Graduate Courses

FOUNDATIONS

  • 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.