Computer Science

The Department of Computer Science accepts both beginning and advanced graduate students for study and research leading to the degree of Master of Science in Engineering (M.S.E.) and Doctor of Philosophy (Ph.D.). These degree programs are sufficiently flexible to adapt to individual plans of study and research.

Applying

Application Deadline:

December 15, 11:59 p.m. Eastern Standard Time

Program Length:

Ph.D. 5 years, M.S.E. 2 years

Application Fee:

$75

Application Requirements:

Statement of Academic Purpose

Resume/Curriculum Vitae

Recommendation Letters

Transcripts

Fall Semester Grades

Required Tests

English Language Tests

Statement of Financial Resources

Statement of Financial Resources:

for M.S.E. applicants only

GRE :

General Test not accepted

Additional Departmental Requirements:

Applicants are required to select a subplan when applying.

M.S.E.: Two supplemental essays are required.

Please describe any teaching experience you have had, in any subject, at any grade level. This can include but is not limited to experience as a teaching assistant, lab assistant, grader, tutor, or any other role in which you interacted with students or mentored your peers. 250 words max.
For those with teaching experience, describe a specific instance when you helped your student/students overcome a misunderstanding or understand a difficult concept. If you do not have any teaching experience, please describe an oral presentation or talk you gave that explains a particularly difficult concept. 250 words max.

M.S.E.: If TOEFL is required, a minimum of 28 on the speaking subsection is required,

Ph.D.

Ph.D. Requirements:

Program Description:

The doctoral program in computer science combines coursework and participation in original research. Most students enter the program with an undergraduate degree in computer science, mathematics, or a related discipline. Some entering students may have a master’s degree, but that is not necessary for success in the program. Every admitted Ph.D. student is given financial support in the form of a first-year fellowship. In addition, all admitted Ph.D. students are automatically considered for the prestigious Wu and Upton Fellowships.

Courses:

In preparation for the general examination, the doctoral candidate, in consultation with a faculty adviser, develops an integrated program of study in one of the departmental areas of research. Such preparation usually requires two academic years for students entering with a bachelor’s degree, and one year for students entering with a master’s. Students are required to stand for the general examination at the end of the second year.

A total of 6 courses are required. Three courses must be taken to satisfy the core breadth requirement, with one course from each of three main areas of computer science: Systems, Artificial Intelligence (AI), and Theory. All students must fulfill the core breadth requirements plus one additional course by the end of the second year, demonstrating minimum competence in three main areas. The remaining three courses can be any 400- or 500-level course from any department in the University. Courses taken outside the Department of Computer Science require approval from the student’s academic adviser and the Director of Graduate Studies.

All courses must be taken for a grade. A grade of B+ or higher is required to get credit towards course requirements, although at most one B will be accepted for a course that does not satisfy the core breadth requirements. Individual research areas may request additional courses in excess of departmental requirements or may require students in that subfield to complete specific required courses in fulfillment of course requirements.

Breadth requirement core course list:

Systems

475 Computer Architecture (See ELE 475)
518 Advanced Computer Systems
561 Advanced Computer Networks
563 Wireless Networks

Artificial Intelligence

511 Theoretical Machine Learning
513 Foundations of Probabilistic Modeling
524 Fundamentals of Machine Learning
529 Advanced Computer Vision
584 Advanced Natural Language Processing

Theory

510 Program Languages
516 Automated Reasoning About Software
521 Advanced Algorithm Design
522 Computational Complexity
585 Information Theory and Applications

General Exam:

The general examination consists of a research seminar prepared under the supervision of a faculty member, followed by an in-depth oral examination on the contents of the seminar and the associated general area of research. The oral examination tests the student's knowledge in a number of topics relevant to the student's research area. These topics are specified beforehand by an examining committee in consultation with the student. The seminar is open to the public, and at least three computer science faculty members must attend. Two are invited by the student; the adviser chooses a third faculty member who could be in any area of Computer Science or related fields. The examining committee and the student agree upon a reading list for the exam. This document is to be made available to anyone present in the oral examination, and only questions pertaining to either the material described in the document or presented during the research seminar can be asked during the oral examination.

Original research results do not have to be presented, but problems whose solution may lead to a thesis should be discussed. In many cases, the student’s thesis is in the same area as the research seminar, but this is not required.

Qualifying for the M.A.:

The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy once a student has successfully completed the general examination. The M.A. may also be awarded to students who, for various reasons, leave the Ph.D. program, provided the student has successfully completed the six required courses from the Breadth Requirement. Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School. Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E.

Teaching:

Teaching experience is considered to be a significant part of graduate education. All Ph.D. candidates are therefore required to assist with course instruction for the equivalent of two terms.

Post-Generals Requirement(s):

Pre-FPO

The preliminary FPO is a research talk given to the anticipated FPO committee approximately six months before the FPO date. The pre-FPO covers results to date and planned research, and serves as a preliminary critique of the proposed dissertation.

Graduate students will present a public talk followed by a private meeting with the committee. The outcome of the pre-FPO is not graded. Graduate students are provided with valuable feedback to the committee expects will guide any final work and will be incorporated into the dissertation.

FPO Committee must be identical to the Pre-FPO committee; any subsequent changes to the committee require approval from the DGS.

Dissertation and FPO:

The Ph.D. is awarded after the acceptance of the dissertation and completion of the final public oral.

M.S.E.

M.S.E. Requirements:

Program Description:

The master's degree program at Princeton is a two-year, full-time program. All admitted students are initially enrolled in the Master of Science in Engineering (M.S.E.), thesis-required track. In the spring of year 1, as part of readmission, all students are given the option to switch to the Master of Engineering (M.Eng.), non-thesis track. Students opting to remain on the M.S.E. track must have a confirmed research adviser and should also have a preliminary thesis proposal. Switching tracks will be permitted through January of year 2.

Teaching experience is considered to be a significant part of graduate education. Funding is normally awarded in the form of teaching assistantships. Teaching assistantships cover the four semesters of the program. Nonnative English speakers must have a TOEFL speak score of 27 or better to be considered for a teaching assistantship. Summer funding for M.S.E. candidates in the form of a research assistantship may be offered at the adviser's discretion.

Students who wish to continue on for a Ph.D. must apply through the normal application process during the fall of their second year of study.

Princeton undergraduate students who wish to apply to the master's program must do so through the regular admission process, and by the December 15 deadline. Admission is competitive. Princeton undergraduates interested in admission to the M.S.E. program may inquire in the spring of the third year. Interested students should submit a one-page (1-page) personal statement describing preparation to date and interest in the master's program; an unofficial copy of the undergraduate transcript; and letters of recommendation from two COS professors. The letters of recommendation should be emailed directly to the graduate coordinator. Once these materials have been received, the director of graduate studies will perform an informal review and provide feedback about whether admission into the master's program is "likely," "unlikely," or "possible." This feedback is not binding and is intended to help with course planning in the student’s senior year.

Courses:

Candidates choose a subarea of computer science on which to focus their coursework. Course requirements are fulfilled by taking six courses for a grade. As least three of the six courses must be 500-level, and the additional courses may be chosen from 318, 320, 324, 326, 343, 352, 375, or any 400-level course or 500 level COS course. Students must take a minimum of 4 courses in year 1. If, due to scheduling conflicts, this is not possible, approval by the director of graduate studies is required. All courses must be completed by the end of the second year of enrollment.

A full course list is available on the department website. Relevant courses from outside the department may be taken with adviser's consent. All coursework must be taken for a grade. Candidates must maintain a B average, and may receive no more than one C. In order to be readmitted for a second year, candidates must have a confirmed thesis adviser and preliminary thesis proposal by the end of the first year.

Please note: Candidates electing to switch to the M.Eng. degree track must complete a total of eight courses over two years, and are not required to submit a thesis. At least three of the eight must be 500-level, and the additional courses may be chosen from 318, 320, 324, 326, 343, 352, 375, or any 400-level course, or any 500 level COS course. Relevant courses from outside the department may be taken with DGS's consent. A full list of approved courses can be found on the department website. All courses must be taken for a grade. Candidates must maintain a B average, with no more than one C allowed.

Princeton Option

Graduate students who received their undergraduate degrees from Princeton University may use credits towards the master's degree from two Princeton courses taken when the students were undergraduates, provided that the two courses were in excess of the requirements of the computer science department for the bachelor's degree. Those two courses must be upper-level COS courses that also fulfill requirements of the master’s degree.

Teaching:

The master’s program is fully funded by teaching assistantships. Master's students are required to hold a full teaching assistantship each semester that they are enrolled.

Thesis:

Candidates for the M.S.E. must prepare and submit an original thesis as well as present a public seminar on the research. The thesis will be reviewed and graded by the student’s adviser plus one additional reader from the Princeton faculty. If the reader is from outside the Department of Computer Science, approval by the director of graduate studies is required. The public seminar is an ungraded 20-minute talk, followed by a 10-minute question session, given in the spring of year 2. This will allow the student’s adviser and reader to give preliminary feedback prior to submission of the final thesis.

The written thesis should be a research paper of scholarly quality, making a novel contribution to scholarship in the field. The thesis should motivate the chosen research problem, evaluate the proposed solution (e.g., via analysis, measurement, simulation, or prototype implementation), and compare the approach to the related work in the field. While there is no specific length requirement, a reasonable target is a typical conference paper (e.g., 10-15 pages in two-column format or 20-40 pages in single-column, double-spaced format). Due date will be Dean's Date in the spring term of year 2. After being graded, four copies of the final version must be submitted to the department: two bound copies, following the formatting guidelines from Mudd Library, one unbound hard-copy, and the fourth as a .pdf file.

Faculty

Chair

Jennifer L. Rexford
Szymon M. Rusinkiewicz

Vice Chair

Szymon M. Rusinkiewicz

Associate Chair

Adam Finkelstein

Director of Graduate Studies

Michael J. Freedman (co-director) (fall)
Kyle A. Jamieson (co-director) (spring)

Director of Undergraduate Studies

Brian W. Kernighan (co-director)
David P. Walker (co-director)

Professor

Ryan P. Adams
Andrew W. Appel
Sanjeev Arora
David I. August
Mark Braverman
Bernard Chazelle
David P. Dobkin
Zeev Dvir
Barbara E Engelhardt
Adam Finkelstein
Michael J. Freedman
Tom Griffiths
Aarti Gupta
Elad Hazan
Kyle A. Jamieson
Brian W. Kernighan
Kai Li
Margaret R. Martonosi
Ben Raphael
Ran Raz
Jennifer L. Rexford
Szymon M. Rusinkiewicz
Robert Sedgewick
H. Sebastian Seung
Jaswinder P. Singh
Mona Singh
Robert E. Tarjan
Olga G. Troyanskaya
David P. Walker

Associate Professor

Wyatt A. Lloyd
Arvind Narayanan

Assistant Professor

Danqi Chen
Jia Deng
Adji Bousso Dieng
Felix Heide
Zachary Kincaid
Gillat Kol
Amit A. Levy
Jonathan Mayer
Andrés Monroy-Hernández
Karthik Narasimhan
Ravi A. Netravali
Yuri Pritykin
Olga Russakovsky
Matt Weinberg
Huacheng Yu
Mark L. Zhandry

Associated Faculty

Amir Ali Ahmadi, Oper Res and Financial Eng
Yuxin Chen, Electrical & Comp Engineering
Jianqing Fan, Oper Res and Financial Eng
Jaime Fernandez Fisac, Electrical & Comp Engineering
Chi Jin, Electrical & Comp Engineering
Jason D. Lee, Electrical & Comp Engineering
Ruby B. Lee, Electrical & Comp Engineering
Anirudha Majumdar, Mechanical & Aerospace Eng
Prateek Mittal, Electrical & Comp Engineering
Paul Seymour, Mathematics
John D. Storey, Integrative Genomics
Robert J. Vanderbei, Oper Res and Financial Eng
Janet A. Vertesi, Sociology
Mengdi Wang, Electrical & Comp Engineering
David Wentzlaff, Electrical & Comp Engineering

University Lecturer

Kevin Wayne

Lecturer

Robert M. Dondero
Robert S. Fish
Ruth C. Fong
Donna S. Gabai
Maia Ginsburg
Alan Kaplan
Mihir E. Kshirsagar
Dan Leyzberg
Xiaoyan Li
Jérémie Lumbroso
Christopher M. Moretti
Iasonas Petras
Esin Tureci

For a full list of faculty members and fellows please visit the department or program website.

Courses

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

COS 510 Programming Languages Fundamental concepts underlying all programming languages; semantic aspects, including binding times, visibility, retention, storage management, abstraction mechanisms and extensibility; operational and denotational semantic specifications; and design and implementation issues, particularly for very high-level languages, including data representations, control regimes, code representations, and portability. Prerequisites: 226 and 320.

COS 511 Theoretical Machine Learning Course introduces the mathematical foundations of machine learning, including theoretical models of machine learning, and the design and analysis of learning algorithms. Topics include: bounds on the number of random examples needed to learn; learning from non-random examples in the on-line learning model (i.e., for investment portfolio selection); how to boost the accuracy of a weak learning algorithm; learning with queries; Fourier-based algorithms and support-vector machines.

COS 513 Foundations of Probabilistic Modeling (also

SML 513

) A study of the essential tools for analyzing the vast amount of data that have become available in modern scientific research. Mathematical foundations of the field will be studied, along with the methods underlying the current state of the art. Probabilisitc graphical models and a unifying formalism for descrtibing and extending previous methods from statistics and engineering will be considered. Prerequisites COS402 or COS424. Undergraduates by permission only.

COS 516 Automated Reasoning about Software (also

ECE 516

) An introduction to algorithmic techniques for reasoning about software. Basic concepts in logic-based techniques including model checking, invariant generation, symbolic execution, and syntax-guided synthesis; automatic decision procedures in modern solvers for Boolean Satisfiability (SAT) and Satisfiability Modulo Theory (SMT); and their applications in automated verification, analysis, and synthesis of software. Emphasis on algorithms and automatic tools.

COS 518 Advanced Computer Systems Survey of operating systems covering: early systems, virtual memory, protection, synchronization, process management, scheduling, input/output, file systems, virtual machines, performance analysis, software engineering, user interfaces, distributed systems, networks, current operating systems, case studies. Survey of research papers from classic literature through contemporary research. Prerequisite: COS 318 or equivalent.

COS 521 Advanced Algorithm Design Advanced methods of algorithmic design and analysis: data structures, network flows, and linear programming. Solution of linear programs: Karmarkar and Ellipsoid algorithms. Probabilistic techniques. A selection of topics from on-line computation, approximation algorithms for NP-hard problems, number theoretic algorithms, geometric algorithms, and parallel computation.

COS 522 Computational Complexity (also

MAT 578

) Introduction to research in computational complexity theory. Computational models: nondeterministic, alternating, and probabilistic machines. Boolean circuits. Complexity classes associated with these models: NP, Polynomial hierarchy, BPP, P/poly, etc. Complete problems. Interactive proof systems and probabilistically checkable proofs: IP=PSPACE and NP=PCP (log n, 1). Definitions of randomness. Pseudorandomness and derandomizations. Lower bounds for concrete models such as algebraic decision trees, bounded-depth circuits, and monotone circuits.

COS 524 Fundamentals of Machine Learning Computers have made it possible to collect vast amounts of data from a variety of sources. It is not always clear, however, how to use those data, and how to extract useful information from them. This course focuses on some of the most useful approaches to the problem of analyzing large complex data sets, exploring both theoretical foundations and practical applications of machine learning. Course covers classification, regression, clustering, dimension reduction, and time series models. Students gain experience analyzing a variety of data. Prerequisites are introductory linear algebra and statistics.

COS 526 Advanced Computer Graphics Advanced topics in computer graphics, with focus on learning recent methods in rendering, modeling, and animation. Appropriate for students who have taken COS426 (or equivalent) and who would like further exposure to computer graphics.

COS 528 Data Structures and Graph Algorithms Data structures and algorithms for graph and network problems, including disjoint set union, heaps, search trees, search on graphs, minimum spanning trees, shortest paths, network flows, and matchings. The intent of the course is to examine the most efficient algorithms known for a variety of combinatorial problems and to discover the principles underlying the design and analysis of these algorithms. The emphasis is on asymptotic worst-case and amortized analysis. Prerequisite: 423 or the equivalent.

COS 529 Advanced Computer Vision Advanced topics in computer vision, with a focus ~n recent methods and current research. Topics include 3D vision, recognition, and the intersection of computer vision and other fields. Appropriate for students who have taken COS 429 or equivalent and would like further exposure to computer vision.

COS 532 Computer Graphics: Modeling Advanced topics in geometric modeling. Topics to be covered include methods for describing geometric primitives such as implicit surfaces and parametric patches, solid modeling and constructive solid geometry, boundary representations and topological representations, procedural models, and models appropriate for natural and biological shapes. Prerequisite: 426 or the equivalent.

COS 533 Advanced Cryptography This course covers a selection of advanced topics in cryptography, including some or all of the following: fully homomorphic encryption, zero knowledge proofs, traitor tracing, identity-based encryption, private information retrieval, garbled circuits, secret sharing, multiparty computation, lattice-based cryptography, and elliptic curve-based cryptography.

COS 534 Fairness in Machine Learning The course covers: sources of bias in machine learning; methods for detecting, measuring, and mitigating bias; individual fairness, group fairness, and the tension between them; data modeling versus algorithmic modeling;connections between fairness and privacy; bias in algorithmic decision making; bias in unsupervised machine learning; interpretability in ML and its connection to fairness. The syllabus is predominantly technical, supplemented by a few readings from social science, law, and public policy. Students take on hands-on empirical projects of their choosing.

COS 551 Introduction to Genomics and Computational Molecular Biology (also

MOL 551

QCB 551

) Introduction to basic computational and genomic methods for analysis of biological systems. Topics include: sequence similarity and alignment, phylogenic inference, gene recognition, gene expression analysis, transcriptional networks, structure prediction, functional genomics and proteomics. This is primarily a graduate-level course; interested undergraduates will require permission from instructors.

COS 557 Analysis & Visualization of Large-Scale Genomic Data Sets (also

MOL 557

) Introduces students to computational issues involved in analysis and display of large-scale biological data sets. Algorithms covered will include clustering and machine learning techniques for gene expression and proteomics data analysis, biological networks, joint learning from multiple data sources, and visualization issues for large-scale biological data sets. No prior knowledge of biology or bioinformatics is required; an introduction to bioinformatics and the nature of biological data will be provided. In depth knowledge of computer science is not required, but students should have some understanding of programming and computation.

COS 561 Advanced Computer Networks Survey of computer networks covering end-to-end principle, multiplexing, virtualization, packet switching vs. circuit switching, router design, network protocols, congestion control, internet routing architecture, network measurement, network management, and overlay networks. Survey of research papers from classic literature through contemporary research.

COS 563 Wireless Networks This course is a graduate-level class that explores recent developments in wireless networks and wireless sensing systems. The class aims to develop students' taste in research: what constitutes a good research problem, and what constitutes convincing scientific evidence that a design solves a problem. Students conduct a semester-long project that reproduces research or creates new research, and read/discuss papers in small groups. Topics include abstracting underlying and overlying hardware/layers in the networking stack, integration with overlying applications, and concurrency, performance, and resource allocation in wireless networks.

COS 583 Great Moments in Computing (also

ECE 583

) Course covers pivotal developments in computing, including hardware, software, and theory. Material will be covered by reading seminal papers, patents, and descriptions of highly-influential architectures. Course emphasizes a deep understanding of the discoveries and inventions that brought computer systems to where they are today, and class is discussion-oriented. Final project or paper required. Graduate students and advanced undergraduates from ELE, COS, and related fields welcome.

COS 584 Advanced Natural Language Processing Natural Language Processing (NLP) is witnessing exciting developments in core technologies and applications to a wide variety of domains. This graduate-level course focuses on an advanced study of frameworks, algorithms and methods in NLP -- including state-of-the-art techniques for problems such as language modeling, text classification, machine translation, and question answering. The course contains multiple programming assignments, paper readings, a mid-term and a final project. Students are expected to have taken at least one introductory course in machine learning prior to this class, and be comfortable with programming in Python.

COS 585 Information Theory and Applications The notions of entropy and information, originated in statistical physics and electrical engineering, have become central in almost all branches of modern science. The course gives an introduction to information theory and its applications, from the perspective of math, computer science and theoretical computer science.The course is intended for students from all areas of computer science, as well as math, physics, bio-informatics and electrical engineering. A basic knowledge in probability theory and linear algebra is required.

COS 589 Extramural Summer Research Project Summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor that will provide practical experience relevant to the student's research area. Start date no earlier than June 1. A final paper is required.

COS 590 Extramural Research Internship One-term full time research internship at a host institution to perform scholarly research directly relevant to a student's dissertation work. Research objectives will be determined by the student's advisor in consultation with the outside host. Monthly progress reports and a final paper are required. Enrollment is limited to post-generals students. Students will be permitted to enroll in this one-semester course at most twice. Participation will be considered exceptional.

COS 597A Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597B Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597C Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597D Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597E Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597F Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597G Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 597I Advanced Topics in Computer Science An in-depth study of compiler backend techniques for modern computer architectures. The course includes coverage of the fundamentals and a survey of current research. Students work together on a research project. Familiarity with both computer architecture and compilers is recommended.

COS 597J Advanced Topics in Computer Science This seminar prepares computer science graduate students and advanced undergraduate students to effectively engage on matters of public policy and law. The core of the course is a survey of computer science research that has successfully influenced government decision making or commercial practices. Topics include consumer privacy, data security, net neutrality, government surveillance, artificial intelligence fairness, election integrity, and cryptocurrencies. Assignments challenge participants to develop their own research interests into deliverables for public policy and law audiences.

COS 598 Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598A Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598B Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598C Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598D Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598E Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598F Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598G Advanced Topics in Computer Science Topics involving current research in computer science and applications in other fields.

COS 598H Advanced Topics in Computer Science This seminar reviews the latest developments in the theory of natural algorithms with a focus on biology. The course covers a number of topics from theoretical computer science, dynamical systems, statistical mechanics, machine learning, and evolutionary biology. No prerequisites are assumed except for a solid, general mathematical background.

ECE 539 Special Topics in Data and Information Science (also

COS 512

) Advanced studies in selected areas in signal processing, communication and information theory, decision and control, and system theory. Emphasis on recent developments and current literature. Content varies from year to year according to the instructor's and students' interests.

ECE 579 Pervasive Information Systems (also

COS 579

) Devices and systems that provide information anywhere, anytime. Goals of pervasive information: business, entertainment, government, etc. Components of pervasive information systems: low power electronics, audio/video, networking, etc. Human/computer interaction. Geographically distributed systems.

ECE 580U Advanced Topics in Computer Engineering (also

COS 598U

) Selected research topics in computer engineering. Emphasis is on new results and emerging areas. (More detailed outlines are contained in the booklet Course Outlines, issued by the department each year.)

SPI 586F Topics in STEP (also

COS 586

) Currently unavailable