Math and Computer Science Courses

600-Level Courses

MTH 609 : Cryptography and Data Security 3 cr.
Encryption algorithms; cryptographic techniques; access, information flow and inference controls.
Prerequisite: MTH 509.

MTH 611. Theory of Computation 3 cr.
Recursive functions, Markov algorithms, Turing machines. Unsolvability.
Prerequisite. MTH 509 and at least one programming course.

MTH 612. Complexity Theory 3 cr.
Models of computations, Blum's axioms, intractability, NP-completeness
Prerequisite: MTH 611.

MTH 613. Computer System Performance Evaluation 3 cr.
Queueing models of computer systems. Inputs and outputs Models with job classes. Flow equivalence and hierarchical modeling. Memory, disk l/O, processors.
Prerequisite: MTH 544.

MTH 621. Mathematical Probability 3 cr.
Development of the measure-theoretic approach to probability. Random variables, central limit theory, laws of large numbers, martingales.
Prerequisite: Permission of department chairman.

MTH 623. Theory of Relational Databases 3 cr.
Relational operators, dependencies, covers for functional dependencies, and normal forms. Representation theory query systems, acyclic database schemes.
Prerequisite: MTH 523.

MTH 625. Multivariate Analysis 3 cr.
Sampling theory for multivariate normal populations. Component and factor analysis Stochastic difference equations.
Prerequisite: MTH 525.

MTH 628. Parallel Algorithms 3 cr.
Parallel computation models; sorting networks; parallel algorithms for sorting, searching, graph problems, prefix computation, pattern matching, and fast Fourier transforms; theory of P-completeness, the class NC.
Prerequisite: MTH 540.

MTH 630, MTH 631. Real Variables 3 cr. each
Lebesgue measure and the Lebesque Integral for R1, Banach Spaces. General measure theory. topological groups and Haar Measure.
Prerequisite: MTH 532.

MTH 632, MTH 633. Complex Variables 3 cr. each
Complex numbers line or transformations, analytic function, conformality. Cauchy's Theorem, representation theorems. harmonic functions.
Prerequisite: MTH 531.

MTH 638. Stochastic Processes 3 cr.
Prerequisite: MTH 631.

MTH 640, MTH 641. Algebraic Topology 3 cr. each
Homotopy, covering space, Eilenberg-Steenrod axioms for (co) homology theories, Mayer-Vietoris sequences Universal Coefficient theorem, Kunneth formula, computations and applications.
Prerequisite: MTH 532.

MTH 644. Advanced Computer Modeling 3 cr.
Formal theories and axiomatic approaches. Process, interactive and robot-oriented simulation. Large systems and computer networks Emulation and dynamic system evaluation. Modeling using Fuzzy concepts. Simulation and expert systems.
Prerequisite: MTH 544.

MTH 645. Introduction to Expert Systems 3 cr.
Overview of expert systems, architecture of expert systems, knowledge base and representation, inference engine, expert system tools, reasoning under uncertainty, explaining the reasoning, evaluation of expert systems.
Prerequisite: MTH 545.

MTH 651, MTH 652. Differential Geometry 3 cr. each

MTH 657. Lie Groups 3 cr.

MTH 661, MTH 662. Abstract Algebra 3 cr. each
Prerequisite: MTH 562

MTH 670. Directed Readings of Research 24 cr.

MTH 680, MTH 681. Topics in Analysis 3 cr. each

MTH 682, MTH 683. Topics in Topology 3 cr. each

MTH 685. Topics in Algebra 3 cr.

MTH 686, MTH 687. Topics In Mathematics 3 cr. each

MTH 688, MTH 689. Topics in Computer Science 3 cr. each

MTH 690. Seminar for Beginning Graduate Students 1-3 cr.
The selection of topics will be flexible but will be of interest to beginning graduate students.

MTH 692. Seminar 1-2 cr.

700-Level Courses

MTH 710. Master's Thesis 1-6 cr.
The student working on his/her master's thesis enrolls for the number of credits as determined by his/her advisor. Credit is not awarded until the thesis has been accepted.

MTH 725. Continuous registration - Master's study 0 cr.
To establish residence for non-thesis master's students who are preparing for a major examination. Credit not granted. Regarded as full time residence.

MTH 730. Doctoral Dissertation 1-12 cr.
Required for all candidates for the Ph.D. The student will enrol for credit as determined by his/her advisor, but for not less than a total of 12 hours. Up to 12 hours may be taken in a regular semester, but not more than six in a summer session.

MTH 740. Research project 1-6 cr.
Required for all candidates for the Doctor of Arts degree. Students enrolls for a credit as determined by advisor. Credit is not awarded until the doctoral project has been accepted. Total enrollment may not exceed six credits.

MTH 750. Research in residence 0 cr.
Used to establish research in residence for the Ph.D. and D.A., after the student has been enrolled for the permissible cumulative total in appropriate doctoral research. Credit not granted. May be regarded as full-time residence as determined by the Dean of the Graduate School.

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