Department of Mathematical, Computing, and Information Sciences

Department Head: Dr. Jan Case, jcase@jsu.edu

MS in Computer Systems and Software Design Graduate Coordinator: Dr. Eric Gamess, egamess@jsu.edu

MS in Mathematics Graduate Coordinator: Dr. Thomas Leathrum, leathrum@jsu.edu

The Department of Mathematical, Computing, and Information Sciences offers courses leading to the Master of Science (MS) with a major in Mathematics and the Master of Science (MS) with a major in Computer Systems and Software Design with two concentrations, as well as supporting courses for the Master of Arts (MA) degree with a major in Integrated Studies. Students pursuing graduate degrees in Secondary Education who meet Mathematical, Computing, and Information Sciences Department admission requirements may take mathematics courses in their teaching field.

NOTE:   Prerequisite for all Mathematics Courses. Graduate courses in Mathematics are open only to students who:

  1. Are admitted to a graduate program of study in Mathematics; or
  2. Are admitted to a graduate program of study in Secondary Education with a teaching field of Mathematics and with all undergraduate deficiencies in Mathematics removed; or
  3. Have completed 32 semester hours in Mathematics with at least 19 upper division hours.
  4. In addition, students must have successfully completed at least one course equivalent to MS 415 Advanced Calculus I (WI) (3) or MS 441 Abstract Algebra I (WI) (3).
  5. Some individual courses have further prerequisites; see the course descriptions below. Exemptions from course prerequisites require permission of the department head.

Mathematics

MS 403  Vector Analysis  (3)  

Prerequisite(s): MS 227.

Algebra and calculus of vectors, Stokes theorem, and divergence theorem; applications to geometry, mass potential functions, electricity, and fluid flow.

MS 404  Mathematical Statistics II  (3)  

Prerequisite(s): MS 227 and 304.

Continuation of MS 304. The Central Limit Theorem, order statistics, functions of random variables, properties of estimators, confidence intervals, hypothesis testing, and least squares regression models.

MS 416  Advanced Calculus II  (3)  

Prerequisite(s): MS 415.

Selected topics from advanced calculus, elements of partial differentiation including the general theorems, Jacobians, topics on the theory of integration.

MS 423  Survey of Geometries  (3)  

Prerequisite(s): MS 323.

Selected topics from advanced Euclidean geometry, finite geometries, non-Euclidean geometry, and other geometries.

MS 451  Functions of a Complex Variable  (3)  

Prerequisite(s): MS 415.

Undergraduate Prerequisite: MS 227 and 300 and 415. Graduate Fundamental operations with complex numbers, differentiation and integration theorems, mapping, series, and residues.

MS 475  Seminar in Mathematics (WI)  (3)  

Prerequisites or corequisites for undergraduate: MS 415 or MS 441 or MS 451. Prerequisites for graduate: See Prerequisites for All Graduate Mathematics Courses. Goals include examining deeply the fundamental ideas of mathematics and connections among various branches of mathematics, exploring the historical development of major concepts, and further developing the habits of mind that define mathematical approaches to problems. (Writing Intensive Course)

MS 480  Introductory Topology  (3)  

Prerequisite(s): MS 415.

Basic topological concepts to include topological spaces, mapping, compactness, connectedness, and separation axioms.

MS 484  Partial Differential Equations  (3)  

Prerequisite(s): MS 227 and 344.

Standard methods of solution; separation of variables, Fourier Series, Laplace Transforms; selected applications.

MS 504  Applied Statistical Methods  (3)  

Prerequisite(s): MS 204 or MS 302 or ST 261.

Fundamental concepts of descriptive and inferential statistics, probability distributions, estimation, and hypothesis testing. Statistical software and/or scripting are used to facilitate analysis and interpretation of results. Emphasis on statistical techniques to analyze data.

MS 505  Basic Logic and Set Theory  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Basic topics in symbolic logic and naive set theory, including sets and set operations, symbolic logic, the language of set theory, and applications of set theory.

MS 515  Real Variables I  (3)  

Prerequisite(s): MS 416 or permission of the instructor.

Measure and measurable sets, measurable functions, Lebesgue integration, and convergence theorems.

MS 516  Real Variables II  (3)  

Prerequisite(s): MS 515.

Selected topics from absolute continuity and differentiation, LP-spaces, Hilbert spaces, and Banach spaces.

MS 517  Introduction to Functional Analysis  (3)  

Prerequisite(s): MS 352 and MS 415.

Introduction to the fundamental topics of functional analysis. Topics include metric spaces, completeness, linear operators, normed spaces and Banach spaces, inner product spaces, and Hilbert spaces. Objectives include the Riesz Representation Theorem, the Hahn-Banach Theorem, and the Contraction Mapping Theorem.

MS 523  Topics in Geometry for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Classical theorems, ideas, and constructions of Euclidean and non-Euclidean geometry in theorems of Ceva, Menelaus, Pappus, and Fererback; homothetic transformations, inversion, harmonic sets of points, and cevians.

MS 526  Topics in Analytical Geometry for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Applications of Euclidean and homogeneous coordinates, geometric transformations, trigonometric, and vector techniques to geometric problems.

MS 528  Theory of Equations and Functions for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Topics in the theory of polynomial and other equations, and in the properties of transcendental functions. The goal is the development of a deeper understanding of the equations and functions commonly encountered in precalculus mathematics. May require the use of computer software.

MS 530  Foundations in Calculus for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Theory, problem solving techniques, and applications of differential and integral calculus, including the use of graphing calculators and computer software. Recommended for students who are teaching or planning to teach Advanced Placement Calculus.

MS 533  Topics in Modern Analysis for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Logic and set theory, functions and sequences, structure and development of the real number system including completeness.

MS 535  Topics in Finite Mathematics for Teachers  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Elementary combinatorial analysis, probability, vectors and matrices, game theory, linear programming, and model building in the social and physical sciences.

MS 537  Foundations in Algebra for the Secondary Teacher  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Concepts of high school algebra from the perspective of ring theory.

MS 541  Abstract Algebra I  (3)  

Prerequisite(s): MS 441.

General group theory including cyclic groups and permutation groups, homomorphism and isomorphism theorems.

MS 542  Abstract Algebra II  (3)  

Prerequisite(s): MS 441.

Theory of rings, ideals, fields, and integral domains.

MS 549  Selected Topics in Mathematics for the Secondary Teacher  (3)  

Prerequisite(s): See Prerequisites for All Graduate Mathematics Courses.

Selected topics suitable for the secondary teacher; problem solving; secondary school mathematics from an advanced standpoint.

MS 552  Linear Algebra  (3)  

Prerequisite(s): MS 352 and MS 441.

Abstract treatment of finite dimensional vector spaces. Linear transformations, determinants, eigenvalues and eigenvectors, invariant subspaces, Rational and Jordan Canonical Forms, inner product spaces, unitary and normal operators, bilinear forms.

MS 588  Mathematics Internship  (6)  

Requires a faculty recommendation and permission of the department head.

MS 591  Seminar in Algebra  (3)  

Prerequisite(s): MS 541 and 542 or permission of instructor.

Selected topics in modern algebra beyond the scope of the graduate algebra sequence. Topics may be chosen from the theory of groups, rings, fields, or modules; linear algebra; homological algebra; or other topics, depending on student and instructor interests. May be duplicated for credit for a total of 6 semester hours.

MS 595  Seminar in Analysis  (3)  

Prerequisite(s): MS 515 and 516 or permission of the instructor.

Selected topics in modern analysis beyond the scope of the graduate analysis sequence. Topics may be chosen from the fields of real analysis (measure theory and integration, special functions, finite differences, functional equations, sequences and series), complex variables, Fourier and harmonic analysis, integral transforms, operator theory, or other topics, depending on student and instructor interests. May be duplicated for credit for a total of 6 semester hours.

MS 598  Directed Readings  (3)  

Prerequisite(s): Students must have two courses in the topical area chosen and approval by the faculty advisor in mathematics and the instructor.

Algebra, analysis, geometry, and topology. May be duplicated for credit for a total of 6 semester hours.

MS 599  Thesis  (3)  

Prerequisite(s): Approval of application for thesis option.

See "Thesis Option and Procedures." May be duplicated for credit for a total of 6 semester hours. Grade: Pass/Fail.

Computer Science

CS 501  Database Management Systems  (3)  

Prerequisite(s): A programming language.

Information as corporate resource, data modeling, database design, implementation strategies and administration; security, information centers, decision support systems, mini- and microcomputer environment; teams of students will design and implement a relational database application.

CS 502  Research Methods and System Evaluation  (3)  

Prerequisite(s): Undergraduate or graduate statistics course.

Introduction to the research techniques and methodologies used to evaluate systems such as control systems, computer systems, security systems, and information systems. Topics include methodological foundations, qualitative research methods and quantitative research methods.

CS 521  Applied Software Engineering I  (3)  

Prerequisite(s): Admission to the MS in SSD program or permission of instructor.

Focuses specifically on methods that guide software engineers from requirements to code; provides broad understanding of current methods, and specific skills in using these methods.

CS 523  Applied Software Engineering II  (3)  

Prerequisite(s): SSD major or permission of instructor.

Provides knowledge and skills necessary to lead a project team, understand the relationship of software development to overall product engineering, and understand the software process.

CS 525  Advanced Web Applications Using Web Services  (3)  

Prerequisite(s): Undergraduate software engineering course or equivalent.

Utilization of various technologies and tools for developing Web applications using Web Services, emphasizing organizational issues, challenges, and security concerns related to the effective deployment of those applications. Students will evaluate real-world applications of Web services as well as the unique decision-making framework involved with their adoption while employing those lessons learned in practical solutions.

CS 530  Human-Computer Interaction  (3)  

Prerequisite(s): Comprehensive undergraduate course in software engineering or industrial software engineering experience with a large project.

Human-computer interface, human performance, diversity, and mental models, interaction devices, dialog and interface styles, documentation, and usability testing.

CS 534  Emerging Software Architectures and Methodologies  (3)  

Prerequisite(s): Comprehensive undergraduate course in software engineering or industrial software engineering experience with a large project.

Explores emerging technologies and contemporary development methodologies for large scale software systems; difficulties and benefits of software by component composition, component reuse and software architectures.

CS 536  Computational Intelligence  (3)  

Prerequisite(s): Experience with an object oriented programming language.

Introducing concepts, models, algorithms, and tools for development of intelligent systems. Example topics include artificial neural networks, genetic algorithms, fuzzy systems, swarm intelligence, ant colony optimization, artificial life, and hybridizations of the above techniques. Additional focus will be placed on research methodologies and preparing research papers and reports.

CS 538  Business Intelligence and Data Mining  (3)  

Prerequisite(s): Undergraduate or graduate statistics course.

Introduction to business intelligence and data mining methodologies and tools that enable users to analyze new patterns/relationships and develop insight for decision making. This course provides students thorough conceptual framework, discussion, and hands-on experience in business intelligence and data mining. Techniques that the course covers include, but not limited to, linear modeling, decision trees, association rules, classification rules, clustering & visualization, text mining methodologies. Topics covered will include business intelligence, data mining methods, predictive analysis, information quality, and a term project that applies the skills learned.

CS 540  Bioinformatics Algorithms  (3)  

Prerequisite(s): Basic knowledge in probability and statistics, data structures, and algorithms.

Provides fundamental background in bioinformatics, both theoretical and practical, to students in computer science or biological sciences. Provides the principles that drive an algorithm's design. Covers various topics such as DNA and RNA structure, gene structure and control, protein structure, sequence alignment production, homologous sequences searches, phylogenetic trees structure and interpretation.

CS 541  Digital Media: Theory and Processing  (3)  

Study of the fundamentals of image and video processing. This course will use a mathematical framework to describe and analyze images and videos as two- and three-dimensional signals in the spatial, spatio-temporal, and frequency domains. Techniques for image and video compression, morphological processing, segmentation, enhancement and recovery will be presented.

CS 544  Applied Artificial Intelligence  (3)  

Prerequisite(s): Undergraduate artificial intelligence course or equivalent.

Survey of artificial intelligence emphasizing applications in business, industrial, and scientific system development; autonomous agents, data mining, pattern recognition, and machine vision.

CS 546  Advanced Management of Information Systems  (3)  

In-depth study of the theories of information systems and their relationship to organization, decision-making and information management processes. Topics include information systems' impact, strategic uses of information systems, technology adoption, enterprise computing architectures and infrastructures, information security and assurance, IT policy compliance, knowledge management and performance measurement.

CS 547  Wireless Networking and Security  (3)  

Prerequisite(s): SSD major or permission of instructor.

A study of advanced topics in computer networks with emphasis on wireless communications. Fundamentals of cellular communications, CDMA systems, wireless security, Wireless Application Protocols (WAP), Bluetooth, and new wireless technologies are also covered.

CS 550  Distributed Computing Systems  (3)  

Prerequisite(s): Undergraduate course in computer networking or equivalent.

Design and analysis of distributed computing systems; system architecture; load balancing and scheduling; remote procedure calls and message passing; distributed operating systems and database systems.

CS 565  Embedded and Real-Time Software Development  (3)  

Prerequisite(s): SSD major or permission of instructor.

In-depth study of requirements or real-time and embedded software; examination of operating systems, languages, and devices that support these systems; real-time multimedia applications emphasized.

CS 570  Advanced Computer Security  (3)  

Prerequisite(s): Undergraduate operating system course or equivalent.

Study of advanced network security architectures, models, benchmarks and metrics, cryptography, authentication and authorization protocols, secure application and systems development, federal regulations and compliance, and advanced security topics on intrusion detection, biometrics, web services, and data mining. Emphasis is on security professional certification.

CS 591  Special Topics in Computer Science  (3)  

Prerequisite(s): Approval of the advisor and approval of the department head.

(3) (3). Selected topics from current problems in computing; topics vary from semester to semester.

CS 592  Special Topics in Computer Science  (3)  

Prerequisite(s): Approval of the advisor and approval of the department head.

Selected topics from current problems in computing; topics vary from semester to semester.

CS 595  Studio Component  (3)  

Prerequisite(s): Approval of the advisor and approval of department head.

Provides students with a laboratory for direct application of concepts learned in course work; students will produce a variety of software products.

CS 596  Studio Component  (3)  

Prerequisite(s): Approval of the advisor and approval of department head.

Provides students with a laboratory for direct application of concepts learned in course work; students will produce a variety of software products.