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.
The department offers a broad range of introductory courses to meet the needs of students with varying backgrounds and interests. Except for CPSC 200 andCPSC 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 five core courses: CPSC 201; CPSC 202 or MATH 244; CPSC 223; CPSC 323; and CPSC 365 or 366. CPSC 480 and 490 may not be counted toward these core courses.
B.S. degree program The B.S. degree program requires a total of twelve courses, six additional intermediate or advanced courses in Computer Science and the senior requirement.
B.A. degree program The B.A. degree program requires a total of ten courses, four additional intermediate or advanced course in Computer Science and the senior requirement.
Combined B.S./M.S. degree 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.
Credit/D/Fail Courses taken Credit/D/Fail may not be counted toward the major. All courses in the major must be taken for a letter grade.
Roadmap See visual roadmap of the requirements.
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.
All Computer Science majors in the sophomore, junior, and senior years should have their programs approved by the director of undergraduate studies. Students majoring in Computer Science are advised to complete CPSC 201 and 223 by the end of the sophomore year.
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.
Typical programs For students who already know how to program, typical B.S. programs starting in the freshman and sophomore years are indicated below. For typical B.A. programs, two of the electives would be omitted.
|CPSC 201||CPSC 202||Two electives||CPSC 490|
|CPSC 223||CPSC 365 or 366||Two electives||One elective|
|CPSC 223||CPSC 365 or 366||Two electives|
|CPSC 201||CPSC 323||CPSC 490|
|CPSC 202||One elective||Two electives|
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)
FACULTY OF THE DEPARTMENT OF COMPUTER SCIENCE
Professors Dana Angluin, James Aspnes, †Dirk Bergemann, †Ronald Coifman, Julie Dorsey, Stanley Eisenstat, Joan Feigenbaum, Michael Fischer, David Gelernter, †Mark Gerstein, †Rajit Manohar, Drew McDermott, Dragomir Radev, Vladimir Rokhlin, Holly Rushmeier, Brian Scassellati, Martin Schultz (Emeritus), Zhong Shao (Chair), Avi Silberschatz, Daniel Spielman, †Leandros Tassiulas, Y. Richard Yang, Steven Zucker
Associate Professors Mahesh Balakrishnan, Minlan Yu
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, Scott Petersen, †Patrick Rebeschini, Brad Rosen, Andrew Sherman, Xiyin Tang
†A joint appointment with primary affiliation in another department or school.
* 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 078b / ARCH 009b, See it, Change it, Make it Julie Dorsey
Hands-on introduction to the theory and practice of digital capture, modeling, and fabrication. Topics include digital representations of shape, 3D scanning, shape modeling and editing, and physical production, including 3D printing, milling, and laser cutting. Architectural forms at a variety of scales used as vehicles for exploration and experimentation. There are no course prerequisites. Students are expected to be proficient in high school-level algebra, trigonometry, and geometry. No prior knowledge of architecture is expected. Enrollment limited to freshmen. Preregistration required; see under Freshman Seminar Program. QR
CPSC 100a, Introduction to Computing and Programming Benedict Brown and Natalie Melo
CPSC 112b, Introduction to Programming Benedict Brown
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 Stephen Slade
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. QR
CPSC 202a, Mathematical Tools for Computer Science James Aspnes
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 Staff
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 257a, Information Security in the Real World Stephen Slade
Introduction to information security, the practice of protecting information from unauthorized actions, in the context of computer systems. Topics include current security-related issues, basic adversarial models and threats to computer systems, potential defenses, security tools, and common security breaches and their wider impacts. Prerequisite: CPSC 100, 112, or equivalent programming experience, or with permission of instructor. QR
CPSC 262a / AMTH 262a / S&DS 262a, Computational Tools for Data Science Sahand Negahban
An introduction to computational tools for data science. The analysis of data using regression, classification, clustering, principal component analysis, independent component analysis, dictionary learning, topic modeling, dimension reduction, and network analysis. Optimization by gradient methods and alternating minimization. The application of high performance computing and streaming algorithms to the analysis of large data sets. Prerequisites: linear algebra, multivariable calculus, programming. Prerequisites: 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 276b, Applications in the Digital Humanities Benedict Brown
Introduction to applications of computer and data science in the humanities, including web technologies, visualization, and database design. Students work in teams to develop a variety of applications proposed by faculty and staff from the Digital Humanities Lab, the Institute for the Preservation of Cultural Heritage, and the Computer Science department. Prerequisite: CPSC 110, CPSC 112, equivalent programming experience, or permission of the instructor. QR
* CPSC 290a or b, Directed Research Staff
Individual research. Requires a faculty supervisor and the permission of the director of undergraduate studies. May be taken more than once for credit.
CPSC 323a, Introduction to Systems Programming and Computer Organization Dana Angluin
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 338b / EENG 348b, Digital Systems Rajit Manohar
Development of engineering skills through the design and analysis of digital logic components and circuits. Introduction to gate-level circuit design, beginning with single gates and building up to complex systems. Hands-on experience with circuit design using computer-aided design tools and programmable logic devices. Recommended preparation: EENG 201b. RP
* CPSC 366b, Intensive Algorithms Daniel Spielman
Mathematically sophisticated treatment of the design and analysis of algorithms and the theory of NP completeness. Algorithmic paradigms including greedy algorithms, divide and conquer, dynamic programming, network flow, approximation algorithms, and randomized algorithms. Problems drawn from the social sciences, Data Science, Computer Science, and engineering. For students with a flair for proofs and problem solving. Either CPSC 365 or CPSC 366 may be taken for credit. Prerequisites: MATH 244 and CPSC 223. QR
CPSC 365b, Algorithms James Glenn
Paradigms for algorithmic problem solving: greedy algorithms, divide and conquer, dynamic programming, and network flow. NP completeness and approximation algorithms for NP-complete problems. Algorithms for problems from economics, scheduling, network design and navigation, geometry, biology, and optimization. Provides algorithmic background essential to further study of computer science. Either CPSC 365 or CPSC 366 may be taken for credit. Prerequisites: CPSC 202 and 223. QR
* 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 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 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 426a, Building Distributed Systems Ennan Zhai
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 James Glenn
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 433a, Computer Networks Yang Yang
An introduction to the design, implementation, analysis, and evaluation of computer networks and their protocols. Topics include layered network architectures, applications, transport, congestion, routing, data link protocols, local area networks, performance analysis, multimedia networking, network security, and network management. Emphasis on protocols used in the Internet. After CPSC 323. QR
[ CPSC 435, Internet-Scale Applications ]
[ CPSC 436, Networked Embedded Systems and Sensor Networks ]
CPSC 437a, Introduction to Database Systems 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 439b, Software Engineering Ruzica Piskac
Introduction to fundamental concepts in software engineering and to the development and maintenance of large, robust software systems. The process of collecting requirements and writing specifications; project planning and system design; methods for increasing software reliability, including delta debugging and automatic test-case generation; type systems, static analysis, and model checking. Students build software in teams. After CPSC 323. QR RP
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 453a, Machine Learning for Biology 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 454a, Software Analysis and Verification Ruzica Piskac
Introduction to concepts, tools, and techniques used in the formal verification of software. State-of-the art tools used for program verification; detailed insights into algorithms and paradigms on which those tools are based, including model checking, abstract interpretation, decision procedures, and SMT solvers. After CPSC 202 and 323 or equivalents. QR RP
[ CPSC 455, Economics and Computation ]
* CPSC 457b, Sensitive Information in a Connected World Michael Fischer
Issues of ownership, control, privacy, and accuracy of the huge amount of sensitive information about people and organizations that is collected, stored, and used by today's ubiquitous information systems. Readings consist of research papers that explore both the power and the limitations of existing privacy-enhancing technologies such as encryption and "trusted platforms." After or concurrently with CPSC 365 and 467. QR
[ CPSC 462, Graphs and Networks ]
[ CPSC 465, Theory of Distributed Systems ]
CPSC 467a, Cryptography and Computer Security Michael Fischer
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 Dana Angluin
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 366, or with permission of instructor. QR
[ CPSC 469, Randomized Algorithms ]
CPSC 470a, Artificial Intelligence Dragomir Radev
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 472b, 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 474b, Computational Intelligence for Games James Glenn
Introduction to techniques used for creating computer players for games, particularly board games. Topics include combinatorial and classical game theory, stochastic search methods, applications of neural networks, and procedural content generation. Prerequisites: CPSC 202 and CPSC 223. 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 476b / BENG 476b, Advanced Computational Vision Steven Zucker
Advanced view of vision from a mathematical, computational, and neurophysiological perspective. Emphasis on differential geometry, machine learning, visual psychophysics, and advanced neurophysiology. Topics include perceptual organization, shading, color and texture analysis, and shape description and representation. After CPSC 475. QR, SC
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 478a, 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 479b, Advanced Topics in Computer Graphics Julie Dorsey
An in-depth study of advanced algorithms and systems for rendering, modeling, and animation in computer graphics. Topics vary and may include reflectance modeling, global illumination, subdivision surfaces, NURBS, physically-based fluids systems, and character animation. After CPSC 202 and 223. QR
* 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, Senior Project 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.