FACULTY OF THE DEPARTMENT OF COMPUTER SCIENCE
Professors Dana Angluin, James Aspnes, †Dirk Bergemann, †Ronald Coifman, Julie Dorsey, Stanley Eisenstat, Joan Feigenbaum (Chair), Michael Fischer, David Gelernter, †Mark Gerstein, Drew McDermott, Vladimir Rokhlin, Holly Rushmeier, Brian Scassellati, Martin Schultz (Emeritus), Zhong Shao, Avi Silberschatz, Daniel Spielman, †Leandros Tassiulas, Y. Richard Yang, Steven Zucker
Associate Professors Daniel Abadi, Mahesh Balakrishnan
Assistant Professors †Wenjun Hu, †Amin Karbasi,†Smita Krishnaswamy,†Sahand Negahban, Ruzica Piskac, Mariana Raykova, †Frederick Shic, †Jakub Szefer
Senior Lecturer Stephen Slade
Lecturers Jason Hirschhorn, †Kyle Jensen, Eric Koskinen, Scott Petersen, Patrick Rebeschini, Brad Rosen, Andrew Sherman, Xiyin Tang
†A joint appointment with primary affiliation in another department or school.
The Department of Computer Science offers both B.S. and B.A. degree programs, as well as three combined majors in cooperation with other departments: Electrical Engineering and Computer Science, Computer Science and Mathematics, and Computer Science and Psychology. Each major program not only provides a solid technical education but also allows students either to take a broad range of courses in other disciplines or to complete the requirements of a second major.
The Computer Science and combined major programs share a common core of five computer science courses. The first is CPSC 201, a survey that demonstrates the breadth and depth of the field to students who have taken the equivalent of an introductory programming course. The remaining core courses cover discrete mathematics, data structures, systems programming and computer architecture, and algorithm analysis and design. Together these courses include the material that every major should know.
The core courses are supplemented by electives (and, for the combined majors, core courses in the other discipline) that offer great flexibility in tailoring a program to each student's interests. The capstone is the senior project, through which students experience the challenges and rewards of original research under the guidance of a faculty mentor.
Prospective majors are encouraged to discuss their programs with the director of undergraduate studies as early as possible.
Introductory courses The department offers a broad range of introductory courses to meet the needs of students with varying backgrounds and interests. Except for CPSC 200 and CPSC 201, none assumes previous knowledge of computers.
- CPSC 100, taught jointly with Harvard University, teaches students majoring in any subject area how to program a computer and solve problems. No prior experience is required.
- CPSC 112 teaches students majoring in any subject area how to program a computer and solve problems using the language Java. Students with previous programming experience should consider taking CPSC 201 instead.
- CPSC 134 provides an introduction to computer music, including musical representations for computing, automated music analysis and composition, interactive systems, and virtual instrument design.
- CPSC 150 explores how some of the key ideas in computer science have affected philosophy of mind, cognitivism, connectionism, and related areas. This humanities-style course has significant readings and a paper, and satisfies the writing and the humanities and arts distributional requirement.
- CPSC 151 studies the history of the graphical user interface in an attempt to guess its future. This course also satisfies the writing distributional requirement.
- CPSC 183 explores the myriad ways that law and technology intersect, with a special focus on the role of cyberspace. This course satisfies the social science distributional requirement.
- CPSC 200, intended as a survey course for non-majors, focuses on practical applications of computing technology while examining topics including computer hardware, computer software, and related issues such as security and software engineering.
- CPSC 201 surveys the field of computer science, including systems (computers and their languages) and theory (algorithms, complexity, and computability). Students with sufficient programming experience may elect CPSC 201 without taking CPSC 112. (These courses meet at the same time so that students are easily able to change levels if necessary.)
- CPSC 202 presents the formal methods of reasoning and the concepts of discrete mathematics and linear algebra used in computer science and related disciplines.
Requirements of the major The B.S. and the B.A. degree programs have the same required core courses: CPSC 201; CPSC 202 or MATH 244; CPSC 223, 323, 365, and 490. The B.S. degree program requires six additional intermediate or advanced courses in Computer Science, for a total of twelve; the B.A. degree program, four, for a total of ten. CPSC 480 and 490 may not be counted toward these electives. All courses in the major must be taken for a letter grade.
For students who already know how to program, typical B.S. programs starting in the freshman and sophomore years are:
|CPSC 201a||CPSC 202a||Two electives||CPSC 490a|
|CPSC 223b||CPSC 365b||Two electives||One elective|
|CPSC 201a||CPSC 323a||CPSC 490a|
|CPSC 202a||One elective||Two electives|
|CPSC 223b||CPSC 365b||Two electives|
For typical B.A. programs, two of the electives would be omitted.
Electives The Computer Science department encourages interdisciplinary study in which computer science plays a major role. Advanced courses in other departments that involve concepts from computer science and are relevant to an individual program may, with permission of the director of undergraduate studies, be counted toward the requirements.
Students considering graduate study in computer science are advised to take CPSC 421 and 422, as well as courses covering the breadth of computer science, including programming languages and systems, artificial intelligence, scientific computing, and theoretical computer science.
Students interested in using computers to solve scientific and engineering problems are advised to take CPSC 440 as well as computational courses offered in Applied Mathematics and in Engineering and Applied Science.
The core mathematical background necessary to complete the Computer Science major is provided in CPSC 202. However, many advanced courses in graphics, computer vision, neural networks, and numerical analysis assume additional knowledge of linear algebra and calculus. Students who plan to take such courses as electives and who are unsure whether they have the appropriate mathematical background are encouraged to take MATH 222 or 225 and MATH 120.
Senior requirement In the senior year students must take CPSC 490, an independent project course in which students select an adviser to guide them in research in a subfield of computer science. With permission of the director of undergraduate studies, students may enroll in 490 more than once or before their senior year.
Schedule approval All Computer Science majors in the sophomore, junior, and senior years should have their programs approved by the director of undergraduate studies.
Combined B.S./M.S. degree program in Computer Science Exceptionally able and well-prepared students may complete a course of study leading to the simultaneous award of the B.S. and M.S. degrees after eight terms of enrollment. Eligibility requirements are described under "Simultaneous Award of the Bachelor's and Master's Degrees" in Section K, Special Arrangements, in the Academic Regulations. Specific requirements for the combined degree in Computer Science are as follows:
- Candidates must satisfy the Yale College requirements for the B.S. degree in Computer Science.
- In fulfilling these requirements, students must complete eight graduate courses from the approved list, up to two of which may, with the permission of the director of undergraduate studies and the director of graduate studies, also be applied toward completion of the B.S. degree. At most one of these eight courses may be CPSC 690, 691, or 692.
- At the end of their fifth term of enrollment students must have achieved at least three-fourths A or A– grades in all of their course credits directly relating to the major.
REQUIREMENTS OF THE MAJOR
Number of courses B.S.—12 term courses taken for letter grades (incl senior project); B.A.—10 term courses taken for letter grades (incl senior project)
Distribution of courses B.S.—6 addtl intermediate or advanced Comp Sci courses; B.A.—four addtl intermediate or advanced Comp Sci courses
Substitution permitted Advanced courses in other depts, with DUS permission
Senior requirement Senior project (CPSC 490)
* CPSC 035b, Twenty-First Century Electronic and Computer Music Techniques Scott Petersen
Exploration of twenty-first century electronic and computer music through the diverse subjects and issues at the intersection of technology and new music. How computers have changed and challenged the analysis, composition, production, and appreciation of music over the last fifty years. Knowledge of basic music theory and the ability to read Western musical notation is assumed. Enrollment limited to freshmen. Preregistration required; see under Freshman Seminar Program.
* CPSC 079b, Digital Photorealism Julie Dorsey
Basic methods used to define shapes, materials, and lighting when creating computer-generated images. Mathematical models for shape, texture models, and lighting techniques. Principles are applied through the use of modeling/rendering/animation software. Proficiency in high school–level mathematics is assumed. No previous programming experience necessary. Enrollment limited to freshmen. Preregistration required; see under Freshman Seminar Program. QR
CPSC 100a, Introduction to Computing and Programming Patrick Rebeschini and Jason Hirschhorn
CPSC 112b, Introduction to Programming Yang Yang
Development on the computer of programming skills, problem-solving methods, and selected applications. No previous experience with computers necessary. QR
CPSC 134a / MUSI 372a, Programming Musical Applications Scott Petersen
Topics in computer music, including musical representations for computing, automated music analysis and composition, interactive systems, and virtual instrument design. Use of domain-specific programming languages and libraries to explore how the principles of computer science can be applied to music to create new interfaces, instruments, and tools. Recommended preparation: the ability to read music or play an instrument. QR
* CPSC 150a, Computer Science and the Modern Intellectual Agenda David Gelernter
Introduction to the basic ideas of computer science (computability, algorithm, virtual machine, symbol processing system), and of several ongoing relationships between computer science and other fields, particularly philosophy of mind. No previous experience with computers necessary. Enrollment limited to 25. WR, HU
CPSC 183a, Law, Technology, and Culture Brad Rosen
An exploration of the myriad ways in which law and technology intersect, with a special focus on the role of cyberspace. Topics include digital copyright, free speech, privacy and anonymity, information security, innovation, online communities, the impact of technology on society, and emerging trends. No previous experience with computers or law necessary. SO
* CPSC 184b, Intellectual Property in the Digital Age Xiyin Tang
The evolving and oftentimes vexing intellectual property regime of the new digital age. Focus on copyright, fair use, remix culture, access to knowledge, technological innovations, the increasing relevance of trademarks in the new information society, the tension between creativity/creating and the intellectual property rules which either foster or inhibit it, and the new information culture of the digital age. Prerequisite: CPSC 183 or permission of instructor. HU, SO
* CPSC 185b, Control, Privacy, and Technology Brad Rosen
The evolution of various legal doctrines with and around technological development. Topics include criminal law, privacy, search and seizure, digital rights, and the implications of technologically permitted methods of control on the law. Special attention to case law and policy. After CPSC 183. WR, SO
CPSC 200b, Introduction to Information Systems Stephen Slade
The real-world artifacts and implementations that comprise the vital computational organisms that populate our world. Hardware and software and the related issues of security, privacy, regulation, and software engineering. Examples stress practical applications of technology, as well as limitations and societal issues. After CPSC 100 or 112 or equivalent. QR
CPSC 201a or b, Introduction to Computer Science Staff
Introduction to the concepts, techniques, and applications of computer science. Topics include computer systems (the design of computers and their languages); theoretical foundations of computing (computability, complexity, algorithm design); and artificial intelligence (the organization of knowledge and its representation for efficient search). Examples stress the importance of different problem-solving methods. After CPSC 112 or equivalent.
Math: Stat/Applied Math
CPSC 202a, Mathematical Tools for Computer Science Dana Angluin
Introduction to formal methods for reasoning and to mathematical techniques basic to computer science. Topics include propositional logic, discrete mathematics, and linear algebra. Emphasis on applications to computer science: recurrences, sorting, graph traversal, Gaussian elimination. QR
CPSC 213b, Apps, Software, and Entrepreneurship Kyle Jensen
Programming, software development, management, and entrepreneurship techniques used to build successful software start-ups. After CPSC 100, CPSC 112, or the equivalent. Not to be taken before, concurrently, or after CPSC 413.
CPSC 223a or b, Data Structures and Programming Techniques Stephen Slade
Topics include programming in C; data structures (arrays, stacks, queues, lists, trees, heaps, graphs); sorting and searching; storage allocation and management; data abstraction; programming style; testing and debugging; writing efficient programs. After CPSC 201 or equivalent. QR RP
CPSC 262a / AMTH 262a / STAT 262a, Computational Tools for Data Science Daniel Spielman and Sahand Negahban
Introduction to the core ideas and principles that arise in modern data analysis, bridging statistics and computer science and providing students the tools to grow and adapt as methods and techniques change. Topics include principle component analysis, independent component analysis, dictionary learning, neural networks, clustering, streaming algorithms (streaming linear algebra techniques), online learning, large scale optimization, simple database manipulation, and implementations of systems on distributed computing infrastructures. Students require background in linear algebra, multivariable calculus, and programming. after or concurrently with MATH 222, 225, or 231; after or concurrently with MATH 120, 230, or ENAS 151; after or concurrently with CPSC 100, 112, or ENAS 130. QR
* CPSC 290a or b, Directed Research James Aspnes
Individual research. Requires a faculty supervisor and the permission of the director of undergraduate studies. May be taken more than once for credit.
MATH 244a / AMTH 244a, Discrete Mathematics Linh Tran
Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems. Recommended preparation: MATH 115 or equivalent.
Math: Stat/Applied Math
Math: Algebra/Number Theory
CPSC 323a, Introduction to Systems Programming and Computer Organization Stanley Eisenstat
Machine architecture and computer organization, systems programming in a high-level language, issues in operating systems, software engineering, prototyping in scripting languages. After CPSC 223. QR RP
CPSC 365b, Design and Analysis of Algorithms Daniel Spielman
Paradigms for problem solving: divide and conquer, recursion, greedy algorithms, dynamic programming, randomized and probabilistic algorithms. Techniques for analyzing the efficiency of algorithms and designing efficient algorithms and data structures. Algorithms for graph theoretic problems, network flows, and numerical linear algebra. Provides algorithmic background essential to further study of computer science. After CPSC 202 and 223.
Math: Stat/Applied Math
* CPSC 410a, The Law and Technology of Cyber Conflict Oona Hathaway, Joan Feigenbaum, and Scott Shapiro
A cross-disciplinary seminar that addresses both technical and legal aspects of cyber conflict. Recent events, including the hacks of Sony and the U.S. Office of Personnel Management, illustrate the need for new thinking about the particular issues raised when cyber attacks originate from state or quasi-state actors. Professors from Yale Law School and the Computer Science Department will lead in-depth explorations of cyber conflict from both legal and technical points of view. Enrollment is limited to ten Yale College students. This is the first half of a yearlong course; the second half is CPSC 411. Students are required to make a yearlong, two term commitment. CPSC 201 and 223 or the equivalent and/or PLSC 233 or the equivalent, and/or GLBL 390 or the equivalent.
* CPSC 411b, The Law and Technology of Cyber Conflict: Practicum Oona Hathaway, Joan Feigenbaum, and Scott Shapiro
A cross–disciplinary practicum that addresses both technical and legal aspects of cyber conflict. Recent events, including the hacks of Sony and the U.S. Office of Personnel Management, illustrate the need for new thinking about the particular issues raised when cyber attacks originate from state or quasi–state actors. Professors from Yale Law School and the Computer Science Department will oversee intensive student projects on both legal and technical aspects of cyber conflict. Enrollment is limited to ten Yale College students. This is the second half of a yearlong course; the first half is CPSC 410. Students are required to make a yearlong, two term commitment. Prerequisite: CPSC 410.
* CPSC 412a / ECON 421a, Designing the Digital Economy Eric Weyl
Digitization is transforming a variety of markets from personal transportation services to advertising. This course explores the economic tools (market design, price theory, causal inference, etc.) and technical tools from computer science (machine learning, the analysis of algorithms, user interface design, etc.) students need to contribute meaningfully to this transformation. Prerequisites: elementary training in both economics and computer science and some intermediate/advanced training in at least one relevant field. SO
* CPSC 421b, Compilers and Interpreters Zhong Shao
Compiler organization and implementation: lexical analysis, formal syntax specification, parsing techniques, execution environment, storage management, code generation and optimization, procedure linkage and address binding. The effect of language-design decisions on compiler construction. After CPSC 323. QR
CPSC 422a, Design and Implementation of Operating Systems Zhong Shao
The design and implementation of operating systems. Topics include synchronization, deadlock, process management, storage management, file systems, security, protection, and networking. After CPSC 323. QR
CPSC 423b, Principles of Operating Systems Abraham Silberschatz
A survey of the underlying principles of modern operating systems. Topics include process management, memory management, storage management, protection and security, distributed systems, and virtual machines. Emphasis on fundamental concepts rather than implementation. After CPSC 323. QR
CPSC 424b, Parallel Programming Techniques Andrew Sherman
Practical introduction to parallel programming, emphasizing techniques and algorithms suitable for scientific and engineering computations. Aspects of processor and machine architecture. Techniques such as multithreading, message passing, and data parallel computing using graphics processing units. Performance measurement, tuning, and debugging of parallel programs. Parallel file systems and I/O. After CPSC 223 and MATH 222 or 225, or equivalents. QR
CPSC 425b, Cloud Networking and Systems Minlan Yu
Study of critical technology trends and new challenges in cloud and data center designs for different trade-offs of performance, scalability, manageability, and cost in the networking layers and big data analytical frameworks. Consideration of cloud infrastructure, including network topology, network traffic management, network management, transport protocols, programmable switches, network functions, virtualization, network reliability, and security. After CPSC 433 or with permission of instructor. QR
CPSC 426a, Building Distributed Systems Mahesh Balakrishnan
Ubiquitous services such as Google, Facebook, and Amazon run on the back of massive distributed systems. This course covers the fundamental principles, abstractions, and mechanisms that inform the design of such systems, as well as the practical details of real-world implementations. Technical topics covered include properties such as consistency, availability, durability, isolation, and failure atomicity; as well as protocols such as RPC, consensus, consistent hashing, and distributed transactions. The final project involves implementing a real-world distributed service. After CPSC 323. QR
CPSC 427a, Object-Oriented Programming Michael Fischer
Object-oriented programming as a means to efficient, reliable, modular, reusable code. Use of classes, derivation, templates, name-hiding, exceptions, polymorphic functions, and other features of C++. After CPSC 223. QR
[ CPSC 428, Language-Based Security ]
[ CPSC 430, Formal Semantics ]
CPSC 431a / MUSI 427a, Computer Music: Algorithmic and Heuristic Composition Scott Petersen
Study of the theoretical and practical fundamentals of computer-generated music, with a focus on high-level representations of music, algorithmic and heuristic composition, and programming languages for computer music generation. Theoretical concepts are supplemented with pragmatic issues expressed in a high-level programming language. Ability to read music is assumed. After CPSC 202 and 223. QR
CPSC 432b / MUSI 428b, Computer Music: Sound Representation and Synthesis Scott Petersen
Study of the theoretical and practical fundamentals of computer-generated music, with a focus on low-level sound representation, acoustics and sound synthesis, scales and tuning systems, and programming languages for computer music generation. Theoretical concepts are supplemented with pragmatic issues expressed in a high-level programming language. Ability to read music is assumed. After CPSC 202 and 223. QR
[ CPSC 433, Computer Networks ]
* CPSC 434b, Topics in Networked Systems Yang Yang
Study of networked systems such as the Internet and mobile networks which provide the major infrastructure components of an information-based society. Topics include the design principles, implementation, and practical evaluation of such systems in new settings, including cloud computing, software-defined networking, 5G, Internet of things, and vehicular networking. Concurrently with or after CPSC 323. QR
[ CPSC 435, Internet-Scale Applications ]
[ CPSC 436, Networked Embedded Systems and Sensor Networks ]
CPSC 437a, Introduction to Databases Abraham Silberschatz
Introduction to database systems. Data modeling. The relational model and the SQL query language. Relational database design, integrity constraints, functional dependencies, and normal forms. Object-oriented databases. Database data structures: files, B-trees, hash indexes. After CPSC 223. QR
[ CPSC 438, Database System Implementation and Architectures ]
[ CPSC 439, Software Engineering ]
CPSC 440b, Numerical Computation Vladimir Rokhlin
Algorithms for numerical problems in the physical, biological, and social sciences: solution of linear and nonlinear systems of equations, interpolation and approximation of functions, numerical differentiation and integration, optimization. After CPSC 112 or an equivalent introductory programming course; MATH 120; and MATH 222 or 225 or CPSC 202.
Math: Stat/Applied Math
CPSC 445a / AMTH 445a, Introduction to Data Mining Guy Wolf
Study of algorithms and systems that allow computers to find patterns and regularities in databases, to perform prediction and forecasting, and to improve their performance generally through interaction with data. After CPSC 202, 223, and MATH 222, or equivalents. QR
* CPSC 451b, The User Interface David Gelernter
The user interface (UI) in the context of modern design, where tech has been a strong and consistent influence from the Bauhaus and U.S. industrial design of the 1920s and 1930s through the IBM-Eames design project of the 1950s to 1970s. The UI in the context of the windows-menus-mouse desktop, as developed by Alan Kay and Xerox in the 1970s and refined by Apple in the early 1980s. Students develop a detailed design and simple implementation for a UI. Prerequisite: CPSC 223 or equivalent.
CPSC 453a, Computational Methods for Analysis and Modeling of Biological Data Smita Krishnaswamy
Applications of machine learning methods in the analysis of high-throughput biological data with focus on genomic and proteomic data. Topics include methods for denoising data; non-linear dimensionality reduction for visualization and progression analysis; unsupervised clustering; and information theoretic analysis of gene regulatory and signaling networks.
[ CPSC 454, Software Analysis and Verification ]
[ CPSC 455, Economics and Computation ]
[ CPSC 457, Sensitive Information in a Connected World ]
CPSC 458a, Automated Decision Systems Stephen Slade
The spectrum of automated decision models and tools, with a focus on their costs and effectiveness. Examples from a variety of fields, including finance, risk management, robotics, medicine, and politics. After CPSC 223 or equivalents. QR
[ CPSC 462, Graphs and Networks ]
[ CPSC 465, Theory of Distributed Systems ]
CPSC 467a, Cryptography and Computer Security Mariana Raykova
A survey of such private and public key cryptographic techniques as DES, RSA, and zero-knowledge proofs, and their application to problems of maintaining privacy and security in computer networks. Focus on technology, with consideration of such societal issues as balancing individual privacy concerns against the needs of law enforcement, vulnerability of societal institutions to electronic attack, export regulations and international competitiveness, and development of secure information systems. Some programming may be required. After CPSC 202 and 223. QR
CPSC 468b, Computational Complexity James Aspnes
Introduction to the theory of computational complexity. Basic complexity classes, including polynomial time, nondeterministic polynomial time, probabilistic polynomial time, polynomial space, logarithmic space, and nondeterministic logarithmic space. The roles of reductions, completeness, randomness, and interaction in the formal study of computation. After CPSC 365 or with permission of instructor. QR
CPSC 469a, Randomized Algorithms James Aspnes
A study of randomized algorithms from several areas: graph algorithms, algorithms in algebra, approximate counting, probabilistically checkable proofs, and matrix algorithms. Topics include an introduction to tools from probability theory, including some inequalities such as Chernoff bounds. After CPSC 365; a solid background in probability is desirable. QR
CPSC 470a, Artificial Intelligence Drew McDermott
Introduction to artificial intelligence research, focusing on reasoning and perception. Topics include knowledge representation, predicate calculus, temporal reasoning, vision, robotics, planning, and learning. After CPSC 201 and 202. QR
[ CPSC 471, Advanced Topics in Artificial Intelligence ]
CPSC 472a, Intelligent Robotics Brian Scassellati
Introduction to the construction of intelligent, autonomous systems. Sensory-motor coordination and task-based perception. Implementation techniques for behavior selection and arbitration, including behavior-based design, evolutionary design, dynamical systems, and hybrid deliberative-reactive systems. Situated learning and adaptive behavior. After CPSC 201 and 202 or equivalents. May not be taken after CPSC 473. QR
* CPSC 473b, Intelligent Robotics Laboratory Brian Scassellati
Students work in small teams to construct novel research projects using one of a variety of robot architectures. Project topics may include human-robot interaction, adaptive intelligent behavior, active perception, humanoid robotics, and socially assistive robotics. Enrollment limited to 20. After CPSC 472. QR
CPSC 475a / BENG 475a / EENG 475a, Computational Vision and Biological Perception Steven Zucker
An overview of computational vision with a biological emphasis. Suitable as an introduction to biological perception for computer science and engineering students, as well as an introduction to computational vision for mathematics, psychology, and physiology students. Prerequisite: CPSC 112 and MATH 120, or with permission of instructor. QR, SC RP
[ CPSC 476, Advanced Computational Vision ]
CPSC 477b, Natural Language Processing Dragomir Radev
Linguistic, mathematical, and computational fundamentals of natural language processing (NLP). Topics include part of speech tagging, Hidden Markov models, syntax and parsing, lexical semantics, compositional semantics, machine translation, text classification, discourse, and dialogue processing. Additional topics such as sentiment analysis, text generation, and deep learning for NLP. Prerequisites: CPSC 202 and CPSC 223, or permission of instructor. QR
CPSC 478b, Computer Graphics Holly Rushmeier
Introduction to the basic concepts of two- and three-dimensional computer graphics. Topics include affine and projective transformations, clipping and windowing, visual perception, scene modeling and animation, algorithms for visible surface determination, reflection models, illumination algorithms, and color theory. After CPSC 202 and 223. QR
[ CPSC 479, Advanced Topics in Computer Graphics ]
* CPSC 480a or b, Directed Reading James Aspnes
Individual study for qualified students who wish to investigate an area of computer science not covered in regular courses. A student must be sponsored by a faculty member who sets the requirements and meets regularly with the student. Requires a written plan of study approved by the faculty adviser and the director of undergraduate studies. May be taken more than once for credit.
* CPSC 490a or b, Special Projects James Aspnes
Individual research intended to fulfill the senior requirement. Requires a faculty supervisor and the permission of the director of undergraduate studies. The student must submit a written report about the results of the project.