College of Engineering

Computer Science

www.cs.vt.edu
E-mail: csundg@vt.edu

Dennis J. Kafura, Head
Professors: O. Balci; I. R. Chen; R. W. Ehrich; E. A. Fox; L. S. Heath; D. G. Kafura; F. Quek; L. T. Watson
Associate Professors: J. D. Arthur; S. Bohner; A. Bouguettaya; D. Bowman; S. H. Edwards; C. J. Egyhazy; W. R. Frakes;
N. Ramakrishnan; C. J. Ribbens; A. Sandu; E. E. Santos, C. A. Shaffer; D. G. Tatar; S. Varadarajan
Assistant Professors: G. Back; V. Choi; D. Gracanin; G. W. Kulczycki; C. T. Lu; T. M. Murali; D. S. McCrickard; C. L. North;
A. Onufriev; M. A. Perez-Quinones; L. Zhang
Instructors: N. D. Barnette; W. McQuain
Virtual experience

The Field of Computer Science

    In a contemporary world where every educated person must have some knowledge of computers, the Department of Computer Science offers courses to meet a variety of needs. The department offers a bachelor of science program to prepare specialists in the area of computer science itself, a minor in computer science, and individual courses directed to the needs of non-majors who will be using computers as tools in their chosen career areas. The department also offers the M.S. and Ph.D. in computer science and the master of information systems (see Graduate Catalog).

    As a major, computer science involves far more than just the writing of computer programs. It is a technically rigorous field that requires a strong background in mathematics. Computer scientists must be good at problem solving. Their work requires the ability to think abstractly and to represent real-world objects as symbols that can be manipulated by a computer. The field of computer science is characterized by tremendously rapid change. It is continuously evolving both as new uses are discovered for existing computers and as technological advances lead to new computing systems with expanded capabilities.

Degree Requirements

    The curriculum in computer science is designed to provide a broad general computer science background that will prepare a student either to enter a professional career as a computer scientist or to continue training at the graduate level. All CS majors are required to take the same courses at the freshman and sophomore levels. Juniors take a combination of two required courses and two elective courses from a restricted list. At the senior level, students select one theory course and three specialty courses which correspond to their individual interests within the field. In all, a minimum of 37 credit hours of computer science is required: 1705, 1706, 2204, 2604, 2704, 3204, 3604, (3304 or 3414), (3704 or 3724), (4104 or 4114 or 4124), six credits in two other 4000-level courses, and an approved technical elective. To qualify for a B.S. degree in Computer Science, a student must earn a “C” (2.0) or better in 1705, 1706, 2204, 2604, and 2704.

    Computer science majors are required to take an additional 39 credits distributed over six disciplines. Mathematics comprises 22 of these credits, which include Math 1114, 1205, 1206, 1224, 2214, 2224, 2534, and 3134. CS/Math double majors take 3034 and 3124 in place of 2534 and 3134. Depending on their selection of CS courses, CS majors may need zero or one additional math course to obtain a math minor.

    The other specific disciplines represented in the departmental requirements are engineering education, electrical and computer engineering, statistics, and communication studies. Students must take ENGE 1024 and 1104, ECE 2504, Stat 4714, and COMM 2004. The final four additional credits come from taking one more natural science lab course beyond the two required by the core curriculum.

Opportunities for Majors

    The department offers computer science majors the opportunity to enhance their education through a variety of curricular and extracurricular activities. Students who meet the requirements for independent study/ undergraduate research can pursue research or individualized study under the direction of a faculty member. Through the honors program, superior students can work toward earning their degree "in honors" or even elect to earn both the bachelor's and master's degrees within five years. The Cooperative Education Program makes it possible for students to acquire professional experience while pursuing their degree.

    The department sponsors chapters of two national computer science organizations. There is a student chapter of the Association for Computing Machinery (ACM), the national professional organization for computer scientists. Membership is open to all computer science majors. The other departmentally sponsored organization is Upsilon Pi Epsilon (UPE), the national computer science honor society. Its members are elected in their junior or senior year. Selection is based on superior academic performance. Additional recognition of scholastic excellence is made during each year's graduation ceremonies. At that time awards are presented to the outstanding senior, junior, and lower-division student for the preceding academic year. The Gorsline award, in memory of former faculty member George Gorsline, annually recognizes a rising senior who has overcome freshman-year academic difficulties and subsequently demonstrated the greatest academic improvement.

Information for Non-Majors

    In addition to its service courses for non-majors, (1004, 1034, 1044, 1054), the computer science department jointly offers with the Departments of Mathematics and Statistics a series of courses which provide a liberal arts approach to the study of mathematical sciences. (Please see "Mathematical Sciences" in this catalog).

    For non-majors seeking a strong background in computer science, the department offers a CS minor. The requirements for the minor include: (CS 1604 or ENGE 1104 or 1204), 1705, 1706, 2204, 2604, 2704, and three credits in a three-hour 3000/4000-level course except 3604, 4004, or 4014. Minors must meet the same prerequisites as majors. This includes Math 2534 as a prerequisite for CS 2604 and achievement of a "C" (2.0) or better in all CS courses which are prerequisites for subsequent CS courses.

    Students interested in teacher certification are encouraged to consider the IDST degree program requiring three areas of concentration in Computer Science, Mathematics, and Education. The purpose of the degree is to prepare computer science/mathematics teachers for the secondary schools.

Computational Facilities

    The Department of Computer Science possesses extensive facilities for both instruction and research. There are several undergraduate teaching laboratories and a number of specially equipped research laboratories. These include two large parallel computing clusters and numerous computer and file servers for research and instruction in digital libraries, software engineering, and bioinformatics. The department also operates an extensively equipped Human-Computer Interaction Laboratory, and shares an interdisciplinary Virtual Environments Laboratory with state-of-the-art 3D and head-mounted displays, and a 4-wall CAVE immersive theater.

Satisfactory Progress

    University policy requires that students who are making satisfactory progress toward a degree meet minimum criteria toward the University Core (see Academics) and toward the degree in computer science.

    Satisfactory progress toward the B.S. in Computer Science requires that during the first 72 hours attempted at the university (including including transfer, advanced placement, advanced standing, credit by examination, and course withdrawal hours), a Computer Science major must:

  1. be registered in at least one 3-credit course required in the major during each on-campus semester of the regular academic year;
  2. achieve a GPA of 2.0 or better in the major no later than having attempted 72 hours toward the degree;
  3. not take any CS course required in the major more than twice, including attempts ending in course withdrawal; and
  4. not repeat more than 3 CS courses required in the major, including attempts ending in course withdrawal.

Undergraduate Course Descriptions (CS)

1004: COMPUTER LITERACY
Introduction to personal computer applications. Overview of basic computer hardware and system software concepts. Projects using various application software packages including word processing, spreadsheets, databases, and graphics (analytical and presentation), using electronic-mail, computer network browsers, and on-line training systems. Not for CS major or minor credit. Duplicates ACIS 1504, ALS 1514. (3H,3C)

1034: PROGRAMMING IN PASCAL
Fundamental concepts underlying software solutions to many problems. Structured data, statement sequencing, logic control, input/output, procedures, and functions. (3H,3C) II.

1044: INTRODUCTION TO PROGRAMMING IN C
Fundamental concepts underlying software solutions of many problems. Structured data, statement sequencing, logic control, input/output, and functions. The course will be taught using a structured approach to programming. Partially duplicates 1344. (3H,3C) I, II, III, IV.

1054: INTRODUCTION TO PROGRAMMING IN JAVA
This course provides an introduction to object oriented programming using the Java language. Fundamental concepts underlying programming and software solutions to many problems. Structured data, statement sequencing, logic control, classes, objects, methods, instantiation of classes, sending messages to objects. (2H,2L,3C)

1104: INTRODUCTION TO COMPUTER SCIENCE
This course (a) presents the fundamental concepts of computer programming, (b) introduces the history of computing, (c) provides an introduction to and preliminary investigation of the fundamental concepts found throughout the computer science discipline, and (d) overviews computer science subdisciplines such as algorithms, artificial intelligence, computer architecture, human-computer interaction, language translation, operating systems, parallel computation, and software engineering. Co: 1044 or 1344. (3H,3C) I,II,III.

1114: INTRODUCTION TO PROBLEM SOLVING AND COMPUTING
Introduction to problem solving techniques fundamental to computer programming. Definition of algorithm. Algorithmic structures: sequencing, selection, iteration. Tracing of algorithms. Implementation of algorithms in a high-level programming language. Essential programming concepts: data types, input/output, control constructs, simple functions, arrays. (2H,2C)

1204: INTERNET AND SYSTEM SOFTWARE
An on-line self-paced tutorial to the Internet and World Wide Web, Program Development Tools, and common applications. Introduction to Web publishing, communication, and searching. Instruction in the use of an integrated program development environment, debugger, and related program development tools. Introduction to spreadsheets, databases, and slide presentation software package. Partially duplicates 1604. Co: 1044, 1344. (1H,1C)

1304: INTRODUCTION TO COMPUTER SCIENCE LABORATORY
A lab course designed to build on prior knowledge of a high-level programming language and to teach the fundamentals of structured programming in Pascal. Expression, statement, and unit level constructs are discussed; programming assignments are used to reinforce concepts and to provide the requisite experience to pursue advanced Computer Science courses. Partially duplicates CS 1034. Pre: 1014. (3L,1C) I.

1344: PROGRAMMING IN C
A course designed to build on prior knowledge of a high level programming language and to teach the fundamentals of structured programming in C. Expression, statement, and module level constructs are discussed; programming assignments are used to reinforce concepts and to provide the requisite experience to pursue advanced Computer Science courses. Partially duplicates 1044. Pre: 1014 or 1034. (1H,1C) I.

1604: INTRODUCTION TO THE INTERNET
Introduces the concepts, software, data organization and issues involved with using networked information. Also covers file formats (as applied in networked hypermedia and multimedia sound/video documents), local and global (Internet) network access, electronic mail, transferring files, network news, the World Wide Web, digital libraries, on-line public access catalogs and electronic journals, CD-ROMs and on-line databases, and commercial and other networks. Partially duplicates 1205. Word processing ability required. (1H,1C) I,II, III.

1704: INTRODUCTION TO DATA STRUCTURES AND SOFTWARE ENGINEERING
Introduces a disciplined approach to problem-solving and emphasizes the utility of software engineering principles applied to programming practices. Also stressed are program design and implementation involving multiple modules, verification of program correctness, and abstract data types and objects such as strings, arrays, sets, linked lists, stacks, queues, and files. Pre: 1044 or 1344. Co: 1206, 2304. (3H,3C)

1705-1706: INTRODUCTION TO OBJECT-ORIENTED DEVELOPMENT
Fundamental concepts of programming from an object-oriented perspective. Basic software engineering principles and programming skills taught with a programming language that supports the object-oriented paradigm. 1705: Simple data types, control structures, array and string data structures and algorithms, testing and debugging. 1706: Detailed coverage of data structures, algorithms, and the methods of object-oriented design and software construction. Design and construction of medium-sized object-oriented programming projects with an emphasis on teamwork and software engineering. Programming experience in C++ or Java may be substituted for ENGE 1024 prerequisite. Pre: (MATH 1205 or MATH 1526), ENGE 1024 for 1705; 1705 for 1706. (2H,2L,3C)

1705H-1706H: HONORS INTRODUCTION TO OBJECT-ORIENTED DEVELOPMENT
(2H,2L,3C)

1944: COMPUTER SCIENCE FIRST YEAR SEMINAR
An introduction to academic and career planning for computer science majors. Pass/Fail only. (1H,1C)

2204: UNIX
A hands-on introduction to the modern operating system UNIX. Introduction to the basic operating systems concepts employed by UNIX. Students gain experience with basic system usage, system installation and administration, the UNIX programming environment, and system utilities. Duplicates 2304 (UNIX). A grade of C or better required in CS prerequisite 1706. Pre: 1706 or ECE 2574. (2H,2C)

2304: SELF STUDY IN A PROGRAMMING SYSTEM
Guided self-study in a specific programming system, its syntax and applications; based on prior knowledge of the programming process and experience in programming with some high level language; may be taken three times for credit with different system each time; may be taken only twice for CS major or minor credit; systems to be offered may include FORTRAN, COBOL, C, UNIX, LISP. 2304 (UNIX) partially duplicates 1206. A grade of C or better required in CS prerequisite 1706. Pre: 1706. (1C) I,II.

2504: INTRODUCTION TO COMPUTER ORGANIZATION
Basic computer organization at the machine language and assembly language level. Digital logic and circuits. Basic components of computer hardware and their implementation. Interaction with the operating system. Alternative computer organizations and implementations. Partially duplicates ECPE 2504. A grade of C or better required in CS prerequisites 2204 and 2704. Pre: 2204, 2704. (3H,3C) I,II.

2604: DATA STRUCTURES AND FILE MANAGEMENT
This course extends the concepts of primitive data types by teaching the student a classical set of data structures that pervades both the theoretical and practical domains of computer science. Topics discussed include lists, trees, graphs, searching, sorting, file system organization and access methods. A grade of C or better required in CS prerequisites 2204 and 2704. I,II,IV Pre: 2204, 2704, MATH 2534. (3H,3C)

2704: ORJECT-ORIENTED SOFTWARE DESIGN AND CONSTRUCTION
Introduces the principles of object-oriented programming with emphasis on objects, classes, inheritance, and polymorphism. A programming language such as C++ is used to apply these principles in several application domains. Also stressed are tools and techniques for testing, debugging, and organizing and managing larger programs. A grade of C or better required in CS prerequisite 1706. I,II,III Pre: 1706, ECE 2574. (3H,3C)

2964: FIELD STUDY
Pass/Fail only. Variable credit course.

2974: INDEPENDENT STUDY
Variable credit course.

2984: SPECIAL STUDY
Variable credit course.

3204: OPERATING SYSTEMS
Covers the concept of a "process", its abstract and physical representations, its creation, management and scheduling. Study of: a thread process and how it relates to the parent; asynchronous concurrently executing processes, shared memory access, synchronization via semaphones, critical regions and monitors. Additional topics: deadlock prevention, avoidance, and detection, including Banker's Algorithm; memory management strategies including virtual memory; file representation and storage management; and device management. UNIX will be the reference system and the one used for project development and submission. A grade of c or better required in CS prerequisites 2504 and 2604. X-grade allowed. Pre: (2504 or ECE 2504), 2604. (3H,3C)

3304: COMPARATIVE LANGUAGES
This course in programming language constructs emphasizes the run-time behavior of programs. The languages are studied from two points of view: (1) the fundamental elements of languages and their inclusion in commercially available systems; and, (2) the differences between implementations of common elements in languages. A grade of C or better required in CS prerequisite 2604. I,II Pre: 2604. (3H,3C)

3414 (MATH 3414): NUMERICAL METHODS
Computational methods for numerical solution of non-linear equations, differential equations, approximations, iterations, methods of least squares, and other topics. Partially duplicates Math 4554. A grade of C or better required in CS prerequisite 1044 or 1705. II Pre: MATH 2214, MATH 2224, CS 1044 or CS 1705. (3H,3C)

3604: PROFESSIONALISM IN COMPUTING
Studies the ethical, social, and professional concerns of the computer science field. Covers the social impact of the computer, implications and effects of computers on society, and the responsibilities of computer professionals in directing the emerging technology. The topics are studied through case studies of reliable, risk-free technologies, and systems that provide user friendly processes. Specific studies are augmented by an overview of the history of computing, interaction with industrial partners and computing professionals, and attention to the legal and ethical responsibilities of professionals. This is a web-supported course, incorporating writing intensive exercises, making extensive use of active learning technologies. A grade of C or better required in CS prerequisite 2604. Pre: (2604, COMM 2004). (3H,3C)

3704: INTERMEDIATE SOFTWARE DESIGN AND ENGINEERING
Explores the principles of software design in detail, with an emphasis on software engineering aspects. Includes exposure of software lifecycle activities including design, coding, testing, debugging, and maintenance, highlighting how design affects these activities. Peer reviews, designing for software reuse, CASE tools, and writing software to specifications are also covered. A grade of C or better required in CS prerequisite 2604. II Pre: 2604. (3H,3C)


3724: INTRODUCTION TO HUMAN-COMPUTER INTERACTION
Survey of human-computer interaction concepts, theory, and practice. Basic components of human-computer interaction. Interdisciplinary underpinnings. Informed and critical evaluation of computer-based technology. User-oriented perspective, rather than system-oriented, with two thrusts: human (cognitive, social) and technological (input/output, interactions styles, devices). Design guidelines, evaluation methods, participatory design, communication between users and system developers. A grade of C or better required in CS prerequisite 2604. Pre: 2604. (3H,3C)I.

4004: DATA AND INFORMATION STRUCTURES
Formal underpinnings of computer science: logic, sets, relations as they apply to computer science. Principles of data structures, algorithm analysis, file management, databases. Not for CS major or minor credit; not for graduate credit in CSA program. Pre: 1704. (3H,3C) I.

4014: PRINCIPLES OF COMPUTER ARCHITECTURE AND OPERATING SYSTEMS
Principles of computer hardware organization and operating systems. From individual microprocessor hardware components to computer network architectures. Operating system principles, with emphasis on concurrency and synchronization, deadlock, memory, scheduling and performance. Not for CS major or minor credit; not for graduate credit in CSA program. Pre: 4004. (3H,3C) II.

4104: DATA AND ALGORITHM ANALYSIS
This course emphasizes the understanding of data structures and algorithms from an analytical perspective rather than from an implementation standpoint. The concepts developed allow discussion of the efficiency of an algorithm and the comparison of two or more algorithms with respect to space and run-time requirements. Analytical methods are used to describe theoretical bounds as well as practical ones. In general, this course addresses the constraints that affect problem solvability. A grade of C or better required in CS prerequisite 2604. I Pre: 2604, (MATH 3134 or MATH 3034). (3H,3C)

4114: INTRODUCTION TO FORMAL LANGUAGES AND AUTOMATA THEORY
The course presents a study of formal languages and the correspondence between language classes and the automata that recognize them. Formal definitions of grammars and acceptors, deterministic and nondeterministic systems, grammar ambiguity, finite state and push-down automata, and normal forms will be discussed. Pre: MATH 3134 or MATH 3034. (3H,3C) II.

4124: THEORY OF COMPUTATION
Theoretical analysis of the computational process; fundamental concepts such as abstract programs, classes of computational machines and their equivalence, recursive function theory, unsolvable problems, Church's thesis, Kleene's theorem, program equivalence, and generability, acceptability, decidability will be covered. Pre: MATH 3134 or MATH 3034. (3H,3C) I.

4204: COMPUTER GRAPHICS
Hardware and software techniques for the display of graphical information. 2D and 3D geometry and transformations, clipping and windowing, software systems. Interactive graphics, shading, hidden surface elimination, perspective depth. Modeling and realism. A grade of C or better required in CS prerequisite 2604. I Pre: 2604, (MATH 3134 or MATH 3034). (3H,3C)

4214: SIMULATION AND MODELING
Overview of discrete-event digital computer simulation and modeling. Fundamentals of model development, Monte Carlo simulation, the life cycle of a simulation study, input and output data analysis, world views and time control, random number and variate generation, credibility assessment of simulation results, simulation languages, applications of simulation using the General Purpose Simulation System (GPSS). A grade of C or better required in CS prerequisite 1706. I Pre: 1704, STAT 4714. (3H,3C)

4224: PERFORMANCE EVALUATION OF COMPUTER SYSTEMS
Overview of techniques for measuring, improving, and tuning the performance of computer systems. Procurement, workload characterization, measurement principles, the representation of measurement data, software and hardware monitors, capacity planning, bottleneck detection, system and program tuning, simulation and analytic models and their applications, case studies. Pre: 3204, (STAT 4714 or STAT 4105 or STAT 4705). (3H,3C) II.

4234: PARALLEL AND DISTRIBUTED COMPUTATION
Survey of parallel computer architectures, models of parallel computation, and interconnection networks. Parallel algorithm development and analysis. Programming paradigms and languages for parallel computation. Example applications. Performance measurement and evaluation. A grade of C or better required in CS prerequisite 3204. I Pre: 3204. (3H,3C)

4244: INTERNET PROGRAMMING
Key technology underlying the World-Wide Web. Web architecture, including server design, caching, network protocols, and related standards (e.g. http, SHTTP, TCP/IP, MIME). Programming systems (e.g. Java, Active-X, component models). Security and cryptography. Document representations (e.g. XML, HTML, PDF, VRML). Legal and social issues of the Web. A grade of C or better required in CS prerequisite 3204. I Pre: 3204. (3H,3C)

4254: COMPUTER NETWORK ARCHITECTURE AND PROGRAMMING
Introduction to computer network architecture, and methods for programming network services and applications (e.g. DNS, Email and MIME, http, SNMP, multimedia). Wired, wireless, and satellite network architectures. OSI protocol model, with an emphasis on upper layers. Congestion control, quality of service, routing. Internet protocol suite (e.g. IP, TCP, ARP, RARP). Server design (e.g. connectionless, concurrent). Network programming abstractions (e.g. XDR, remote procedure calls, sockets, DCOM). Case studies (e.g. TELNET). A grade of C or better required in CS prerequisite 3204. II Pre: 3204. (3H,3C)

4304: COMPILER DESIGN AND IMPLEMENTATION
This course includes the theory, the design, and the implementation of a large language translator system. Lexical analysis, syntatic analysis, code generation, and optimization are emphasized. A grade of C or better required in CS prerequisite 3204. II Pre: 3204. (3H,3C)

4414 (MATH 4414): ISSUES IN SCIENTIFIC COMPUTING
Theory and techniques of modern computational mathematics, computing environments, computational linear algebra, optimization, approximation, parameter identification, finite difference and finite element methods and symbolic computation. Project-oriented course; modeling and analysis of physical systems using state-of-the-art software and packaged subroutines. Pre: MATH 2214, MATH 3214. (2H,3L,3C) I,II.

4504 (ECE 4504): COMPUTER ORGANIZATION
Information representation and transfer; instructions and data access methods; the control unit and microprogramming; memories; input/output and interrupts; secondary storage; the von Neumann SISD organization; high level language machines; the RISC concept; special purpose processors including operating system, file, text, floating point, communication, etc. Multicomputers; multiprocessors; concurrent processing support; Pipeline machines, processor arrays, database machines; the data flow/data directed approach; computer networks. A grade of C or better required in CS prerequisite 3204. I,II Pre: 3204. (3H,3C)

4570 (ECE 4570): WIRELESS NETWORKS AND MOBILE SYSTEMS
Multidisciplinary, project-oriented design course that considers aspects of wireless and mobile systems including wireless networks and link protocols, mobile networking including support for the Internet Protocol suite, mobile middleware, and mobile applications. Students complete multiple experiments and design projects. Pre: 4254 or ECE 4564. (3H,3C)

4604: INTRODUCTION TO DATA BASE MANAGEMENT SYSTEMS
Emphasis on introduction of the basic data base models, corresponding logical and physical data structures, comparisons of models, logical data design, and data base usage. Terminology, historical evolution, relationships, implementation, data base personnel, future trends, applications, performance considerations, data integrity. Senior standing required. A grade of C or better required in CS prerequisite 2604. II Pre: 2604. (3H,3C)

4624: MULTIMEDIA, HYPERTEXT AND INFORMATION ACCESS
Introduces the architectures, concepts, data, hardware, methods, models, software, standards, structures, technologies, and issues involved with: networked multimedia (e.g., image, audio, video) information, access and systems; hypertext and hypermedia; electronic publishing; virtual reality. Coverage includes text processing, search, retrieval, browsing, time-based performance, synchronization, quality of service, video conferencing and authoring. Senior standing required. A grade of C or better required in CS prerequisite 2604. II Pre: 2604. (3H,3C)

4634: DESIGN OF INFORMATION
w become information, that is, to inform people. The course focuses on the design of user interface layouts, and on the design of texts and hypertexts, as well as on the information development process. Senior standing required. A grade of C or better required in CS prerequisite 2604. Pre: 2604. (3H,3C)

4704: SOFTWARE ENGINEERING
Introduction to the basic principles of software engineering. Issues in the software life cycle. Emphasis on methods for software design and testing. Project management and quality assurance. Significant software project required. A grade of C or better required in CS prerequisite 3704 I Pre: 3704. (2H,3L,3C)

4804: INTRODUCTION TO ARTIFICIAL INTELLIGENCE
Overview of the areas of problem solving, game playing, and computer vision. Search trees and/or graphs, game trees, block world vision, syntactic pattern recognition, object matching, natural language, and robotics. Senior standing required. A grade of C or better required in CS prerequisite 2604. Pre: 2604. (3H,3C) I.

4944: SEMINAR
Pass/Fail only.
(1H,1C)

4964: FIELD STUDY
Pass/Fail only. Variable credit course.

4974: INDEPENDENT STUDY
Variable credit course.

4984: SPECIAL STUDY
Variable credit course.

4994: UNDERGRADUATE RESEARCH
Variable credit course.

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