer Structures and Programming
I & II (3,3)
Abstract data types. Data abstraction. Module development.
Principles of structured programing. CPS 5911 must
be taken before CPS 5912.
CPS 5915 Computer in a Research Setting 3
Emerging computing technology as an adjunct in all
phases of scientific research project: initial background
study and literature search, data collection, data
analysis, preparation and dissemination of results.
CPS 5920 Database Systems 3
Relational and object-oriented databases: design and
implementation. Exploration of data warehousing, data
mining and on-line analytical processing (OLAP).
Prerequisite: CPS 5921
CPS 5930 Operating Systems Concepts 3
Analysis of concepts and functions of an operating
system. Interrelationships of the operating system
and hardware; file organization and access; storage
and process management in a multiprocessor environment.
Prerequisite:CPS 2440 Data Structures or equivalent
or permission of the instructor.
MIS Prerequisite: MIS 5140.
CPS 5931 Network Systems Concepts 3
Principles, concepts, design and development of Network
Systems. Topics will include concurrent operating
systems and database requirements for the successful
development of a transaction processing application
in a network environment, using the Client/Server
paradigm.
Prerequisite: CPS 3250 or CPS 5930.
CPS 5940 Concepts of Artificial Intelligence
3
An introduction to the central concepts of artificial
intelligence: search, knowledge representation and
reasoning, expert systems, and neural nets.
Prerequisite: MSA 5104 or knowledge of a high level
programming language through data structures.
CPS 5950 Software Engineering 3
Methods and techniques used in the management and
development of large scale information systems. Project
management, joint applications development, rapid
applications development, cost models, functional
vs. object oriented analysis and design, implementation
strategies, testing techniques, quality and maintenance
issues.
Prerequisite: MSA 5104 or CPS 5912 or permission of
the instructor.
CPS 5960 Operations Research: Models and Algorithms
3
Deterministic models of operations research including
linear programming, network folws, gradients, sequential
unconstrained minimizations and their interpretation.
Prerequisite: Six credits of calculus or permission
of the instructor.
CPS 59XX Computer Security and Information Theory
3
Information and coding, measurement and transmission
of information, redundancy, noise, data bank security
in government and industry, computer network weakness,
data encryption.