¶¡ÏãÔ°AV

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Topics as for Math 151 with a more extensive review of functions, their properties and their graphs. Recommended for students with no previous knowledge of Calculus. In addition to regularly scheduled lectures, students enrolled in this course are encouraged to come for assistance to the Calculus Workshop (Burnaby), or Math Open Lab (Surrey). Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B+, or MATH 100 with a grade of at least B-, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 151, 154 or 157 may not take MATH 150 for further credit. Quantitative.

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Logarithmic and exponential functions, trigonometric functions, inverse functions. Limits, continuity, and derivatives. Techniques of differentiation, including logarithmic and implicit differentiation. The Mean Value Theorem. Applications of differentiation including extrema, curve sketching, Newton's method. Introduction to modeling with differential equations. Polar coordinates, parametric curves. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least A, or MATH 100 with a grade of at least B, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 154 or 157 may not take MATH 151 for further credit. Quantitative.

Designed for students specializing in the biological and medical sciences. Topics include: limits, growth rate and the derivative; elementary functions, optimization and approximation methods, and their applications; mathematical models of biological processes. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 151 or 157 may not take MATH 154 for further credit. Quantitative.

Designed for students specializing in business or the social sciences. Topics include: limits, growth rate and the derivative; logarithmic, exponential and trigonometric functions and their application to business, economics, optimization and approximation methods; introduction to functions of several variables with emphasis on partial derivatives and extrema. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 151 or 154 may not take MATH 157 for further credit. Quantitative.

Riemann sum, Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, applications of integration. First-order separable differential equations and growth models. Sequences and series, series tests, power series, convergence and applications of power series. Prerequisite: MATH 150 or 151; or MATH 154 or 157 with a grade of at least B. Students with credit for MATH 155 or 158 may not take this course for further credit. Quantitative.

Designed for students specializing in the biological and medical sciences. Topics include: the integral, partial derivatives, differential equations, linear systems, and their applications; mathematical models of biological processes. Prerequisite: MATH 150, 151 or 154; or MATH 157 with a grade of at least B. Students with credit for MATH 152 or 158 may not take this course for further credit. Quantitative.

Designed for students specializing in business or the social sciences. Topics include: theory of integration, integration techniques, applications of integration; functions of several variables with emphasis on double and triple integrals and their applications; introduction to differential equations with emphasis on some special first-order equations and their applications; sequences and series. Prerequisite: MATH 150 or 151 or 154 or 157. Students with credit for MATH 152 or 155 may not take MATH 158 for further credit. Quantitative.

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphasis and includes proofs of the basic theorems. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

An introduction to business statistics with a heavy emphasis on applications and the use of EXCEL. Students will be required to use statistical applications to solve business problems. Prerequisite: MATH 150, MATH 151, MATH 154, or MATH 157; 15 units. MATH 150, MATH 151, MATH 154, or MATH 157 may be taken concurrently with BUS 232. Students with credit for BUEC 232 or ECON 233 may not take this course for further credit. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Prerequisite: or Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Quantitative.

This course provides a basic integrative overview of how cognitive science aspires to integrate the empirical findings, theories, and methods of psychology, neuroscience, linguistics, computing science and philosophy. Prerequisite: Open to all students. Students with credit for COGS 200 may not take COGS 100 for further credit. Breadth-Hum/Social Sci/Science.

An elementary introduction to computing science and computer programming, suitable for students with little or no programming background. Students will learn fundamental concepts and terminology of computing science, acquire elementary skills for programming in a high-level language and be exposed to diverse fields within, and applications of computing science. Topics will include: pseudocode, data types and control structures, fundamental algorithms, computability and complexity, computer architecture, and history of computing science. Treatment is informal and programming is presented as a problem-solving tool. Prerequisite: BC Math 12 or equivalent is recommended. Students with credit for CMPT 102, 128, 130 or 166 may not take this course for further credit. Students who have taken CMPT 125, 129, 130 or 135 first may not then take this course for further credit. Quantitative/Breadth-Science.

A rigorous introduction to computing science and computer programming, suitable for students who already have some background in computing science and programming. Intended for students who will major in computing science or a related program. Topics include: fundamental algorithms; elements of empirical and theoretical algorithmics; abstract data types and elementary data structures; basic object-oriented programming and software design; computation and computability; specification and program correctness; and history of computing science. Prerequisite: CMPT 120. Corequisite: CMPT 127. Students with credit for CMPT 126, 129, 135 or CMPT 200 or higher may not take for further credit. Quantitative.

Builds on CMPT 120 to give a hands-on introduction to programming in C and C++, the basics of program design, essential algorithms and data structures. Guided labs teach the standard tools and students exploit these ideas to create software that works. To be taken in parallel with CMPT 125. Prerequisite: CMPT 120 or CMPT 128 or CMPT 130. Corequisite: CMPT 125.

An introduction to computing science and computer programming, using a systems oriented language, such as C or C++. This course introduces basic computing science concepts. Topics will include: elementary data types, control structures, functions, arrays and strings, fundamental algorithms, computer organization and memory management. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157). Students with credit for CMPT 102, 120, 128 or 166 may not take this course for further credit. Students who have taken CMPT 125, 129 or 135 first may not then take this course for further credit. Quantitative/Breadth-Science.

A second course in systems-oriented programming and computing science that builds upon the foundation set in CMPT 130 using a systems-oriented language such as C or C++. Topics: a review of the basic elements of programming; introduction to object-oriented programming (OOP); techniques for designing and testing programs; use and implementation of elementary data structures and algorithms; introduction to embedded systems programming. Prerequisite: CMPT 130. Students with credit for CMPT 125, 126, or 129 may not take this course for further credit. Quantitative.

This course teaches the fundamentals of informative and persuasive communication for professional engineers and computer scientists. A principal goal of this course is to assist students in thinking critically about various contemporary technical, social, and ethical issues. It focuses on communicating technical information clearly and concisely, managing issues of persuasion when communicating with diverse audiences, presentation skills, and teamwork. Students with credit for ENSC 102, ENSC 105W, MSE 101W or SEE 101W may not take CMPT 105W for further credit. Writing.

Introduction to a variety of practical and important data structures and methods for implementation and for experimental and analytical evaluation. Topics include: stacks, queues and lists; search trees; hash tables and algorithms; efficient sorting; object-oriented programming; time and space efficiency analysis; and experimental evaluation. Prerequisite: (MACM 101 and ((CMPT 125 and 127), CMPT 129 or CMPT 135)) or (ENSC 251 and ENSC 252). Quantitative.

An overview of various techniques used for software development and software project management. Major tasks and phases in modern software development, including requirements, analysis, documentation, design, implementation, testing,and maintenance. Project management issues are also introduced. Students complete a team project using an iterative development process. Prerequisite: One W course, CMPT 225, (MACM 101 or (ENSC 251 and ENSC 252)) and (MATH 151 or MATH 150). MATH 154 or MATH 157 with at least a B+ may be substituted for MATH 151 or MATH 150. Students with credit for CMPT 275 may not take this course for further credit.

The curriculum introduces students to topics in computer architecture that are considered fundamental to an understanding of the digital systems underpinnings of computer systems. Prerequisite: Either (MACM 101 and ((CMPT 125 and CMPT 127) or CMPT 135)) or (MATH 151 and CMPT 102 for students in an Applied Physics program).

Introduction to counting, induction, automata theory, formal reasoning, modular arithmetic. Prerequisite: BC Math 12 (or equivalent), or any of MATH 100, 150, 151, 154, 157. Quantitative/Breadth-Science.

A continuation of MACM 101. Topics covered include graph theory, trees, inclusion-exclusion, generating functions, recurrence relations, and optimization and matching. Prerequisite: MACM 101 or (ENSC 251 and one of MATH 232 or MATH 240). Quantitative.

The description and analysis of language patterns. Focuses on the structure of sounds, words, sentences, and meaning. Breadth-Social Sciences.

Develops skills in writing in linguistics while providing a closer look at fundamental concepts of the discipline. As topics examined may vary by term, this course may be repeated once for credit if the topic is different. Prerequisite: LING 220. Writing/Quantitative.

This course aims to give the student an understanding of what a modern operating system is, and the services it provides. It also discusses some basic issues in operating systems and provides solutions. Topics include multiprogramming, process management, memory management, and file systems. Prerequisite: CMPT 225 and (CMPT 295 or (ENSC 251 and ENSC 252)).

Analysis and design of data structures for lists, sets, trees, dictionaries, and priority queues. A selection of topics chosen from sorting, memory management, graphs and graph algorithms. Prerequisite: CMPT 225, MACM 201, MATH 151 (or MATH 150), and MATH 232 or 240.

Covers professional writing in computing science, including format conventions and technical reports. Attention is paid to group dynamics, including team leadership, dispute resolution, cognitive bias, professional ethics and collaborative writing. Research methods are also discussed. The use of LaTeX and various version control tools are emphasized. Prerequisite: CMPT 105W and (CMPT 275 or CMPT 276). Students with credit for CMPT 376 may not take this course for further credit. Writing.

This course examines the theoretical and applied problems of constructing and modelling systems, which aim to extract and represent the meaning of natural language sentences or of whole discourses, but drawing on contributions from the fields of linguistics, cognitive psychology, artificial intelligence and computing science. Prerequisite: Completion of nine units in Computing Science upper division courses or, in exceptional cases, permission of the instructor.

Provides a unified discussion of the fundamental approaches to the problems in artificial intelligence. The topics considered are: representational typology and search methods; game playing, heuristic programming; pattern recognition and classification; theorem-proving; question-answering systems; natural language understanding; computer vision. Prerequisite: CMPT 225 and (MACM 101 or ENSC 251 and ENSC 252)). Students with credit for CMPT 410 may not take this course for further credit.

The principles involved in using computers for data acquisition, real-time processing, pattern recognition and experimental control in biology and medicine will be developed. The use of large data bases and simulation will be explored. Prerequisite: Completion of 60 units including one of CMPT 125, 126, 128, 135 or (102 with a grade of B or higher).

Formal and foundational issues dealing with the representation of knowledge in artificial intelligence systems are covered. Questions of semantics, incompleteness, non-monotonicity and others will be examined. As well, particular approaches, such as procedural or semantic network, may be discussed. Prerequisite: Completion of nine units in Computing Science upper division courses or, in exceptional cases, permission of the instructor.

Computational approaches to image understanding will be discussed in relation to theories about the operation of the human visual system and with respect to practical applications in robotics. Topics will include edge detection, shape from shading, stereopsis, optical flow, Fourier methods, gradient space, three-dimensional object representation and constraint satisfaction. Prerequisite: MATH 152, and nine units in Computing upper division courses or permission of the instructor.

This course examines the theoretical and applied problems of constructing and modelling systems, which aim to extract and represent the meaning of natural language sentences or of whole discourses, but drawing on contributions from the fields of linguistics, cognitive psychology, artificial intelligence and computing science. Prerequisite: Completion of nine units in Computing Science upper division courses or, in exceptional cases, permission of the instructor.

This course covers various topics in computer vision with the emphasis on the model-based approach. Main subjects include 2-D and 3-D representations, matching, constraint relaxation, model-based vision systems. State-of-the-art robot vision systems will be used extensively as study cases. The solid modelling and CAD aspects of this course should also interest students of computer graphics. Prerequisite: MATH 152 and nine units in CMPT upper division courses, or permission of the instructor.

Intelligent Systems using modern constraint programming and heuristic search methods. A survey of this rapidly advancing technology as applied to scheduling, planning, design and configuration. An introduction to constraint programming, heuristic search, constructive (backtrack) search, iterative improvement (local) search, mixed-initiative systems and combinatorial optimization. Prerequisite: CMPT 225.

Current topics in artificial intelligence depending on faculty and student interest.

This course provides an introduction to the fundamentals of computer graphics. Topics include graphics display and interaction hardware, basic algorithms for 2D primitives, anti-aliasing, 2D and 3D geometrical transformations, 3D projections/viewing, Polygonal and hierarchical models, hidden-surface removal, basic rendering techniques (color, shading, raytracing, radiosity), and interaction techniques. Prerequisite: CMPT 225 and MATH 232 or 240.

This course provides a comprehensive study of user interface design. Topics include: goals and principles of UI design (systems engineering and human factors), historical perspective, current paradigms (widget-based, mental model, graphic design, ergonomics, metaphor, constructivist/iterative approach, and visual languages) and their evaluation, existing tools and packages (dialogue models, event-based systems, prototyping), future paradigms, and the social impact of UI. Prerequisite: CMPT 225.

Multimedia systems design, multimedia hardware and software, issues in effectively representing, processing, and retrieving multimedia data such as text, graphics, sound and music, image and video. Prerequisite: CMPT 225.

Computational Photography is concerned with overcoming the limitations of traditional photography with computation: in optics, sensors, and geometry; and even in composition, style, and human interfaces. The course covers computational techniques to improve the way we process, manipulate, and interact with visual media. The covered topics include image-based lighting and rendering, camera geometry and optics, computational apertures, advanced image filtering operations, high-dynamic range, image blending, texture synthesis and inpainting. Prerequisite: CMPT 361, MACM 201 and 316. Students with credit for CMPT 451 may not take this course for further credit.

Covers advanced topics in geometric modelling and processing for computer graphics, such as Bezier and B-spline techniques, subdivision curves and surfaces, solid modelling, implicit representation, surface reconstruction, multi-resolution modelling, digital geometry processing (e.g. mesh smoothing, compression, and parameterization), point-based representation, and procedural modelling. Prerequisite: CMPT 361, MACM 316. Students with credit for CMPT 469 between 2003 and 2007 or equivalent may not take this course for further credit.

Topics and techniques in animation, including: The history of animation, computers in animation, traditional animation approaches, and computer animation techniques such as geometric modelling, interpolation, camera controls, kinematics, dynamics, constraint-based animation, realistic motion, temporal aliasing, digital effects and post production. Prerequisite: CMPT 361 and MACM 316 or permission of the instructor.

Current topics in computer graphics depending on faculty and student interest. Prerequisite: CMPT 361.

This course aims to give the student an understanding of what a modern operating system is, and the services it provides. It also discusses some basic issues in operating systems and provides solutions. Topics include multiprogramming, process management, memory management, and file systems. Prerequisite: CMPT 225 and (CMPT 295 or (ENSC 251 and ENSC 252)).

This course is an introduction to the modelling, analysis, and computer simulation of complex systems. Topics include analytic modelling, discrete event simulation, experimental design, random number generation, and statistical analysis. Prerequisite: CMPT 225, (MACM 101 or (ENSC 251 and ENSC 252)) and STAT 270.

Data communication fundamentals (data types, rates, and transmission media). Network architectures for local and wide areas. Communications protocols suitable for various architectures. ISO protocols and internetworking. Performance analysis under various loadings and channel error rates. Prerequisite: CMPT 225 and (MATH 151 or MATH 150). MATH 154 or MATH 157 with a grade of at least B+ may be substituted for MATH 151 (MATH 150).

This course covers the key components of a compiler for a high level programming language. Topics include lexical analysis, parsing, type checking, code generation and optimization. Students will work in teams to design and implement an actual compiler making use of tools such as lex and yacc. Prerequisite: MACM 201, (CMPT 295 or ENSC 215) and CMPT 225.

An introduction to distributed systems: systems consisting of multiple physical components connected over a network. Architectures of such systems, ranging from client-server to peer-to-peer. Distributed systems are analyzed via case studies of real network file systems, replicated systems, sensor networks and peer-to-peer systems. Hands-on experience designing and implementing a complex distributed system. Prerequisite: CMPT 300, 371. Students with credit for CMPT 401 before September 2008 may not take this course for further credit.

The basics of embedded system organization, hardware-software co-design, and programmable chip technologies are studied. Formal models and specification languages for capturing and analyzing the behavior of embedded systems. The design and use of tools for system partitioning and hardware/software co-design implementation, validation, and verification are also studied. Prerequisite: CMPT 295 and CMPT 300.

This course covers the fundamentals of higher level network functionality such as remote procedure/object calls, name/address resolution, network file systems, network security and high speed connectivity/bridging/switching. Prerequisite: CMPT 300 and 371.

Current topics in computing systems depending on faculty and student interest. Prerequisite: CMPT 300.

Current topics in computer hardware depending on faculty and student interest. Prerequisite: CMPT/ENSC 250.

Logical representations of data records. Data models. Studies of some popular file and database systems. Document retrieval. Other related issues such as database administration, data dictionary and security. Prerequisite: CMPT 225, and (MACM 101 or (ENSC 251 and ENSC 252)).

This course introduces students to the computing science principles underlying computational biology. The emphasis is on the design, analysis and implementation of computational techniques. Possible topics include algorithms for sequence alignment, database searching, gene finding, phylogeny and structure analysis. Prerequisite: CMPT 307. Students with credit for CMPT 341 may not take this course for further credit.

An advanced course on database systems which covers crash recovery, concurrency control, transaction processing, distributed database systems as the core material and a set of selected topics based on the new developments and research interests, such as object-oriented data models and systems, extended relational systems, deductive database systems, and security and integrity. Prerequisite: CMPT 300 and 354.

Introduction to the essentials of information retrieval and the applications of information retrieval in web search and web information systems. Topics include the major models of information retrieval, similarity search, text content search, link structures and web graphics, web mining and applications, crawling, search engines, and some advanced topics such as spam detection, online advertisement, and fraud detection in online auctions. Prerequisite: CMPT 354.

Current topics in database and information systems depending on faculty and student interest. Prerequisite: CMPT 354.

This course examines: two-tier/multi-tier client/server architectures; the architecture of a Web-based information system; web servers/browser; programming/scripting tools for clients and servers; database access; transport of programming objects; messaging systems; security; and applications (such as e-commerce and on-line learning). Prerequisite: (CMPT 275 or CMPT 276) and CMPT 354.

Web service based systems are fundamentally different from traditional software systems. The conceptual and methodological differences between a standard software development process and the development of a web service based information system. The technology involved during the construction of their own web service based application in an extensive project. Prerequisite: CMPT 371.

Survey of modern software development methodology. Several software development process models will be examined, as will the general principles behind such models. Provides experience with different programming paradigms and their advantages and disadvantages during software development. Prerequisite: CMPT 276 or 275.

Various concepts and principles underlying the design and use of modern programming languages are considered in the context of procedural, object-oriented, functional and logic programming languages. Topics include data and control structuring constructs, facilities for modularity and data abstraction, polymorphism, syntax, and formal semantics. Prerequisite: CMPT 225, and (MACM 101 or (ENSC 251 and ENSC 252)).

This course considers modelling and programming techniques appropriate for symbolic data domains such as mathematical expressions, logical formulas, grammars and programming languages. Topics include recursive and functional programming style, grammar-based data abstraction, simplification and reduction transformations, conversions to canonical form, environment data structures and interpreters, metaprogramming, pattern matching and theorem proving. Prerequisite: CMPT 225, and (MACM 101 or ENSC 251 and ENSC 252)).

Methods for software quality assurance focusing on reliability and security. Test coverage and test data adequacy including combinatorial testing. MC/DC testing, and mutation testing. Security engineering techniques for vulnerability discovery and mitigation including fuzz testing. Testing techniques will be applied to the assessment of external open source software. Prerequisite: (CMPT 275 or CMPT 276) and 15 upper division CMPT units.

Software succeeds when it is well-matched to its intended purpose. Requirements engineering is the process of discovering that purpose by making requirements explicit and documenting them in a form amenable to analysis, reasoning, and validation, establishing the key attributes of a system prior to its construction. Students will learn methodical approaches to requirements analysis and design specification in early systems development phases, along with best practices and common principles to cope with notoriously changing requirements. Prerequisite: CMPT 275 or 276, MACM 201 and 15 units of upper division courses. Recommended: co-op experience.

Introduces, at an accessible level, a formal framework for symbolic model checking, one of the most important verification methods. The techniques are illustrated with examples of verification of reactive systems and communication protocols. Students learn to work with a model checking tool. Prerequisite: CMPT 275 or 276.

Current topics in programming languages depending on faculty and student interest. Prerequisite: CMPT 383.

Analysis and design of data structures for lists, sets, trees, dictionaries, and priority queues. A selection of topics chosen from sorting, memory management, graphs and graph algorithms. Prerequisite: CMPT 225, MACM 201, MATH 151 (or MATH 150), and MATH 232 or 240.

This course introduces students to formal models of computations such as Turing machines and RAMs. Notions of tractability and intractability are discusses both with respect to computability and resource requirements. The relationship of these concepts to logic is also covered. Prerequisite: MACM 201.

The main cryptographic tools and primitives, their use in cryptographic applications; security and weaknesses of the current protocols. The notion of security, standard encryption schemes, digital signatures, zero-knowledge, selected other topics. Prerequisite: MACM 201. CMPT 307 and 308 are recommended.

Models of computation, methods of algorithm design; complexity of algorithms; algorithms on graphs, NP-completeness, approximation algorithms, selected topics. Prerequisite: CMPT 307.

Machine models and their equivalences, complexity classes, separation theorems, reductions, Cook's theorem, NP-completeness, the polynomial time hierarchy, boolean circuit models and parallel complexity theory, other topics of interest to the students and instructor. Prerequisite: CMPT 307.

Current topics in theoretical computing science depending on faculty and student interest. Prerequisite: CMPT 307.

Languages, grammars, automata and their applications to natural and formal language processing. Prerequisite: MACM 201. Quantitative.

An overview of theoretical principles in phonology. Prerequisite: LING 282W; or LING 221 and any lower division W course.

Introduces theories of sentence structure. Prerequisite: LING 282W; or LING 222 and any lower division W course.

Formal systems and their relation to linguistic methods and theory. Topics include the mathematical properties of natural languages, and rigorously defined frameworks for linguistic analysis and their formal properties. Prerequisite: LING 322. Recommended: PHIL 210. Quantitative.

Languages, grammars, automata and their applications to natural and formal language processing. Prerequisite: MACM 201. Quantitative.

Word structure in natural languages and its relationship to phonological and syntactic levels of grammar. Prerequisite: One of LING 301W, 309W or 482W.

Basic formal aspects of meaning (e.g. compositional semantics, truth conditional semantics and quantification in natural language) and how they are distinguished from pragmatic aspects of meaning. Prerequisite: LING 282W; or LING 222 and any lower division W course. Quantitative.

A survey of methods of speech sound description and transcription. Prerequisite: LING 282W; or LING 221 and any lower division W course.

Advanced training in speech sound description and analysis in the impressionistic and instrumental modes. Prerequisite: LING 330.

Investigation of a selected area of linguistic research. This course may be repeated once for credit if the topic is different. Prerequisite: Requirements will vary according to the topic offered.

Investigation of a selected area of linguistic research. This course may be repeated once for credit if the subject is different. Prerequisite: Requirements will vary according to the topic offered.