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DRAFT Undergraduate Catalog 2014-2015 DRAFT

CatalogUndergraduateCollege of Arts and SciencesMATHCourse Descriptions

Mathematics and Computer Science Course Descriptions

All course descriptions carry behind the name and number a parenthesis ( ) indicating the credit hours, lecture hours, and the lab hours per week. For example: NSCI 110 (4-3-2). The first number in the parenthesis indicates the credit value of the course (4); the second number indicates the number of lecture hours (3) per week; and the third number indicates the number of lab hours per week (2).

CSC 100  (3-3-0)  Introduction to Computers: This course covers fundamental concepts of computers and their applications using personal computers in stand-alone and networked environments, including the use of software for word processing, presentations, spreadsheets, and databases. Majors in computer science will not receive credit for this course.
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CSC 101  (3-3-0)  Computer Programming Language (FORTRAN): This course is an introduction to FORTRAN, a problem-oriented computer language for use in scientific and mathematical problem solving.
Prerequisite: MATH 123 Or higher
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CSC 102  (3-3-0)  Introduction to Visual Basic: This course will introduce students to computing using Visual Basic with emphasis on business applications. The topics for the course will include Visual Basic programming, computer concepts in relation to management, the use of an Integrated Development Environment (IDE), flowcharts, algorithms, decision making, control structures, modules, windows programming, procedures and arrays.
Prerequisite: MATH 123 higher
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CSC 104  (3-3-0)  Introduction to Computer Science for Non-Technical Majors: This course explores topics of computer science for non-technical majors. The course covers the fundamental issues of networking, HTML, data representations, computers, algorithms, and programming. Students receive a solid grounding in the central concepts as well as in important uses of computing and information technology.
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CSC 105  (3-3-0)  Introduction to Computer Science for Technical Majors: This course is an introduction to the fundamental concepts and skills needed by students who anticipate majoring in computer science or other technical majors such as mathematics or a natural science. Topics include algorithms as models of computational processes, programming fundamentals such as data models and control structures, and the computing environment and its tools, such as basic hardware, editors, compilers, and debuggers.
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CSC 120  (3-3-0)  Introduction to Programming Methodology: This course is the first course of a two-semester sequence that provides an overview of programming methodology and program writing skills. Topics include basic concepts of computer systems, problem solving and algorithm development, program structures, data types, program development, method and style, coding, debugging, testing, and documentation.
Prerequisite: CSC 105
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CSC 130  (3-3-0)  Program Design and Implementation: This course is the second of a two-semester sequence that focuses on a disciplined approach to design, coding, and testing of programs. Topics include data abstraction, data structures, and searching and sorting algorithms.
Prerequisite: CSC 120
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CSC 201  (3-3-0)  Computer Organization and Architecture I: This course covers the relationship between computing hardware and machine language instruction sets, implementation of high level languages on the machine and some memory related issues. The study is organized into levels in the following order of topics: fundamental building blocks such as logic gates and flip-flops and combinational and sequential logic; machine level representation of data; basic assembly language, implementation of high level language constructs, addressing modes, compilation, assembly and interpretation; memory hierarchy; interrupts. Some real world computer systems and microprocessors are used as examples, along with their hardware and the organization of their instruction sets. Assembly language programming is studied in detail.
Prerequisite: CSC 130 And MATH 150
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CSC 202  (3-3-0)  Object Oriented Programming in C/ C++: This course focuses on object oriented programming and software development strategies in C/C++ programming language. Material includes syntax and semantics of C/C++, memory management, file processing, and network programming. Directed projects in C/C++ are an integral part of the course.
Prerequisite: CSC 130
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CSC 204  (3-3-0)  Object Oriented Programming in Java: This course focuses on object-oriented programming and software development strategies. Material includes syntax and semantics of Java, file processing, and network programming. Directed projects in Java are an integral part of the course.
Prerequisite: CSC 130
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CSC 205  (3-3-0)  Programming for Geographical Information Systems: This course covers a wide variety of programming topics necessary for gaining the ability and knowledge to develop software applications in Geographical Information Systems (GIS). The course will teach knowledge of file types, database models, visualization and graphical user interface customization for databases. Hands on exercises on these topics will provide students with the practical knowledge necessary to build GIS applications on spatial and spatiotemporal databases. The course will also cover the use of dominant software in the GIS industry and also how to build custom applications on such platforms using special purpose scripting languages.
Prerequisite: CSC 105 or permission of instructor
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CSC 207  (3-3-0)  Symbolic Programming: This course introduces the basic concepts and methods of symbolic programming. Symbolic programming involves the construction and analysis of complex symbolic expressions that can be used to represent different types of information. This course also introduces functional programming and logic programming as two widely used paradigms for symbolic computation. Course topics include recursion, list processing, tree processing, backtracking, unification and resolution.
Prerequisite: CSC 130 And MATH 150
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CSC 209  (3-3-0)  Windows Environment Programming: This course involves how to develop and program graphical user-interfaces (GUI) using current programming toolkits and GUI tools.
Prerequisite: CSC 130
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CSC 220  (3-3-0)  Data Structure/ Algorithms: This course explores data structures from various viewpoints: data structure design in response to a specific need, the expression of an algorithm in terms of the operations on the data structure, and complexity of operations. This course reinforces the knowledge of data structures gained in CSC 130 and extends it, particularly with regard to complexity of corresponding algorithms.
Prerequisite: CSC 130 And MATH 150
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CSC 270  (3-3-0)  Networking Basics: This course introduces the architecture, structure, functions, components, and models of the Internet and other computer networks. It uses the OSI and TCP layered models to examine the nature and roles of protocols and services at the application, network, data link, and physical layers. The principles and structure of IP addressing and the fundamentals of Ethernet concepts, media, and operations are introduced to provide a foundation for the curriculum. Students build simple LAN topologies by applying basic principles of cabling, performing basic configurations of networks devices such as routers and switches, and implementing IP addressing schemes.
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CSC 300  (2-2-0)  Professional Practice in Computing: This course requires preparation and submission of a comprehensive report based on actual employment experience in a computer-science cooperative job or internship. This course is designed for course substitution for Cooperative Education courses, and it may be used only twice for a maximum of six credits. It may not be used twice in the same semester.
Prerequisite: Permission of instructor
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CSC 303  (3-3-0)  Computer Organization and Architecture II: The course is a continuation of CSC 201which covers many aspects of computer architecture and implementation. Topics covered include pipelining, instruction-level parallelism; advanced cache and memory-hierarchy design issues; design issues for shared memory multiprocessors; storage systems and design of input/output systems; architectural implications for networks and distributed systems. In this course a rigorous quantitative approach is taken to examine different system design tradeoffs.
Prerequisite: CSC 201
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CSC 310  (3-3-0)  Introduction to Numerical Method: This course focuses on computer techniques used to translate certain known computational algorithms into computer programs and on practice in use of existing mathematical library routines. Topics include linear systems of equations, curve fitting and interpolation algorithms for differentiation, solution of non-linear equations, solution of ordinary differential equations, and elementary discussion of errors.
Prerequisite: CSC 101 Or CSC 102 Or CSC 120 And MATH 241 And MATH 251
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CSC 320  (3-3-0)  Design and Analysis of Algorithms: This course provides a comprehensive introduction to the design and analysis of computer algorithms. Design techniques include divide-and-conquer, the greedy approach, and dynamic programming. Algorithm analysis topics include asymptotic notation, recurrence relations, time-space complexity, and NP-completeness. Algorithms for sorting, searching, hashing, and advanced data structures are examined.
Prerequisite: CSC 220
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CSC 322  (3-3-0)  Programming Languages: This course considers the principal programming language concepts and shows how they are dealt with in the design and implementation of traditional imperative languages, functional languages, logic languages, and object-oriented languages. Topics include history, virtual machines, representation of data types, sequence control, data control, data sharing, data type checking, run-time storage management, and distributed and parallel programming constructs.
Prerequisite: CSC 201 And CSC 207 And CSC 220
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CSC 323  (3-3-0)  Principles of Database Design: This course emphasizes the concepts and structures necessary to design and implement a database management system. It will acquaint the students with current literature on the subject and give them an opportunity to use a database management system. Topics include database concepts, hierarchical, network and relational data models, data normalization, data description languages, query facilities, file organization, file security, data integrity, and reliability.
Prerequisite: CSC 220
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CSC 332  (3-3-0)  Theory of Computation: This course covers basic theoretical principles embodied in formal languages, automata, computability, and computational complexity. Topics include finite automata, pushdown automata, non-determinism, regular expressions, context-free grammars, Turing machines, Godel numbering, Church's thesis, the halting problem, unsolvability, and computational complexity.
Prerequisite: CSC 220
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CSC 342  (3-3-0)  Software Tools: This course covers software development on a specific platform such as Unix. Topics include general utilities, shell programming, file processing and manipulation, text patterns, software management facilities, linkers, loaders, debuggers, compilers, editors, filters, and macro processing.
Prerequisite: CSC 220
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CSC 350  (2-2-0)  Service Learning: Under the supervision of the Computer Science faculty, students will hold discussion sections for introductory computer science courses and will serve as tutors and assistants in the laboratories. Students will attend a weekly lecture section to become familiar with course materials, problem-solving skills, and approaches that will aid their tutoring and assisting introductory students in completing their assignments. One credit hour shall be awarded for each four (4) hours per week of laboratory assistance. The course may be repeated up to a maximum of six (6) credit hours. Course grade is either pass (P) or not pass (NP).
Prerequisite: 18 hours of CSC credit
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CSC 360  (3-3-0)  Intro to Computer Simulation: This course introduces simulation and modeling of systems with concentration on discrete stochastic systems. Topics include modeling and simulation techniques, Monte Carlo methods, queuing models, and computer simulation languages such as GPSS, and SIMSCRIPT. A simulation project is developed, completed, and presented by each student as a member of a project team.
Prerequisite: MATH 142 And proficiency in a programming language
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CSC 371  (3-3-0)  Routing Protocols: This course describes the architecture, components, and operation of routers, and explains the principles of routing and routing protocols. Students analyze, configure, verify, and troubleshoot the primary routing protocols RIPv1, RIPv2, EIGRP, and OSPF. Students complete a basic procedural lab, followed by basic configuration, implementation, and troubleshooting labs in each chapter.
Prerequisite: CSC 270
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CSC 372  (3-3-0)  LAN Switching and Wireless: The course explains how to configure a switch for basic functionality and how to implement VLANs, VTP, and inter-VLAN routing in a converged network. The different implementations of Spanning Tree Protocol in a converged network are presented. Students complete a basic procedural lab, followed by basic configuration, implementation, and troubleshooting labs in each chapter. Students develop the knowledge and skills necessary to implement a WLAN in a small-to-medium network.
Prerequisite: CSC 270
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CSC 380  (3-3-0)  Introduction to WAN (Wide Area Network): This course discusses the WAN technologies and network services required by converged applications in enterprise networks. The course uses the Cisco Network Architecture to introduce integrated network services and explains how to select the appropriate devices and technologies to meet network requirements. Students learn how to implement and configure common data link protocols and how to apply WAN security concepts, principals of traffic, access control, and addressing services. Finally, students learn how to detect, troubleshot, and correct common enterprise network implementation issues.
Prerequisite: CSC 371 And CSC 372
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CSC 390  (3-3-0)  Topics in Computer Science: This course is designed to cover contemporary topics of current interest and demands in computer and information science at the junior and senior levels. It may be repeated for credit with approval of department.
Prerequisite: CSC 220 or instructor permission
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CSC 395  (1-1-0)  Competitive Programming: This course provides intensive training in programming towards solving particular problems in a timely fashion. The skills obtained will be very useful in the workplace as well as programming competitions. Topics include: mathematical/ logical skills for problem solving; online programming references; restricted programming environments; and collaboration for problem solving.
Prerequisite: CSC 220 Corequisite: CSC 320
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CSC 403  (1-1-0)  Social, Ethical, and Professional Issues: This course discusses the impact of computers on society including people, business, and government. Topics include historical and social issues, security, privacy, professional responsibilities, risks and liability, and intellectual property.
Prerequisite: 18 hours of CSC credit
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CSC 410  (3-3-0)  Introduction to Compiler Design Theory: This course introduces basic mathematical theory underlying the design of compilers and other language processors, and the implementation of the theory in practical design situations.
Prerequisite: CSC 201 And CSC 220 And CSC 332
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CSC 431  (3-3-0)  Operating Systems I: This course is designed to develop an understanding of the organization and architecture of computer systems at the register-transfer and programming levels of system description. Major concept areas of operating systems principles and the inter-relationships between the operating systems and the architecture of computer systems are taught. Topics include system structure, process concept, CPU scheduling, process synchronization, deadlocks, and memory management.
Prerequisite: CSC 220 And Corequisite: CSC 201
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CSC 432  (3-3-0)  Operating Systems II: This course provides for the study of advanced software techniques, especially focusing on operating systems. It presents materials that will enable the student to design, use, and analyze current and future operating systems. Topics include I/O programming, interrupt programming, memory management, processor management, device management, design and implementation of operating systems.
Prerequisite: CSC 431
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CSC 434  (3-3-0)  Artificial Intelligence: An introduction to the history, goals, social impact, and philosophical implications of artificial intelligence. Topics include problem representation as state spaces, search, logic systems, semantic networks, frames, and neural networks. Identification of application areas such as natural language processing, expert systems, robotics, planning, and vision.
Prerequisite: CSC 207
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CSC 451  (3-3-0)  Computer Graphics: This course introduces hardware and software components of graphics systems, and graphic application programming. Programs to deepen understanding of interactive graphics, picture plotting and input handling in an integrated manner will be written. Topics include geometrical transformation, three-dimensional concepts, windowing, clipping, segmentation, logical interaction input methods, raster algorithms, algorithms for hidden surface and hidden line removal, and shading and color.
Prerequisite: CSC 220 And MATH 241 And MATH 251
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CSC 470  (3-3-0)  Software Engineering: This course introduces students to an intensive study of writing large programs, program design and programming style, and object-oriented development techniques in an attempt to manage the complexity of large software systems. Topics include principles of software engineering, object-oriented development, systems development, programming support environments, and software life cycles.
Prerequisite: CSC 220
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CSC 473  (3-3-0)  Parallel Processing: This course gives the students basic knowledge about parallel processing. Topics include hardware architecture of parallel machines; software environment that enables parallel computing; performance analysis of parallel algorithms; techniques for developing parallel algorithms; and case studies on typical parallel algorithms.
Prerequisite: CSC 220
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CSC 480  (3-3-0)  User Interface Development: A course on user-interface technology and human-computer interaction issues including user productivity, system habitability, abstraction barriers, and human factors. Topics include command languages, hierarchical menus, direct manipulation (graphical user interfaces), multimedia interfaces, multimodal interaction, and user interface management systems.
Prerequisite: CSC 220
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CSC 490  (3-3-0)  Senior Project: This course presents a formal approach to state-of-the-art techniques in computer science and provides a means for students to apply the techniques. An integral part of the course is the involvement of students working in teams in the organization, management, and development of a large project. Project topics include software systems and methodology, computer organization and architecture, theory and mathematical background, computer security and social issues.
Prerequisite: Senior standing And 9 hours of CSC at the 300 level And 6 hours of CSC at the 400 level
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ENGR 103  (1-1-0)  Introduction to Computing Environments: This course introduces the students to the computing environments that enable engineering students to get familiar to the hardware/software used in performing computer related tasks. Topics include: basic operation of the computer operating systems; office application tools; engineering application tools; and web page creation. The course will emphasize the computing environment in the field of engineering computation so the students are ready when they transfer to the engineering departments of participating universities.
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ENGR 206  (3-3-0)  Probability and Statistics for Engineers: This course is a calculus based introduction to probability and statistics with emphasis on Monte Carlo simulation and graphical display of data on computer workstations. Statistical methods include point and interval estimation of population parameters and curve surface fitting (regression analysis). The principles of experimental design and statistical process control are introduced.
Prerequisite: MATH 241
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MATH 120  (3-3-0)  Finite Mathematics: An introduction to mathematical sets, logic, probability, statistics, and the metric system.
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MATH 121  (3-3-0)  or (4-3-2) Introduction to College Algebra: This course provides a foundation in algebraic concepts and problem solving skills for students who are preparing to take college algebra or precalculus I. Topics include arithmetic of real numbers, simplifying expressions (polynomial, rational, radical, etc.), and solving equations and inequalities (linear, quadratic, radical, etc.). When taken for 4 credits, two lab hours are included.
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MATH 123  (3-3-0)  or (4-3-2) College Algebra: An algebra course containing the following topics: sets, the real number system, exponents, radicals, polynomials, equations, inequalities, relations and functions, graphing, conic sections, exponential and logarithmic functions, systems of equations, complex numbers, mathematical induction, and the binomial theorem. A graphing calculator is required. When taken for 4 credits, two hours of lab are included.
Prerequisite: MATH 121 Or High School Algebra I, II, And Plane Geometry Or equivalent, And satisfactory profile examination score.
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MATH 124  (3-3-0)  College Trigonometry: A trigonometry course containing the following topics: trigonometric functions defined on angles, circular functions, graphs, inverse trigonometric functions, identities, trigonometric equations, law of cosines, law of sines, and complex numbers. A graphing calculator is required.
Prerequisite: MATH 123 Or High School Algebra I, II, And Plane Geometry Or equivalent, And satisfactory profile examination score.
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MATH 126  (3-3-0)  or (4-3-2) Quantitative Reasoning: This is a basic quantitative reasoning course with emphasis on concepts and applications of mathematical and statistical methods. This activity based quantitative reasoning course introduces students to basic mathematics, probability and risk, summarizing and analyzing data, regression and correlation, geometric modeling, and financial mathematics. Spreadsheets and course specific software will be used to deepen understanding of these concepts and increase student engagement with the course material. When taken for 4 credits, two lab hours are included.
Prerequisite: MATH 121 Or High School Algebra I, II, And Plane Geometry Or equivalent, And satisfactory profile examination score.
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MATH 129  (3-3-0)  or (4-3-2) Precalculus Mathematics I: This course is the first of a two-semester sequence that provides a background for students who are preparing to take calculus. Topics include sets, the real number system, exponents, radicals, polynomials, equations, inequalities, functions, relations, graphing, conic sections, and rational, exponential, and logarithmic functions. A graphing calculator is required. When taken for four credits, two hours of lab are included.
Prerequisite: High School Algebra I, II, And Plane Geometry Or equivalent, And satisfactory profile examination score.
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MATH 130  (3-3-0)  or (4-3-2) Precalculus Mathematics II: This course is the second of a two-semester sequence that provides the background for students who are preparing to take calculus. Topics include graphing, systems of equations, matrices, complex numbers, mathematical induction, the binomial theorem, sequences and series, polar coordinates, parametric equations, trigonometric functions, inverse trigonometric functions, law of sines, law of cosines, and trigonometric identities. A graphing calculator is required. When taken for four credits, two hours of lab are included.
Prerequisite: MATH 129
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MATH 131  (3-3-0)  or (4-3-2) Algebra and Trigonometry: An in-depth study of the topics covered in MATH 129 and MATH 130. A graphing calculator is required. When taken for four credits, two hours of lab are included.
Prerequisite: High School Algebra I, II, And Plane Geometry Or equivalent, And satisfactory profile examination score.
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MATH 140  (4-4-0)  Applied Calculus: A course in calculus applicable to business and the social sciences incorporating a review of college algebra and studies of linear equations, functions and their limits, derivations, applications of derivatives, exponential and logarithmic functions, antiderivatives, definite integrals and applications, and numerical techniques and applications.
Prerequisite: MATH 123 Or MATH 129
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MATH 142  (4-3-2)  Calculus with Analytic Geometry I: The first course of a three-semester sequence in calculus with analytic geometry, including studies of graphs, functions, limits, differentiation, applications of differentiation, integration, and applications of the definite integral.
Prerequisite: (MATH 129 And MATH 130) Or MATH 131
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MATH 150  (3-3-0)  Discrete Mathematics I: The first course of a two-semester sequence in discrete mathematics, providing the theoretical base and support for computer science and including operations on sets; Cartesian products and tuples; combinatorial objects; Venn diagrams; event spaces and basic probability; number systems; the statement calculus; rules of inference and validity of arguments; inductive proofs; the concept of an algorithm; equivalence relations; partial ordering relations; graphs and digraphs as relations, including trees and shortest paths in digraphs; basic definitions and notations of functions; and recurrences for the analysis of algorithms.
Prerequisite: (MATH 129 And MATH 130) Or MATH 131
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MATH 241  (4-3-2)  Calculus with Analytic Geometry II: The second course of a three-semester sequence in calculus with analytic geometry, including studies of the notion of integral, the Fundamental Theorem of Calculus, techniques of integration, improper integrals, applications of integration, differential equations, infinite series and tests of convergence, power series, and Taylor series.
Prerequisite: MATH 142
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MATH 242  (4-3-2)  Calculus with Analytic Geometry III: The third course of a three-semester sequence in calculus with analytic geometry, including studies of vectors, vector-valued functions, functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integrals and applications, line and surface integrals, Green's Theorem, Stokes' Theorem, and Divergence Theorem.
Prerequisite: MATH 241
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MATH 250  (3-3-0)  Discrete Mathematics II: A continuation of MATH 150, including an introduction to graph theory, graph algorithms, representations of graphs, planar graphs, graph algorithms, minimal spanning trees, tree traversals, decision trees, game trees, network models, max flow min cut theorem, matching, Boolean algebra and combinatorial circuits and applications, automata, grammars and languages, the closest-pair problem, and convex hull.
Prerequisite: MATH 150
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MATH 251  (3-3-0)  Linear Algebra: This course provides a study of topics including vectors, matrices, matrix operations, the system of linear equations, Gauss-Jordan elimination, determinants, vector spaces and subspaces, linear independence, bases, linear transformations, rank and kernel, eigenvalues and eigenvectors, diagonalization, inner products, Euclidean spaces, and the Gram-Schmidt process.
Prerequisite: MATH 130 Or MATH 131
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MATH 260  (3-3-0)  Foundations of Mathematics: A course designed to help students transition to upper level courses in mathematics. Topics include set theory, logic, proof techniques, induction, equivalence relations, functions and cardinality, countable and uncountable sets, and sequences.
Prerequisite: MATH 142 And MATH 150
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MATH 262  (3-3-0)  Modern Geometry: This course in modern geometry focuses on axiomatic methods and proofs. Topics from Euclidean geometry include lines, angles, triangles, quadrilaterals, congruent and similar triangles, circles, polygons, areas, and volumes. Some topics from non-Euclidean geometry are also included.
Prerequisite: (MATH 129 And MATH 130) Or MATH 131
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MATH 312  (3-3-0)  History of Mathematics: A survey of mathematics incorporating biographical accounts of persons who have contributed significantly to the development of mathematics, descriptions of their achievements, and discussions of other major topics of interest in mathematics.
Prerequisite: MATH 142
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MATH 315  (3-3-0)  Applied Cryptography: This course is an introduction to classical and modern cryptography. We apply elementary number theory to the problems of cryptography. Topics include classical cryptosystems, basic number theory, the data encryption standards, the RSA algorithm, discrete logarithms, Hash functions, digital signatures, digital cash, secret sharing schemes, and the zero knowledge techniques. A computer algebra system will be used.
Prerequisite: MATH 150
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MATH 320  (3-3-0)  Difference Equations: An introductory course in difference equations and discrete dynamical systems including studies of difference calculus, first order difference equations, higher order linear difference equations, basic theory of linear systems of difference equations, linear periodic systems, stability theory, Liapunov's second method, Z-transform, asymptotic behavior of solutions.
Prerequisite: MATH 241 And MATH 251
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MATH 325  (3-3-0)  Discrete Optimization: A course including such topics as maximization and minimization problems in graphs and networks, matching theory, (shortest paths, minimum spanning trees, maximum flows, minimum cost flows); transportation and trans-shipment problems, NP-completeness.
Prerequisite: MATH 150
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MATH 331  (3-3-0)  Differential Equations I: The first course of a two-semester sequence in differential equations, emphasizing applications to science and engineering and including the following topics: first order differential equations, second order linear differential equations, higher order linear equations, the Laplace Transform, and series solutions of second order linear equations.
Prerequisite: MATH 242
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MATH 340  (3-3-0)  Topics in Mathematics: A study of major topics of current interest in mathematics not covered in existing courses.
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MATH 345  (3-3-0)  Mathematics of Interest Rates: The course closely follows the financial mathematics syllabus of society of actuaries. The purpose of the course is to develop practical knowledge of the theory of interest in both finite and continuous times, know how these concepts are used in the various annuity functions, and be able to apply the concepts of present and accumulated value for various streams of cash flows as a basis for future use in reserving, valuation, pricing, duration, asset/liability management, investment income, capital budgeting, and contingencies.
Prerequisite: MATH 140 Or MATH 142
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MATH 350  (3-3-0)  Mathematics of Financial Markets: This course covers the usage and pricing of derivatives. Subjects include the basis features of futures and options, binomial option pricing, the Black-Scholes formula, interest rate based derivatives, volatility measurement, and dynamic trading strategies. It also covers arbitrage-based derivatives pricing approaches and quantitative analysis.
Prerequisite: MATH 242 And STAT 301
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MATH 361  (3-3-0)  Introduction to Modern Algebra I: The first course of a two-semester sequence introducing fundamental concepts and proof techniques used in abstract algebra and including studies of groups, normal subgroups, quotient groups, homomorphisms, rings, ideals, quotient rings, integral domains, fields, and related topics.
Prerequisite: MATH 251 And MATH 260
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MATH 362  (3-3-0)  Introduction to Modern Algebra II: This course is a continuation of MATH 361 and presents a deeper and more extended study of rings, ring homomorphisms and ideals, factor rings, properties of ideals, integral domains, unique factorization domains, polynomial rings, irreducibility tests, field extensions, algebraic extensions, an introduction to Galois Theory, and related topics.
Prerequisite: MATH 361
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MATH 372  (3-3-0)  Linear Programming: A study of methods and applications of optimizing a linear function subject to linear constraints, the theory of the simplex method and duality; parametric linear programs; sensitivity analysis; modeling and computer implementation.
Prerequisite: MATH 251
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MATH 380  (3-3-0)  Nonlinear Programming: This course includes methods for unconstrained optimization such as golden section search method, gradient method, Newton's method and conjugate direction method; and methods for constrained optimization, including Lagrange multipliers, Kuhn-Tucker Theory, and duality.
Prerequisite: MATH 251
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MATH 400  (3-3-0)  Diag/Prescript Math: A course examining diagnostic teaching in the context of a general approach to mathematics instruction, with emphasis on strengthening students' knowledge of mathematics and instructional psychology.
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MATH 405  (3-3-0)  Principals of Discrete Applied Mathematics: This course is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory and data compression, coding theory, secret codes, generating functions, Fourier transforms, linear programming, game theory. There is an emphasis on topics that have direct application in the real world.
Prerequisite: MATH 150 And STAT 202
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MATH 410  (3-3-0)  Introduction to Calculus of Variations and Optimal Control: Introduction to calculus of variations and optimal control for dynamical systems; the Pontryagin Maximum Principle, necessary conditions for optimality and computational techniques for solution of the necessary conditions.
Prerequisite: MATH 331
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MATH 412  (3-3-0)  Advanced Calculus: A comprehensive and rigorous study of the concepts of limit, continuity, topology on the real line, properties of continuous functions, Mean Value Theorem and Taylor's Formula, and calculus of one variable.
Prerequisite: MATH 242 And MATH 260
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MATH 415  (3-3-0)  Intro to Wavelets and Data Compression: This course presents the basic principles of wavelets and data compression. Wavelets have had quite a huge impact in the signal processing community, especially with regard to applications like compression (speech, audio, image and video, modeling and restoration). The course will cover topics including: inner products and norms of n-dimensional vectors, orthogonal matrices and block matrix arithmetic, Entropy and Cumulative Energy, peak signal to noise ratio, complex numbers and Euler's formula, Fourier series, convolutions, lowpass/highpass filters, Haar Transformations, Daubechies filters, Gaussian white noise, and the VISUShrink denoising technique. A significant amount of the course is dedicated to programming.
Prerequisite: MATH 241 And MATH 251
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MATH 420  (3-3-0)  Mathematical Modeling: This is a multi-disciplinary course that enables students to learn the techniques of mathematical modeling. There will be an overview of differential equations as well as the axioms of modeling and model validation. Topics will be selected from mathematical medicine, Markovian combat models, fractals, computational fluid dynamics, Navier-Stokes equations, and applications in weather forecasting, hydrodynamics, and traffic queuing processes. Computer simulations will be part of the course.
Prerequisite: MATH 251 And MATH 331
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MATH 431  (3-3-0)  Differential Equations II: A continuation of MATH 331, including the following topics: numerical methods; nonlinear differential equations and stability; Fourier Series and classical partial differential equations; boundary value problems and the Sturm-Liouville Theory; the system of linear differential equations; and the existence theory.
Prerequisite: MATH 251 And MATH 331
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MATH 432  (3-3-0)  Read/Honors in Math: An introduction to methods of research and independent study in mathematics. For seniors and/or honor students.
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MATH 433  (3-3-0)  Math Conc/Elem Sch Tch: A course for pre-service and in-service teachers at the intermediate level, emphasizing sets and the set theory, the development of the real number system, measurements, the use of manipulative materials, elements of geometry, computer utilization, and problem solving.
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MATH 435  (3-3-0)  Partial Differential Equations with Applications: A course containing the following topics: first order partial differential equations; the wave equation; the diffusion equation; the Laplace equation; d'Alembert's solution; Duhamel's principle; the classification of partial differential equations; elliptic, parabolic, and hyperbolic partial differential equations; Stability theory; energy conservation; Sturm-Liouville problems; Fourier series; integral transforms; Laplace transforms; Greens's functions; and variational methods. Applications in medicine, engineering, meteorology, and industry will be discussed. Mathematical software such as ACSL, Maple, and Mathematica will be used.
Prerequisite: MATH 242 And MATH 331
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MATH 440  (3-3-0)  Applied Numerical Methods: A course on numerical methods including topics such as: nonlinear equations, linear systems, interpolation and polynomial approximation, curve fitting numerical differentiation, numerical integration, numerical optimization, solution of differential equations, eigenvalues, and eigenvectors. Mathematical software such as Maple, Matlab, and Mathematica will be used.
Prerequisite: MATH 431
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MATH 450  (3-3-0)  Selected Topics in Mathematics: Advanced study of major topics in mathematics from fields such as topology, advanced calculus, complex analysis, or modern algebra. Course may be repeated for credit with approval of department.
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MATH 461  (3-3-0)  Theory of Real Variables: A comprehensive and rigorous study of real variable functions including differentiability, the Riemann Integral, sequences of functions, infinite series, the generalized Riemann integral, and an introduction to the Lebesgue Integral.
Prerequisite: MATH 412
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MATH 472  (3-3-0)  Theory of Numbers: A study of the elementary properties of integers, invisibility, Euclid's Algorithm, prime numbers, and congruences.
Prerequisite: MATH 260
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MATH 481  (3-3-0)  Introduction to Topology: A study of topics in the field of point set topology, including topological and metric spaces and an overview of various topological properties such as separation axioms, countability, compactness, connectedness, continuity, and homeomorphisms.
Prerequisite: MATH 412
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MATH 485  (3-3-0)  Teaching Secondary School Mathematics Using Technology I: This course is a comprehensive study of teaching secondary mathematics with technology. The emphasis is placed on algebra, calculus, data analysis, probability, and statistics.
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MATH 486  (3-3-0)  Teaching Secondary School Mathematics Using Technology II: This course is a continuation of MATH 485. It provides a comprehensive study of teaching secondary school mathematics using technology, with emphasis on geometry and measurement.
Prerequisite: MATH 485
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MATH 492  (3-3-0)  Complex Variables: A rigorous study of elementary functions, differentiation and integration of analytic functions, Taylor and McLaurin series, Residue Theorem, and contour integration.
Prerequisite: MATH 412 Or MATH 461
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STAT 202  (3-3-0)  Basic Probability and Statistics: An introduction to the study of probability and statistical inference.
Prerequisite: MATH 123 Or MATH 126
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STAT 301  (3-3-0)  Introduction to Probability: An introduction to the mathematical theory of probability, including such topics as random variables, distributions (normal, binomial, Poisson, and related ones), moment generating functions, and applications of probability theory.
Prerequisite: MATH 241
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STAT 302  (3-3-0)  Mathematical Statistics: A study of probability distributions of random samples, the theory of point and interval estimation, hypothesis testing, and decision theory concepts.
Prerequisite: STAT 301
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STAT 315  (3-3-0)  Introduction to Regression Analysis: A course including such topics as simple linear regression: the error model, algebraic derivation of least square estimators, estimating confidence intervals, hypothesis testing, the ANOVA approach to testing, assessing model validity, transformations, residual plots; multiple regression: the general linear model, least square estimation, prediction, residuals; and Logistic regression.
Prerequisite: STAT 202
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STAT 400  (3-3-0)  Applied Statistics: A course incorporating the use of statistical software packages and including discussions of such topics as descriptive statistics, statistical inference, inference from a single sample, samples from two populations, one-way analysis of variance, linear regression and correlation, multiple regression, two-way analysis of variance, fixed effects models, factorial designs, and hierarchical or nested design.
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STAT 401  (3-3-0)  Intermediate Probability: An intermediate-level study of such topics as conditional probability, basic classical theorems, methods of convergence, central limit theorem, and characteristic functions.
Prerequisite: STAT 301
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STAT 402  (3-3-0)  Intermediate Statistics: An intermediate-level course including such topics as the axiomatic treatment of the fundamentals of probability and distribution theory, characteristic functions (random variables, convergence, and approximation), and common distributions.
Prerequisite: STAT 301
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STAT 412  (3-3-0)  Operations Research: A review of topics pertaining to deterministic and probabilistic models of operations research, including linear programming, queuing theory, inventory models, and Markov chains.
Prerequisite: STAT 301
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STAT 415  (3-3-0)  Applied Time Series Analysis: A study of stationary stochastic processes, auto-regressions and ARMA-processes, parameter estimation and model selection for time series, trends and seasonality, forecasting by exponential smoothing and the Box-Jenkins method, linear filters.
Prerequisite: STAT 301 And STAT 315
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STAT 421  (3-3-0)  Quality Control: A study of the construction of control charts for variables, attributes, and tolerances; sampling techniques; and current techniques in quality control methodology.
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STAT 422  (3-3-0)  Statistical Methods for Research: A course incorporating the use of statistical software packages for the study of probability distributions, measurements of precision and accuracy, control charts, confidence intervals, tests of significance, analyses of variance, multiple correlation and regression, design and analysis of experiments.
Prerequisite: STAT 400
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