Mathematics and Computer Science
The Department of Mathematics and Computer Science in the College of Science and Technology offers Bachelor of Science degrees in cybersecurity and mathematics, as well as a Bachelor of Arts in computer information systems and the Bachelor of Science degree in computer science. The Computer Science program is accredited by the Computing Accreditation Commission of ABET, https://www.abet.org. Minors are offered in mathematics and computer science.
Ai, Chunyu, Professor
Bhatta, Dilli, Assoc Professor
Davis, Melissa, Director, Cyber-security Laboratory; ABET Coordinator, Senior Instructor
Elnagar, Gamal, Professor
Hameed, Muhammad, Professor
Hudak, Michael, Senior Instructor
Hyun, Steve, Professor
Li, Frank, Assoc Professor
Majumder, Akm Jahingir, Asst Professor
Omolo, Bernard, Professor
Owenga, George, Instructor
Schlingmann, Dirk, Professor
Sohrabi, Elham, Asst Professor
Summers, Victor, Asst Professor
Waddell, Elizabeth, Asst Chair for Math, Senior Instructor
Zhang, Xudong "Jimmy", Asst Professor
Zhong, Wei, Asst Chair for Computer Science, Professor
Computer Science
Introduction to graphical user interface, word processing, spreadsheet, database, Internet, cross-platform training, computer components and peripherals, input/output concepts, storage concepts, and computer buyer's guide considerations.
Current application, security and systems software, hardware devices, social and ethical issues in computing and information technology, propositional logic, search engines, and computer programming concepts. Basic problem solving, logic, and computer programming are introduced through an active learning environment.
Design, analysis and testing of algorithms and classes, including programming from an Object-Oriented perspective, simple data types, control structures, and arrays.
Computer organization, logic gates and expressions, circuits, CPU, memory, numbering systems, assembly language programming, instruction formats, and addressing modes.
An introduction to computer and system architecture and operating systems for system development personnel. Topics include OS platforms, storage architectures, CPU architectures, instruction sets, memory, registers, input-output, and operating system modules such as process, memory, and file management.
Introduction to Python Programming as an object-oriented language with concepts of OO programming, functions, selection statements, iteration statements, argument passing, strings, arrays, lists, dictionaries, files IO, dynamic typing, sequences, sets, assignments, multiple-target assignments, recursion, polymorphism and Python timing methods and tools.
Introduction to C++ as a second object-oriented language with concepts of OO programming, data abstraction, polymorphism, inheritance, graphical user interface design with MFC, and memory management issues.
Advanced design, analysis and testing of algorithms and classes, including inheritance, polymorphism, UML, complexity analysis, recursion, search and sorting techniques, linked lists, stacks and queues.
Computer organization and architecture, basic processor design, hard wired and microprogrammed control, ALU, memory organization, data paths, pipelining, and interfacing and communications.
Design, analysis and testing of advanced data structures, including priority queues, trees, binary search trees, tree traversals and balancing techniques, hashing, and graph theory.
Methods, tools and techniques used to maximize efficiency in investigations that involve digital devices, including malicious code analysis, techniques of evaluation of the physical memory of a compromised machine, digital forensics tools, challenges of anti-forensics phenomena, and use and management of storage area network technology for evidence storage.
Introduction of information security practices and needs including concepts of information security, types of attacks, risk analysis and management, security technologies, and basic information security implementation.
Supervised practical experience related to the student's major in Computer Science, Computer Information Systems, or Cybersecurity in an elected setting planned in conjunction with the appropriate faculty member. The course may be applied for a maximum of three hours as an Upper Level Elective (CS/CIS) or Major Elective (Cybersecurity).
As needed.
Basic concepts required to securely design, implement, maintain, and monitor networks. Topics covered include the OSI model, topologies, safety procedures, network addressing, VLANs, routing protocols, security protocols, security policies and hardware devices, security risks, physical vs. logical security, IoT security, packet sniffing, virtualization, and cloud computing.
Concepts and fundamental strategies of algorithm design; the analysis of computing time and memory requirements; the theory of computational complexity (NP-hard and NP-complete); graph manipulation algorithms (connected components, minimum spanning trees, traveling salesman, cycles in a graph, and coloring of graphs); search algorithms (depth-first, breadth-first, best-first, and alpha-beta minimax); and computational algorithms (matrix multiplication, systems of linear equations, expression evaluation, and sorting).
A project-oriented course involving the complete application development of an online commercial Web site. Basic Web page design, including HTML and Style Sheets is covered, but the focus is on what happens behind the scenes of a business Web site, including client versus server-side information processing, CGI and Event-Driven programming, data transmission, storage and compressions, risk analysis, and security issues.
A survey of the fundamentals of information security, including risks and vulnerabilities, policy formation, controls and protection methods, database security, encryption, authentication technologies, host-based and network-based security issues, personnel and physical security issues, issues of law and privacy.
Symmetric-key cryptography including Stream ciphers and Advanced Encryption Standard, password-based encryption, public-key cryptography, session-key encryption, digital signatures, hash functions and message authentication codes. The hands-on laboratories provide extensive practice on file encryption using public-key cryptography, password storage and authentication by message digest, utilization of key transport and key agreement to establish secure channel for socket programming and RSA encryption implementation.
An investigation of technical papers from the instructor's area of research. The composition and presentation of technical papers that either survey the existing literature or make an original contribution to the research area is required.
Selected topics of special interest in computer science. May be repeated for credit.
Introduces the fundamentals of operating systems design and implementation, including an overview of the components of an operating system, mutual exclusion and synchronization, I/O, interrupts, implementation of processes, scheduling algorithms, memory management, and file systems.
Wireless and mobile computing, integration of wireless and wired networks, networking cabling and infrastructure, network performance, recovery, interconnecting LANs and WANs, design and diagrams, packet transmission, datagram encapsulation and fragmentation, network security, and network troubleshooting.
Fundamental concepts and techniques employed in wireless and mobile networks such as cellular networks, wireless LANs, and ad-hoc networks. Topics include wireless communication basics, access technologies, medium access control, naming and addressing, routing, mobility support and management, security, and power management.
Design and implementation of distributed application and network communication programs, including network application development with UCP and TCP/IP protocols, introduction to distributed systems and computing, RIM, socket programming, client/server models, and communication primitives, such as datagrams, packet retransmission, routing, addressing, error handling, and flow control.
Database Management System (DBMS) architecture and organization, design and implementation of DBMS, data models, internal databases structures, conceptual modeling, data independence, data definition language, data manipulation language, normalization, transaction processing, recovery, and security.
Design and implementation of database and client/server applications, in-depth treatments of embedded queries and stored procedures, database triggers, database extended languages, architectures and design patterns of distributed application, transaction processing, performance tuning, recovery and backups, auditing, and security.
Extraction and discovery of knowledge from large databases, data integration and data warehousing, data mining algorithms, models, and applications including association rule mining information retrieve (IR) and mining of text databases, decision tree, decision rules, classification techniques, cluster analysis, and evaluation, visualization, and interpretation of patterns.
Paradigms and fundamental concepts of programming languages, such as scope, binding, abstraction, encapsulation, typing, and language syntax and semantics. Functional and logic programming paradigms are also introduced through sample programming languages.
Methods and tools of software engineering, software life cycle, iterative development processes including the Agile Method and Unified Process, object oriented analysis and design of software, software testing, cost and effort estimation, project management, risk analysis, and documentation. A relatively large software system is developed in a team environment.
Cryptography, telecommunication and network security, applications and system development security, Business Continuity Planning (BCP), cyber-crimes and countermeasures. The hands-on laboratories provide extensive practices on firewalls, Virtual Private Networks (VPN), Intrusion Detection Systems (IDS), and other computer security tools.
Difference calculus, direct and interactive techniques for matrix inversion, eigen value problems, numerical solutions of initial value problems in ordinary differential equations, stability, error analysis, and laboratory applications.
Introduction and analysis of IP security, in-depth technical treatment of authentication, email security, web security, network management security, intruders, malicious software, and firewalls.
Introduction to practical concepts and principles of personal, organizational, and national cybersecurity, including hands-on labs and examples in computer security, network security, web security, encryption, security policies, countering cyber stalking, social engineering, fraud and abuse, malware, computer viruses, techniques used by hackers, and how to detect and combat cyber threats.
Intelligent agents, expert systems, heuristic searching, knowledge representation and reasoning, artificial neural networks, ontologies, and natural language processing.
Integration of knowledge at an advanced level, a review of recent developments in theoretical and applied computer science, the exploration of ethical issues, along with research and oral presentation.
Mathematics
The fundamentals of modern statistical methods, descriptive and inferential statistics, probability and sampling; primarily for students in fields other than mathematics who need a working knowledge of statistics.
Linear equations and inequalities, exponential equations, mathematics of finance, fundamental set theory, fundamentals of probability and statistics. This course may not be used to satisfy any prerequisite requirement for higher-numbered mathematics courses.
Linear equations and inequalities, exponential equations, mathematics of finance, fundamental set theory, fundamentals of probability and statistics. This course may not be used to satisfy any prerequisite requirement for higher-numbered mathematics courses.
Equations and inequalities, graphing, polynomial, rational, exponential, logarithmic, and other functions; matrices and systems of equations. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit. For students who need a more intensive study, an expanded version of college algebra (MATH U121A) is available. MATH U121A is open to students who have an appropriate score on the placement test, have completed MATH U120 with the mandatory lab, or if the student, in consultation with his or her advisor, determines that extra instruction is needed in order to succeed in MATH U121.
Equations and inequalities, graphing, polynomial, rational, exponential, logarithmic, and other functions; matrices and systems of equations. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit. Prerequisites: Appropriate score on placement test and high school Algebra I and II. For students who need a more intensive study, an expanded version of College Algebra (MATH U121A) is available.
Derivatives and integrals of elementary algebraic, exponential and logarithmic functions; maxima, minima, rate of change, area under a curve, and volume. Problems and examples are drawn from a variety of areas which include economics, psychology, biology, geography, and geology.
Subsets of the real number line; polynomial, rational, absolute value, exponential and logarithmic relations and functions. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit.
Trigonometric functions, trigonometric identities, solution of equations and triangles, inverse trigonometric functions, vectors, polar coordinates; analytic geometry.
Limits, continuity, the derivative, differentiation with applications in the natural sciences and engineering, antiderivatives, basic integrals with applications.
Applications of integration, techniques of integration, differential equations, parametric equations, and finite sequences and series.
Topics in basic logic; proof techniques; sets, relations, and functions; counting; and elementary number theory.
An expansion of topics taught in the first semester of elementary statistics such as hypothesis testing; inferences; correlation and regression. Additional topics to be covered include: multinomial experiments and contingency tables; analysis of variance; statistical process control; and individual projects.
The meaning of number, fundamental operations of arithmetic, the structure of the real number system and its subsystems, elementary number theory. Open only to students in early childhood, elementary, middle grades, or special education.
A continuation of the development of the real number system and its subsystems, basic concepts of probability, and elementary data analysis. Open only to students in early childhood, elementary, middle grades, or special education.
A study of properties and relationships of shape, size, and symmetry in two and three dimensions; explorations of concepts of motion in two and three dimensions through transformations. Open only to students in early childhood, elementary, middle grades, or special education.
Vectors and geometry of space, vector functions, partial derivatives, multiple integration, vector calculus and second order differential equations.
Ordinary differential equations of first order, higher order linear equations, Laplace transform methods, series methods; numerical solutions of differential equations; applications to the physical sciences and engineering.
Programming language and techniques designed specifically for programs that rely on the application of mathematics for solution. Topics include variables, assignment statements, expressions, vectors and matrices, MATLAB scripts, input and output, selection statements, flow control, program organization, M-files, optimizing M-files, string manipulations, data structures, advanced functions, plotting, symbolic math toolboxes, variable precision arithmetic, and tricks and tips in MATLAB programming.
Review of descriptive statistics, testing statistical hypothesis, introduction to correlation, regression and linear regression models, model building, variable selection and model diagnostics.
Graphs of functions as models, modeling using proportionality and geometric similarity, model fitting and models requiring optimization, experimental modeling, modeling using the derivative and interactive dynamic systems.
Topics in set theory, logic, elementary application of logic, methods of mathematical proofs, equivalence relations and partial orderings, functions and mappings, and number systems.
Matrices, systems of linear equations, vectors, Euclidean vector spaces, linear transformations, eigenvalues and eigenvectors.
Basic linear Partial Differential Equations (PDEs) of hyperbolic, parabolic, and elliptic types used in mathematical modeling of physical, chemical, biological and other phenomena, systems, technical devices and financial markets. Selected topics such as the boundary value and initial value problems are covered.
Group theory and introduction to rings. Topics include abelian groups, cyclic groups, permutations, group homomorphisms and isomorphisms, Cayley's theorem, normal subgroups, quotient groups, Lagrange's theorem.
Ordered field properties of the real number system; completeness; theory of limits of sequences, series and functions; continuity (including uniform continuity); introduction to theory of the derivative.
Topics selected from theoretical Boolean algebra, algebraic structures, theory of computing, advanced set theory, and recursive functions.
Supervised practical experience related to the student's major in Mathematics in an elected setting planned in conjunction with the appropriate faculty member. The course may only be applied for a maximum of three hours as an Upper Level Elective.
The methods of the numerical solutions of optimization problems arising in operational research, logistics, economics, etc. Emphasis is on the simplex and Karmarkar's polynomial-time method.
A survey of the major developments and procedures of mathematics, from its origins to the modern era, relating development with the diverse cultures and the aspects of mathematics they contributed.
Geometry as a logical system based upon postulates and undefined terms; fundamental concepts and relations of Euclidean geometry developed rigorously on the basis of a set of postulates; some topics from non-Euclidean geometry.
Vector spaces, and subspaces; bases and dimension; change of basis; linear transformations and their matrices; diagonalization; canonical forms; bilinear forms; eigenspaces.
Advanced topics in groups, rings and fields. These topics include p-groups, polynomial rings, ideals, integral domains, extension fields, isomorphism theorems for groups and rings.
Complex numbers and functions, complex integration, Taylor and Laurent series, residues, and conformal mapping.
Further development of the theory of differential and integral calculus including properties of the derivative and integral, Fundamental Theorem of Calculus, sequences and series of functions.
Difference calculus; direct and iterative techniques for matrix inversion; eigenvalue problems; numerical solutions of initial value problems in ordinary differential equations; stability; error analysis; laboratory applications.
The finite-difference and finite element methods for the numerical solution of basic linear Partial Differential Equations (PDEs) arising in mathematical modeling of physical, chemical, biological and other phenomena, systems, technical devices and financial markets.
Basic applications of PDEs, numerical methods for PDEs and scientific computing to applied problems arising in the natural sciences, industry, and financial engineering. Emphasis is on the formulation and solution of problems of heat transfer and diffusion equations, Maxwell's equations and differential equations governing the financial derivatives.
Intensive study in an area of pure or applied mathematics such as mathematical modeling. Topics are selected to meet current faculty and student interest.
Statistics
Data entry, sorting and merging, data summarization, graphical display, reports, and statistical inferences using statistical software.
Laws of probability and sample space; discrete and continuous distributions; joint, marginal and conditional densities; moment generating functions; univariate and bivariate normal distribution.
Markov chains; Poisson processes; introductory renewal theory, Brownian motion and stationary processes used in mathematical modelling.
A comprehensive development of statistical analysis that builds upon a knowledge of probability and basic statistics. Topics include sampling distributions, interval and point estimation, the law of large numbers, limiting distributions, testing hypotheses and order statistics.
More advanced development of solutions to problems involving statistics. Topics include experimental design, analysis of variance, analysis of covariance, multiple linear regression, curvilinear regression, and logistic regression.
Intensive study in a specialized area of statistics. Selected topic is based on student interest and faculty expertise.