Courses

COMS E3999 Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty advisor.

May be repeated for credit, but no more than 3 total points may be used toward the 128-credit degree requirement. Only for SEAS computer science undergraduate students who include relevant off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. May not be used as a technical or non-technical elective. May not be taken for pass/fail credit or audited.

COMS E4115 PROGRAMMING LANG ＆ TRANSL. 3.00 points.

COMS E4762 Machine Learning for Functional Genomics. 3.00 points.

This course will introduce modern probabilistic machine learning methods using applications in data analysis tasks from functional genomics, where massively-parallel sequencing is used to measure the state of cells: e.g. what genes are being expressed, what regions of DNA (“chromatin”) are active (“open”) or bound by specific proteins

COMS E4773 Machine Learning Theory. 3.00 points.

Theoretical study of algorithms for machine learning and high-dimensional data analysis. Topics include high-dimensional probability, theory of generalization and statistical learning, online learning and optimization, spectral analysis

COMS E4995 COMPUTER ARTS/VIDEO GAMES. 3.00 points.

Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment

COMS E6111 ADVANCED DATABASE SYSTEMS. 3.00 points.

Lect: 2.

Prerequisites: (COMS W4111) and knowledge of Java or instructor's permission.
Prerequisites: (COMS W4111) and knowledge of Java or instructor's permission. Continuation of COMS W4111, covers latest trends in both database research and industry: information retrieval, web search, data mining, data warehousing, OLAP, decision support, multimedia databases, and XML and databases. Programming projects required

COMS E6113 Topics in Database Systems. 3 points.

Lect: 2.Not offered during 2022-23 academic year.

Prerequisites: (COMS W4111)

Concentration on some database paradigm, such as deductive, heterogeneous, or object-oriented, and/or some database issue, such as data modeling, distribution, query processing, semantics, or transaction management. A substantial project is typically required. May be repeated for credit with instructor's permission.

COMS E6114 Advanced Distributed Systems. 3 points.

Prerequisites: COMS W4113 AND COMS W4118

Reviews influential research that provides the basis of most large-scale, cloud infrastructures today. Students read, present, and discuss papers. Topics include distributed consensus, consistency models and algorithms, service-oriented architectures, large-scale data storage, distributed transactions, big-data processing frameworks, distributed systems security. Reviews established results and state-of-the-art research.

COMS E6118 Operating systems, II. 3 points.

Lect: 2.Not offered during 2022-23 academic year.

Prerequisites: (COMS W4118)
Corequisites: COMS W4119

Continuation of COMS W4118, with emphasis on distributed operating systems. Topics include interfaces to network protocols, distributed run-time binding, advanced virtual memory issues, advanced means of interprocess communication, file system design, design for extensibility, security in a distributed environment. Investigation is deeper and more hands-on than in COMS W4118. A programming project is required.

COMS E6121 RELIABLE SOFTWARE. 3.00 points.

Not offered during 2022-23 academic year.

Prerequisites: (COMS W4118) or (COMS W4115) or (COMS W4117) or significant software development experiences.
Topics include automated debugging, automated software repair, concurrent software reliability, software error detection, and more

COMS E6123 PROG ENVIRONMNT-SOFTWARE TOOLS. 3.00 points.

Lect: 2.

Prerequisites: (COMS W4156) or equivalent.
Software methodologies and technologies concerned with development and operation of today’s software systems. Reliability, security, systems management and societal issues. Emerging software architectures such as enterprise and grid computing. Term paper and programming project. Seminar focus changes frequently to remain timely

COMS E6124 Hardware Secuirty. 3 points.

Prerequisites: Required: CSEE W3827 and COMS W3157 Recommended: CSEE W4824 and COMS W4187

Techniques for securing the foundational aspects of all computing devices and systems. Topics include: Hardware-Up Security, Hardware Supply Chain Trust and Security, Storing Secrets in Hardware, Boot Time Trust and Security, Side Channel Attacks and Defenses, Hardware Support for Compartmentalization, Fault Attacks and Defenses, Hardware Support to Strengthen Software: Memory Safety, Control Flow Integrity, Information Flow Tracking, Diversity, Obfuscation, Anomaly etection. Hardware Support for Accelerating Cryptography and Applied Cryptography.

COMS E6125 WEB-ENHANCED INFORMATION MGMT. 3.00 points.

Lect: 2.

Prerequisites: at least one COMS W41xx or COMS E61xx course and/or COMS W4444, or the instructor's permission. Strongly recommended: COMS W4111.
History of hypertext, markup languages, groupware and the web. Evolving web protocols, formats and computation paradigms such as HTTP, XML and Web Services. Novel application domains enabled by the web and societal issues. Term paper and programming project. Seminar focus changes frequently to remain timely

COMS E6156 Topics in Software Engineering. 3 points.

Topics in Software engineering arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes, it may be repeated for credit with advisor approval. Consult the department for section assignment.

COMS E6178 Human-Computer Interaction. 3.00 points.

Human–computer interaction (HCI) studies (1) what computers are used for, (2) how people interact with computers, and (3) how either of those should change in the future. Topics include ubiquitous computing, mobile health, interaction techniques, social computing, mixed reality, accessibility, and ethics. Activities include readings, presentations, and discussions of research papers. Substantial HCI research project required

COMS E6181 ADVANCED INTERNET SERVICES. 3.00 points.

Lect: 2.

In-depth survey of protocols and algorithms needed to transport multimedia information across the internet, including audio and video encoding, multicast, quality-of-service, voice-over IP, streaming media and peer-to-peer multimedia systems. Includes a semester-long programming project

COMS E6183 Advanced Topics in Network Security. 3 points.

Lect: 3.

Prerequisites: (COMS W4180) and (CSEE W4119) COMS W4261 is recommended.

Review the fundamental aspects of security, including authentication, authorization, access control, confidentiality, privacy, integrity, and availability. Review security techniques and tools, and their applications in various problem areas. Study the state of the art in research. A programming project is required.

COMS E6184 ANONYMITY ＆ PRIVACY. 3.00 points.

Lect: 3.

Prerequisites: (COMS W4261) or (COMS W4180) or (CSEE W4119) or instructor's permission.

This course will cover the following topics: Legal and social framework for privacy. Data mining and databases. Anonymous commerce and Internet usage. Traffic analysis. Policy and national security considerations. Classes are seminars with students presenting papers and discussing them. Seminar focus changes frequently to remain timely.

COMS E6185 INTRUSION DETECTION SYSTEMS. 3.00 points.

Lect: 2.

Corequisites: COMS W4180
Corequisite: COMS 4180W. The state of threats against computers, and networked systems. An overview of computer security solutions and why they fail. Provides a detailed treatment for Network and Host-based Intrusion Detection and Intrusion Prevention systems. Considerable depth is provided on anomaly detection systems to detect new attacks. Covers issues and problems in email (spam, and viruses) and insider attacks (masquerading and impersonation)

COMS E6232 ANALYSIS OF ALGORITHMS II. 3.00 points.

Lect: 2.

Prerequisites: (CSOR W4231)
Continuation of CSOR W4231

COMS E6253 ADV TPCS-COMPUT LEARNING THRY. 3.00 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: (COMS W4252) or (CSOR W4231) or equivalent, COMS W4236 recommended.
In-depth study of inherent abilities and limitations of computationally efficient learning algorithms. Algorithms for learning rich Boolean functions in online, Probably Approximately Correct, and exact learning models. Connections with computational complexity theory emphasized. Substantial course project or term paper required

COMS E6261 ADVANCED CRYPTOGRAPHY. 3.00 points.

Lect: 3.

Prerequisites: (COMS W4261)
Prerequisites: (COMS W4261) A study of advanced cryptographic research topics such as: secure computation, zero knowledge, privacy, anonymity, cryptographic protocols. Concentration on theoretical foundations, rigorous approach, and provable security. Contents varies between offerings. May be repeated for credit

COMS E6424 HARDWARE SECURITY. 3.00 points.

COMS E6731 Humanoid Robots. 3 points.

Lect: 2.

Prerequisites: A course in at least one of the following: AI, robotics, computer graphics, or computer vision

Seminar on Humanoid Robots. Analysis of existing hardware and software platforms. Programming of multi-degree-of-freedom robots. Understanding sensor feedback in perceive-act-sense control paradigms. Task-level planning and reasoning. Final project includes implementing a humanoid robot task on either a simulated or physical robot.

COMS E6732 COMPUTATIONAL IMAGING. 3.00 points.

Lect: 3.

Prerequisites: (COMS W4731) or the instructor's permission.
Computational imaging uses a combination of novel imaging optics and a computational module to produce new forms of visual information. Survey of the state-of-the-art in computational imaging. Review of recent papers on omnidirectional and panoramic imaging, catadioptric imaging, high dynamic range imaging, mosaicing and superresolution. Classes are seminars with the instructor, guest speakers, and students presenting papers and discussing them

COMS E6734 Computational Photography. 3 points.

Lect: 3.

Prerequisites: (COMS W4160) or (COMS W4731) or a working knowledge of photography recommended.

Students should have knowledge in any of three core areas: computer vision, computer graphics, or photography. Computational techniques are used to produce a new level of images and visual representations. Topics include: HDR imaging, feature matching using RANSAC, image mosaics, image-based rendering, motion magnification, camera lens arrays, programmable lighting, face detection, single and multi-view geometry, and more.

COMS E6735 VISUAL DATABASES. 3.00 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) or COMS W4731 and COMS W4735 recommended. Contact instructor if uncertain.
The analysis and retrieval of large collections of image and video data, with emphasis on visual semantics, human psychology, and user interfaces. Low-level processing: features and similarity measures; shot detection; key frame selection; machine learning methods for classification. Middle- level processing: organizational rules for videos, including unedited (home, educational), semiedited (sports, talk shows), edited (news, drama); human memory limits; progressive refinement; visualization techniques; incorporation of audio and text. Highlevel processing: extraction of thematic structures; ontologies, semantic filters, and learning; personalization of summaries and interfaces; detection of pacing and emotions. Examples and demonstrations from commercial and research systems throughout. Substantial course project or term paper required

COMS E6737 BIOMETRICS. 3.00 points.

Lect: 3.

Prerequisites: a background at the sophomore level in computer science, engineering, or like discipline.
We will explore the latest advances in biometrics as well as the machine learning techniques behind them. Students will learn how these technologies work and how they are sometimes defeated. Grading will be based on homework assignments and a final project. There will be no midterm or final exam. Shares lectures with COMS W4737. Students taking COMS E6737 are required to complete additional homework problems and undertake a more rigorous final project. Students will only be allowed to earn credit for COMS W4737 or COMS E6737 but not both

COMS E6772 ADV MACHINE LEARNING/PERCEPTN. 3.00 points.

COMS E6863 FORMAL VERIF HW SW SYSTEMS. 3.00 points.

Introduction to the theory and practice of formal methods for the design and analysis of correct (i.e., bug-free) concurrent and embedded hardware/software systems. Topics include temporal logics; model checking; deadlock and liveness issues; fairness; satisfiability (SAT) checkers; binary decision diagrams (BDDs); abstraction techniques; introduction to commercial formal verification tools. Industrial state-of-the-art, case studies, and experiences: software analysis (C/C /Java), hardware verification (RTL)

COMS E6900 Tutorial in Computer Science. 1-3 points.

Prerequisites: Instructor's permission.

A reading course in an advanced topic for a small number of students, under faculty supervision.

COMS E6901 Projects in Computer Science. 1-12 points.

Prerequisites: Instructor's permission.

Software or hardware projects in computer science. Before registering, the student must submit a written proposal to the instructor for review. The proposal should give a brief outline of the project, estimated schedule of completion, and computer resources needed. Oral and written reports are required. May be taken over more than one semester, in which case the grade will be deferred until all 12 points have been completed. No more than 12 points of COMS E6901 may be taken. Consult the department for section assignment.

COMS E6902 Thesis. 1-9 points.

Available to M.S. and CSE candidates. An independent investigation of an appropriate problem in computer science carried out under the supervision of a faculty member. A formal written report is essential and an oral presentation may also be required. May be taken over more than one semester, in which case the grade will be deferred until all 9 points have been completed. No more than 9 points of COMS E6902 may be taken. Consult the department for section assignment.

COMS E6910 Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty adviser.

Only for M.S. in the Computer Science Department who need relevant work experience as part of their program of study. Final report required. This course may not be taken for pass/fail credit or audited. 

COMS E6915 Technical writing for computer scientists and engineers. 1 point.

Prerequisites: Available to M.S. and Ph.D candidates in CS/CE.

Topics to help CS/CE graduate students’ communication skills. Emphasis on writing, presenting clear, concise proposals, journal articles, conference papers, theses, and technical presentations. May be repeated for credit. Credit may not be used to satisfy degree requirements.

COMS E6998 Topics in Computer Science. 3 points.

Prerequisites: Instructor's permission.

Selected topics in computer science. Content varies from year to year. May be repeated for credit.

COMS E9800 Directed Research in Computer Science. 1-15 points.

Prerequisites: Submission of an outline of the proposed research for approval by the faculty member who will supervise.

The department must approve the number of points. May be repeated for credit. This course is only for Eng.Sc.D. candidates.

COMS E9910 Graduate Research I. 1-6 points.

Prerequisites: Submission of an outline of the proposed research for approval by the faculty member who will supervise.

The department must approve the number of credits. May be repeated for credit. This course is only for M.S. candidates holding GRA or TA appointments. Note: It is NOT required that a student take Graduate Research I prior to taking Graduate Research II. Consult the department for section assignment.

COMS E9911 Graduate research II. 1-15 points.

Prerequisites: Submission of an outline of the proposed research for approval by the faculty member who will supervise.

The department must approve the number of points. May be repeated for credit. This course is only for M.S./Ph.D. and Ph.D. students. Note: It is NOT required that a student take Graduate Research, I prior to taking Graduate Research, II. Consult the department for section assignment.

COMS S1005 INTRO-COMPUTER PROGRAMMING. 3.00 points.

COMS S3157 ADVANCED PROGRAMMING. 4.00 points.

COMS S3998 PROJECTS IN COMPUTER SCIENCE. 0.00-3.00 points.

COMS S4111 INTRODUCTION TO DATABASES. 3.00 points.

COMS S4115 PROGRAMMING LANG ＆ TRANSLATORS. 3.00 points.

COMS S4119 COMPUTER NETWORKS. 3.00 points.

COMS S4156 ADVANCED SOFTWARE ENGINEE. 3.00 points.

COMS S4236 INTRO-COMPUTATIONAL COMPL. 3.00 points.

COMS S4733 COMPUTATNL ASPECTS OF ROBOTICS. 3.00 points.

COMS S4901 PROJECTS IN COMPUTER SCIENCE. 0.00-3.00 points.

COMS S4910 CURRICULAR PRACTICAL TRAINING. 1.00 point.

COMS S9911 DOCTORAL RESEARCH. 0.00-12.00 points.

COMS W1001 Introduction to Information Science. 3 points.

Lect: 3.

Basic introduction to concepts and skills in Information Sciences: human-computer interfaces, representing information digitally, organizing and searching information on the internet, principles of algorithmic problem solving, introduction to database concepts, and introduction to programming in Python.

COMS W1002 COMPUTING IN CONTEXT. 4.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Introduction to elementary computing concepts and Python programming with domain-specific applications. Shared CS concepts and Python programming lectures with track-specific sections. Track themes will vary but may include computing for the social sciences, computing for economics and finance, digital humanities, and more. Intended for nonmajors. Students may only receive credit for one of ENGI E1006 or COMS W1002

COMS W1004 Introduction to Computer Science and Programming in Java. 3 points.

Lect: 3.

A general introduction to computer science for science and engineering students interested in majoring in computer science or engineering. Covers fundamental concepts of computer science, algorithmic problem-solving capabilities, and introductory Java programming skills. Assumes no prior programming background. Columbia University students may receive credit for only one of the following two courses: 1004 or 1005.

COMS W1005 Introduction to Computer Science and Programming in MATLAB. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

A general introduction to computer science concepts, algorithmic problem-solving capabilities, and programming skills in MATLAB. Assumes no prior programming background. Columbia University students may receive credit for only one of the following two courses: W1004 or W1005.

COMS W1007 Honors Introduction to Computer Science. 3 points.

Lect: 3.

Prerequisites: AP Computer Science with a grade of 4 or 5 or similar experience.

An honors-level introduction to computer science, intended primarily for students considering a major in computer science. Computer science as a science of abstraction. Creating models for reasoning about and solving problems. The basic elements of computers and computer programs. Implementing abstractions using data structures and algorithms. Taught in Java. 

COMS W1404 Emerging Scholars Program Seminar. 1 point.

Pass/Fail only.

Prerequisites: the instructor's permission. Corequisites: COMS W1002 or COMS W1004 or COMS W1007
Corequisites: COMS W1004,COMS W1007,COMS W1002

Peer-led weekly seminar intended for first and second year undergraduates considering a major in Computer Science. Pass/fail only. May not be used towards satisfying the major or SEAS credit requirements.

COMS W3101 Programming Languages. 1 point.

Lect: 1.

Prerequisites: Fluency in at least one programming language.

Introduction to a programming language. Each section is devoted to a specific language. Intended only for those who are already fluent in at least one programming language. Sections may meet for one hour per week for the whole term, for three hours per week for the first third of the term, or for two hours per week for the first six weeks. May be repeated for credit if different languages are involved.

COMS W3102 Development Technologies. 1-2 points.

Lect: 2. Lab: 0-2.

Prerequisites: Fluency in at least one programming language.

Introduction to software development tools and environments. Each section devoted to a specific tool or environment. One-point sections meet for two hours each week for half a semester, and two point sections include an additional two-hour lab.

COMS W3107 Clean Object-Oriented Design. 3.00 points.

Prerequisites: Intro to Computer Science/Programming in Java (COMS W1004) or instructor’s permission. May not take for credit if already received credit for COMS W1007.

Prerequisites: see notes re: points
A course in designing, documenting, coding, and testing robust computer software, according to object-oriented design patterns and clean coding practices. Taught in Java.Object-oriented design principles include: use cases; CRC; UML; javadoc; patterns (adapter, builder, command, composite, decorator, facade, factory, iterator, lazy evaluation, observer, singleton, strategy, template, visitor); design by contract; loop invariants; interfaces and inheritance hierarchies; anonymous classes and null objects; graphical widgets; events and listeners; Java's Object class; generic types; reflection; timers, threads, and locks

COMS W3134 Data Structures in Java. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W1004) or knowledge of Java.

Data types and structures: arrays, stacks, singly and doubly linked lists, queues, trees, sets, and graphs. Programming techniques for processing such structures: sorting and searching, hashing, garbage collection. Storage management. Rudiments of the analysis of algorithms. Taught in Java. Note: Due to significant overlap, students may receive credit for only one of the following three courses: COMS W3134, COMS W3136, COMS W3137.

COMS W3136 Data Structures with C/C++. 4 points.

Prerequisites: (COMS W1004) or (COMS W1005) or (COMS W1007) or (ENGI E1006)

A second programming course intended for nonmajors with at least one semester of introductory programming experience. Basic elements of programming in C and C++, arraybased data structures, heaps, linked lists, C programming in UNIX environment, object-oriented programming in C++, trees, graphs, generic programming, hash tables. Due to significant overlap, students may only receive credit for either COMS W3134, W3136, or W3137.

COMS W3137 Honors Data Structures and Algorithms. 4 points.

Prerequisites: (COMS W1004) or (COMS W1007)
Corequisites: COMS W3203

An honors introduction to data types and structures: arrays, stacks, singly and doubly linked lists, queues, trees, sets, and graphs. Programming techniques for processing such structures: sorting and searching, hashing, garbage collection. Storage management. Design and analysis of algorithms. Taught in Java. Note: Due to significant overlap, students may receive credit for only one of the following three courses: COMS W3134, W3136, or W3137.

COMS W3157 Advanced Programming. 4 points.

Lect: 4.

Prerequisites: (COMS W3134) or (COMS W3137)

C programming language and Unix systems programming.  Also covers Git, Make, TCP/IP networking basics, C++ fundamentals.

COMS W3203 DISCRETE MATHEMATICS. 4.00 points.

Lect: 3.

Prerequisites: Any introductory course in computer programming.
Prerequisites: Any introductory course in computer programming. Logic and formal proofs, sequences and summation, mathematical induction, binomial coefficients, elements of finite probability, recurrence relations, equivalence relations and partial orderings, and topics in graph theory (including isomorphism, traversability, planarity, and colorings)

COMS W3210 Scientific Computation. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: two terms of calculus.

Introduction to computation on digital computers. Design and analysis of numerical algorithms. Numerical solution of equations, integration, recurrences, chaos, differential equations. Introduction to Monte Carlo methods. Properties of floating point arithmetic. Applications to weather prediction, computational finance, computational science, and computational engineering.

COMS W3251 COMPUTATIONAL LINEAR ALGEBRA. 4.00 points.

COMS W3261 Computer Science Theory. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3203)
Corequisites: COMS W3134,COMS W3136,COMS W3137

Regular languages: deterministic and non-deterministic finite automata, regular expressions. Context-free languages: context-free grammars, push-down automata. Turing machines, the Chomsky hierarchy, and the Church-Turing thesis. Introduction to Complexity Theory and NP-Completeness.

COMS W3410 Computers and Society. 3 points.

Lect: 3.

Broader impact of computers. Social networks and privacy. Employment, intellectual property, and the media. Science and engineering ethics. Suitable for nonmajors.

COMS W3902 Undergraduate Thesis. 1-6 points.

Prerequisites: Agreement by a faculty member to serve as thesis adviser.

An independent theoretical or experimental investigation by an undergraduate major of an appropriate problem in computer science carried out under the supervision of a faculty member. A formal written report is mandatory and an oral presentation may also be required. May be taken over more than one term, in which case the grade is deferred until all 6 points have been completed. Consult the department for section assignment.

COMS W3995 Special Topics in Computer Science. 3 points.

Lect: 3.

Prerequisites: the instructor's permission.

Consult the department for section assignment. Special topics arranged as the need and availability arise. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit.

COMS W3998 Undergraduate Projects in Computer Science. 1-3 points.

Prerequisites: Approval by a faculty member who agrees to supervise the work.

Independent project involving laboratory work, computer programming, analytical investigation, or engineering design. May be repeated for credit, but not for a total of more than 3 points of degree credit. Consult the department for section assignment.

COMS W4111 INTRODUCTION TO DATABASES. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement
Prerequisites: COMS W3134, COMS W3136, or COMS W3137; or the instructor's permission.

Prerequisites: (COMS W3134) or (COMS W3136) or (COMS W3137) or
Prerequisites: (COMS W3134) or (COMS W3137) or (COMS W3136) and fluency in Java); or the instructor's permission. The fundamentals of database design and application development using databases: entity-relationship modeling, logical design of relational databases, relational data definition and manipulation languages, SQL, XML, query processing, physical database tuning, transaction processing, security. Programming projects are required

COMS W4112 DATABASE SYSTEM IMPLEMENTATION. 3.00 points.

Lect: 2.5.

Prerequisites: (COMS W4111) and fluency in Java or C++. CSEE W3827 is recommended.
The principles and practice of building large-scale database management systems. Storage methods and indexing, query processing and optimization, materialized views, transaction processing and recovery, object-relational databases, parallel and distributed databases, performance considerations. Programming projects are required

COMS W4113 FUND-LARGE-SCALE DIST SYSTEMS. 3.00 points.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119)
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119) Design and implementation of large-scale distributed and cloud systems. Teaches abstractions, design and implementation techniques that enable the building of fast, scalable, fault-tolerant distributed systems. Topics include distributed communication models (e.g. sockets, remote procedure calls, distributed shared memory), distributed synchronization (clock synchronization, logical clocks, distributed mutex), distributed file systems, replication, consistency models, fault tolerance, distributed transactions, agreement and commitment, Paxos-based consensus, MapReduce infrastructures, scalable distributed databases. Combines concepts and algorithms with descriptions of real-world implementations at Google, Facebook, Yahoo, Microsoft, LinkedIn, etc

COMS W4115 Programming Languages and Translators. 3 points.

Lect: 3.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3261) and (CSEE W3827) or equivalent, or the instructor's permission.

Modern programming languages and compiler design. Imperative, object-oriented, declarative, functional, and scripting languages. Language syntax, control structures, data types, procedures and parameters, binding, scope, run-time organization, and exception handling. Implementation of language translation tools including compilers and interpreters. Lexical, syntactic and semantic analysis; code generation; introduction to code optimization. Teams implement a language and its compiler.

COMS W4118 Operating Systems I. 3 points.

Lect: 3.

Prerequisites: (CSEE W3827) and knowledge of C and programming tools as covered in COMS W3136, W3157, or W3101, or the instructor's permission.

Design and implementation of operating systems. Topics include process management, process synchronization and interprocess communication, memory management, virtual memory, interrupt handling, processor scheduling, device management, I/O, and file systems. Case study of the UNIX operating system. A programming project is required.

COMS W4119 COMPUTER NETWORKS. 3.00 points.

Introduction to computer networks and the technical foundations of the internet, including applications, protocols, local area networks, algorithms for routing and congestion control, security, elementary performance evaluation. Several written and programming assignments required

COMS W4121 Computer Systems for Data Science. 3 points.

Prerequisites: background in Computer System Organization and good working knowledge of C/C++
Corequisites: CSOR W4246,STAT GU4203

An introduction to computer architecture and distributed systems with an emphasis on warehouse scale computing systems. Topics will include fundamental tradeoffs in computer systems, hardware and software techniques for exploiting instruction-level parallelism, data-level parallelism and task level parallelism, scheduling, caching, prefetching, network and memory architecture, latency and throughput optimizations, specialization, and an introduction to programming data center computers.

COMS W4130 Principles and Practice of Parallel Programming. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3137 or COMS W3136 and experience in Java) and basic understanding of analysis of algorithms.

Principles of parallel software design. Topics include task and data decomposition, load-balancing, reasoning about correctness, determinacy, safety, and deadlock-freedom. Application of techniques through semester-long design project implementing performant, parallel application in a modern parallel programming language.

COMS W4152 Engineering Software-as-a-Service. 3.00 points.

Modern software engineering concepts and practices including topics such as Software-as-a-Service, Service-oriented Architecture, Agile Development, Behavior-driven Development, Ruby on Rails, and Dev/ops

COMS W4156 Advanced Software Engineering. 3 points.

Lect: 3.

Prerequisites: (COMS W3157) or equivalent.

Software lifecycle using frameworks, libraries and services. Major emphasis on software testing. Centers on a team project.

COMS W4160 Computer Graphics. 3 points.

Lect: 3.

Prerequisites: (COMS W3134) or (COMS W3136) or (COMS W3137) COMS W4156 is recommended. Strong programming background and some mathematical familiarity including linear algebra is required.

Introduction to computer graphics. Topics include 3D viewing and projections, geometric modeling using spline curves, graphics systems such as OpenGL, lighting and shading, and global illumination. Significant implementation is required: the final project involves writing an interactive 3D video game in OpenGL.

COMS W4162 Advanced Computer Graphics. 3 points.

Lect: 3.

Prerequisites: (COMS W4160) or equivalent, or the instructor's permission.

A second course in computer graphics covering more advanced topics including image and signal processing, geometric modeling with meshes, advanced image synthesis including ray tracing and global illumination, and other topics as time permits. Emphasis will be placed both on implementation of systems and important mathematical and geometric concepts such as Fourier analysis, mesh algorithms and subdivision, and Monte Carlo sampling for rendering. Note: Course will be taught every two years.

COMS W4167 Computer Animation. 3 points.

Lect: 3.

Prerequisites: Multivariable calculus, linear algebra, C++ programming proficiency. COMS W4156 recommended.

Theory and practice of physics-based animation algorithms, including animated clothing, hair, smoke, water, collisions, impact, and kitchen sinks. Topics covered: Integration of ordinary differential equations, formulation of physical models, treatment of discontinuities including collisions/contact, animation control, constrained Lagrangian Mechanics, friction/dissipation, continuum mechanics, finite elements, rigid bodies, thin shells, discretization of Navier-Stokes equations. General education requirement: quantitative and deductive reasoning (QUA). 

COMS W4170 User Interface Design. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137)

Introduction to the theory and practice of computer user interface design, emphasizing the software design of graphical user interfaces. Topics include basic interaction devices and techniques, human factors, interaction styles, dialogue design, and software infrastructure. Design and programming projects are required.

COMS W4172 3D User Interfaces and Augmented Reality. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W4160) or (COMS W4170) or the instructor's permission.

Design, development, and evaluation of 3D user interfaces. Interaction techniques and metaphors, from desktop to immersive. Selection and manipulation. Travel and navigation. Symbolic, menu, gestural, and multimodal interaction. Dialogue design. 3D software support. 3D interaction devices and displays. Virtual and augmented reality. Tangible user interfaces. Review of relevant 3D math.

COMS W4181 SECURITY I. 3.00 points.

Not offered during 2022-23 academic year.

Prerequisites: COMS W3157 or equivalent.
Introduction to security. Threat models. Operating system security features. Vulnerabilities and tools. Firewalls, virtual private networks, viruses. Mobile and app security. Usable security. Note: May not earn credit for both W4181 and W4180 or W4187

COMS W4182 SECURITY II. 3.00 points.

Not offered during 2022-23 academic year.

Prerequisites: COMS W4181, COMS W4118, COMS W4119
Advanced security. Centralized, distributed, and cloud system security. Cryptographic protocol design choices. Hardware and software security techniques. Security testing and fuzzing. Blockchain. Human security issues. Note: May not earn credit for both W4182 and W4180 or W4187

COMS W4186 MALWARE ANALYSIS＆REVERSE ENGINEERING. 3.00 points.

Not offered during 2022-23 academic year.

Prerequisites: COMS W3157 or equivalent. COMS W3827
Hands-on analysis of malware. How hackers package and hide malware and viruses to evade analysis. Disassemblers, debuggers, and other tools for reverse engineering. Deep study of Windows Internals and x86 assembly

COMS W4203 Graph Theory. 3 points.

Lect: 3.

Prerequisites: (COMS W3203)

General introduction to graph theory. Isomorphism testing, algebraic specification, symmetries, spanning trees, traversability, planarity, drawings on higher-order surfaces, colorings, extremal graphs, random graphs, graphical measurement, directed graphs, Burnside-Polya counting, voltage graph theory.

COMS W4205 Combinatorial Theory. 3 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: (COMS W3203) and course in calculus.

Sequences and recursions, calculus of finite differences and sums, elementary number theory, permutation group structures, binomial coefficients, Stilling numbers, harmonic numbers, generating functions. 

COMS W4232 Advanced Algorithms. 3.00 points.

Prerequisite: Analysis of Algorithms (COMS W4231).

Prerequisites: see notes re: points
Introduces classic and modern algorithmic ideas that are central to many areas of Computer Science. The focus is on most powerful paradigms and techniques of how to design algorithms, and how to measure their efficiency. The intent is to be broad, covering a diversity of algorithmic techniques, rather than be deep. The covered topics have all been implemented and are widely used in industry. Topics include: hashing, sketching/streaming, nearest neighbor search, graph algorithms, spectral graph theory, linear programming, models for large-scale computation, and other related topics

COMS W4236 INTRO-COMPUTATIONAL COMPLEXITY. 3.00 points.

Lect: 3.

Prerequisites: (COMS W3261)
Prerequisites: (COMS W3261) Develops a quantitative theory of the computational difficulty of problems in terms of the resources (e.g. time, space) needed to solve them. Classification of problems into complexity classes, reductions, and completeness. Power and limitations of different modes of computation such as nondeterminism, randomization, interaction, and parallelism

COMS W4241 Numerical Algorithms and Complexity. 3 points.

Lect: 3.

Prerequisites: Knowledge of a programming language. Some knowledge of scientific computation is desirable.

Modern theory and practice of computation on digital computers. Introduction to concepts of computational complexity. Design and analysis of numerical algorithms. Applications to computational finance, computational science, and computational engineering.

COMS W4252 Introduction to Computational Learning Theory. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (CSOR W4231) or (COMS W4236) or COMS W3203 and the instructor's permission, or COMS W3261 and the instructor's permission.

Possibilities and limitations of performing learning by computational agents. Topics include computational models of learning, polynomial time learnability, learning from examples and learning from queries to oracles. Computational and statistical limitations of learning. Applications to Boolean functions, geometric functions, automata.

COMS W4261 INTRO TO CRYPTOGRAPHY. 3.00 points.

Lect: 2.5.

Prerequisites: Comfort with basic discrete math and probability. Recommended: COMS W3261 or CSOR W4231.
Prerequisites: Comfort with basic discrete math and probability. Recommended: COMS W3261 or CSOR W4231. An introduction to modern cryptography, focusing on the complexity-theoretic foundations of secure computation and communication in adversarial environments; a rigorous approach, based on precise definitions and provably secure protocols. Topics include private and public key encryption schemes, digital signatures, authentication, pseudorandom generators and functions, one-way functions, trapdoor functions, number theory and computational hardness, identification and zero knowledge protocols

COMS W4281 Introduction to Quantum Computing. 3 points.

Lect: 3.

Prerequisites: Knowledge of linear algebra. Prior knowledge of quantum mechanics is not required although helpful.

Introduction to quantum computing. Shor's factoring algorithm, Grover's database search algorithm, the quantum summation algorithm. Relationship between classical and quantum computing. Potential power of quantum computers.

COMS W4419 Internet Technology, Economics, and Policy. 3 points.

Not offered during 2022-23 academic year.

Technology, economic and policy aspects of the Internet. Summarizes how the Internet works technically, including protocols, standards, radio spectrum, global infrastructure and interconnection. Micro-economics with a focus on media and telecommunication economic concerns, including competition and monopolies, platforms, and behavioral economics. US constitution, freedom of speech, administrative procedures act and regulatory process, universal service, role of FCC. Not a substitute for CSEE4119. Suitable for non-majors. May not be used as a track elective for the computer science major.

COMS W4444 Programming and Problem Solving. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (CSEE W3827)

Hands-on introduction to solving open-ended computational problems. Emphasis on creativity, cooperation, and collaboration. Projects spanning a variety of areas within computer science, typically requiring the development of computer programs. Generalization of solutions to broader problems, and specialization of complex problems to make them manageable. Team-oriented projects, student presentations, and in-class participation required.

COMS W4460 Principles of Innovation and Entrepreneurship. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) or the instructor's permission.

Team project centered course focused on principles of planning, creating, and growing a technology venture. Topics include: identifying and analyzing opportunities created by technology paradigm shifts, designing innovative products, protecting intellectual property, engineering innovative business models.

COMS W4560 INTRO-COMP APPL-HLTH CRE/BIOMD. 3.00 points.

Lect: 3.

Prerequisites: Experience with computers and a passing familiarity with medicine and biology. Undergraduates in their senior or junior years may take this course only if they have adequate background in mathematics and receive the instructor's permission.
Undergraduates in their senior or junior years may take this course only if they have adequate background in mathematics and receive permission from the instructor. An overview of the field of biomedical informatics, combining perspectives from medicine, computer science, and social science. Use of computers and information in healthcare and the biomedical sciences, covering specific applications and general methods, current issues, capabilities and limitations of biomedical informatics. Biomedical Informatics studies the organization of medical information, the effective management of information using computer technology, and the impact of such technology on medical research, education, and patient care. The field explores techniques for assessing current information practices, determining the information needs of healthcare providers and patients, developing interventions using computer technology, and evaluating the impact of those interventions

COMS W4701 Artificial Intelligence. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and any course on probability. Prior knowledge of Python is recommended.

Provides a broad understanding of the basic techniques for building intelligent computer systems. Topics include state-space problem representations, problem reduction and and-or graphs, game playing and heuristic search, predicate calculus, and resolution theorem proving, AI systems and languages for knowledge representation, machine learning and concept formation and other topics such as natural language processing may be included as time permits.

COMS W4705 Natural Language Processing. 3 points.

Lect: 3.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) or the instructor's permission.

Computational approaches to natural language generation and understanding. Recommended preparation: some previous or concurrent exposure to AI or Machine Learning. Topics include information extraction, summarization, machine translation, dialogue systems, and emotional speech. Particular attention is given to robust techniques that can handle understanding and generation for the large amounts of text on the Web or in other large corpora. Programming exercises in several of these areas.

COMS W4706 Spoken Language Processing. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) or the instructor's permission.

Computational approaches to speech generation and understanding. Topics include speech recognition and understanding, speech analysis for computational linguistics research, and speech synthesis. Speech applications including dialogue systems, data mining, summarization, and translation. Exercises involve data analysis and building a small text-to-speech system.

COMS W4725 Knowledge representation and reasoning. 3 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: (COMS W4701)

General aspects of knowledge representation (KR). The two fundamental paradigms (semantic networks and frames) and illustrative systems. Topics include hybrid systems, time, action/plans, defaults, abduction, and case-based reasoning. Throughout the course particular attention is paid to design trade-offs between language expressiveness and reasoning complexity, and issues relating to the use of KR systems in larger applications. 

COMS W4731 Computer Vision I: First Principles. 3.00 points.

Lect: 3.

Prerequisites: Fundamentals of calculus, linear algebra, and C programming. Students without any of these prerequisites are advised to contact the instructor prior to taking the course.
Introductory course in computer vision. Topics include image formation and optics, image sensing, binary images, image processing and filtering, edge extraction and boundary detection, region growing and segmentation, pattern classification methods, brightness and reflectance, shape from shading and photometric stereo, texture, binocular stereo, optical flow and motion, 2D and 3D object representation, object recognition, vision systems and applications

COMS W4732 Computer Vision II: Learning. 3.00 points.

Advanced course in computer vision. Topics include convolutional networks and back-propagation, object and action recognition, self-supervised and few-shot learning, image synthesis and generative models, object tracking, vision and language, vision and audio, 3D representations, interpretability, and bias, ethics, and media deception

COMS W4733 Computational Aspects of Robotics. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (COMS W3134 or COMS W3136COMS W3137)

Introduction to robotics from a computer science perspective. Topics include coordinate frames and kinematics, computer architectures for robotics, integration and use of sensors, world modeling systems, design and use of robotic programming languages, and applications of artificial intelligence for planning, assembly, and manipulation.

COMS W4735 Visual Interfaces to Computers. 3 points.

Lect: 3.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137)

Visual input as data and for control of computer systems. Survey and analysis of architecture, algorithms, and underlying assumptions of commercial and research systems that recognize and interpret human gestures, analyze imagery such as fingerprint or iris patterns, generate natural language descriptions of medical or map imagery. Explores foundations in human psychophysics, cognitive science, and artificial intelligence.

COMS W4737 Biometrics. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: a background at the sophomore level in computer science, engineering, or like discipline.

In this course. we will explore the latest advances in biometrics as well as the machine learning techniques behind them. Students will learn how these technologies work and how they are sometimes defeated. Grading will be based on homework assignments and a final project. There will be no midterm or final exam. This course shares lectures with COMS E6737. Students taking COMS E6737 are required to complete additional homework problems and undertake a more rigorous final project. Students will only be allowed to earn credit for COMS W4737 or COMS E6737 and not both.

COMS W4762 Machine Learning for Functional Genomics. 3 points.

Prerequisites: Proficiency in a high-level programming language (Python/R/Julia). An introductory machine learning class (such as COMS 4771 Machine Learning) will be helpful but is not required.

Prerequisites: see notes re: points

This course will introduce modern probabilistic machine learning methods using applications in data analysis tasks from functional genomics, where massively-parallel sequencing is used to measure the state of cells: e.g. what genes are being expressed, what regions of DNA (“chromatin”) are active (“open”) or bound by specific proteins.

COMS W4771 Machine Learning. 3 points.

Lect: 3.

Prerequisites: Any introductory course in linear algebra and any introductory course in statistics are both required. Highly recommended: COMS W4701 or knowledge of Artificial Intelligence.

Topics from generative and discriminative machine learning including least squares methods, support vector machines, kernel methods, neural networks, Gaussian distributions, linear classification, linear regression, maximum likelihood, exponential family distributions, Bayesian networks, Bayesian inference, mixture models, the EM algorithm, graphical models and hidden Markov models. Algorithms implemented in MATLAB.

COMS W4772 Advanced Machine Learning. 3 points.

Lect: 3.

Prerequisites: (COMS W4771) or instructor's permission; knowledge of linear algebra & introductory probability or statistics is required.

An exploration of advanced machine learning tools for perception and behavior learning. How can machines perceive, learn from, and classify human activity computationally? Topics include appearance-based models, principal and independent components analysis, dimensionality reduction, kernel methods, manifold learning, latent models, regression, classification, Bayesian methods, maximum entropy methods, real-time tracking, extended Kalman filters, time series prediction, hidden Markov models, factorial HMMS, input-output HMMs, Markov random fields, variational methods, dynamic Bayesian networks, and Gaussian/Dirichlet processes. Links to cognitive science.

COMS W4773 Machine Learning Theory. 3 points.

Prerequisites: Machine Learning (COMS W4771). Background in probability and statistics, linear algebra, and multivariate calculus. Ability to program in a high-level language, and familiarity with basic algorithm design and coding principles.

Prerequisites: see notes re: points

Core topics from unsupervised learning such as clustering, dimensionality reduction and density estimation will be studied in detail. Topics in clustering: k-means clustering, hierarchical clustering, spectral clustering, clustering with various forms of feedback, good initialization techniques and convergence analysis of various clustering procedures. Topics in dimensionality reduction: linear techniques such as PCA, ICA, Factor Analysis, Random Projections, non-linear techniques such as LLE, IsoMap, Laplacian Eigenmaps, tSNE, and study of embeddings of general metric spaces, what sorts of theoretical guarantees can one provide about such techniques. Miscellaneous topics: design and analysis of data structures for fast Nearest Neighbor search such as Cover Trees and LSH. Algorithms will be implemented in either Matlab or Python.

COMS W4774 Unsupervised Learning. 3 points.

Prerequisites: Solid background in multivariate calculus, linear algebra, basic probability, and algorithms.

Prerequisites: see notes re: points

Theoretical study of algorithms for machine learning and high-dimensional data analysis. Topics include high-dimensional probability, theory of generalization and statistical learning, online learning and optimization, spectral analysis.

 

COMS W4775 Causal Inference. 3.00 points.

Prerequisites: Discrete Math, Calculus, Statistics (basic probability, modeling, experimental design), some programming experience.

Prerequisites: see notes re: points
Causal Inference theory and applications. The theoretical topics include the 3-layer causal hierarchy, causal bayesian networks, structural learning, the identification problem and the do-calculus, linear identifiability, bounding, and counterfactual analysis. The applied part includes intersection with statistics, the empirical-data sciences (social and health), and AI and ML

COMS W4776 Machine Learning for Data Science. 3 points.

Lect.: 3

Prerequisites: (STAT GU4001 or IEOR E4150) and linear algebra.

Introduction to machine learning, emphasis on data science. Topics include least square methods, Gaussian distributions, linear classification, linear regression, maximum likelihood, exponential family distributions, Bayesian networks, Bayesian inference, mixture models, the EM algorithm, graphical models, hidden Markov models, support vector machines kernel methods. Emphasizes methods and problems relevant to big data. Students may not receive credit for both COMS W4771 and W4776.

COMS W4824 COMPUTER ARCHITECTURE. 3.00 points.

COMS W4901 Projects in Computer Science. 1-3 points.

Prerequisites: Approval by a faculty member who agrees to supervise the work.

A second-level independent project involving laboratory work, computer programming, analytical investigation, or engineering design. May be repeated for credit, but not for a total of more than 3 points of degree credit. Consult the department for section assignment.

COMS W4995 Special topics in computer science, I. 3 points.

Lect: 3.

Prerequisites: Instructor's permission.

Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment. 

COMS W4996 Special topics in computer science, II. 3 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: Instructor's permission.

A continuation of COMS W4995 when the special topic extends over two terms.

CSEE E6180 Modeling and Performance. 3 points.

Lect: 2.

Prerequisites: (COMS W4118) and (STAT GU4001)

Introduction to queuing analysis and simulation techniques. Evaluation of time-sharing and multiprocessor systems. Topics include priority queuing, buffer storage, and disk access, interference and bus contention problems, and modeling of program behaviors.

CSEE E6824 PARALLEL COMPUTER ARCH. 3.00 points.

Lect: 2.

Prerequisites: (CSEE W4824)
Parallel computer principles, machine organization, and design of parallel systems including parallelism detection methods, synchronization, data coherence and interconnection networks. Performance analysis and special purpose parallel machines

CSEE E6847 Distributed Embedded Systems. 3 points.

Lect: 2.Not offered during 2022-23 academic year.

Prerequisites: Any COMS W411X, CSEE W48XX or ELEN E43XX course, or the instructor's permission.

An interdisciplinary graduate-level seminar on the design of distributed embedded systems. System robustness in the presence of highly variable communication delays and heterogeneous component behaviors. The study of the enabling technologies (VLSI circuits, communication protocols, embedded processors, RTOSs), models of computation, and design methods. The analysis of modern domain-specific applications including on-chip micro-networks, multiprocessor systems, fault-tolerant  architectures, and robust deployment of embedded software. Research challenges such as design complexity, reliability, scalability, safety, and security. The course requires substantial reading, class participation and a research project.

CSEE E6861 CAD OF DIGITAL SYSTEMS. 3.00 points.

Lect: 2.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157) and (CSEE W4823 or equivalent).
Introduction to modern digital CAD synthesis and optimization techniques. Topics include modern digital system design (high-level synthesis, registertransfer level modeling, algorithmic state machines, optimal scheduling algorithms, resource allocation and binding, retiming), controller synthesis and optimization, exact and heuristic two-level logic minimization, advanced multilevel logic optimization, optimal technology mapping to library cells (for delay, power and area minimization), advanced data structures (binary decision diagrams), SAT solvers and their applications, static timing analysis, and introduction to testability. Includes hands-on small design projects using and creating CAD tools

CSEE E6863 Formal verification of hardware and software systems. 3 points.

Lect: 2.

Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3261)

Introduction to the theory and practice of formal methods for the design and analysis of correct (i.e. bug-free) concurrent and embedded hardware/software systems. Topics include temporal logics; model checking; deadlock and liveness issues; fairness; satisfiability (SAT) checkers; binary decision diagrams (BDDs); abstraction techniques; introduction to commercial formal verification tools. Industrial state-of-art, case studies and experiences: software analysis (C/C++/Java), hardware verification (RTL).

CSEE E6868 EMBEDDED SCALABLE PLATFORMS. 3.00 points.

Lect: 2.

Prerequisites: (CSEE W4868) or the instructor permission.
Prerequisites: (CSEE W4868) or the instructor permission. Inter-disciplinary graduate-level seminar on design and programming of embedded scalable platforms. Content varies between offerings to cover timely relevant issues and latest advances in system-on-chip design, embedded software programming, and electronic design automation. Requires substantial reading of research papers, class participation, and semester-long project

CSEE S4119 COMPUTER NETWORKS. 3.00 points.

CSEE W3827 Fundamentals of Computer Systems. 3 points.

Lect: 3.

Prerequisites: an introductory programming course.

Fundamentals of computer organization and digital logic. Boolean algebra, Karnaugh maps, basic gates and components, flipflops and latches, counters and state machines, basics of combinational and sequential digital design. Assembly language, instruction sets, ALU’s, single-cycle and multi-cycle processor design, introduction to pipelined processors, caches, and virtual memory.

CSEE W4140 NETWORKING LABORATORY. 3.00 points.

Lect: 3.

Prerequisites: (CSEE W4119) or equivalent.
In this course, students will learn how to put principles into practice, in a hands-on-networking lab course. The course will cover the technologies and protocols of the Internet using equipment currently available to large internet service providers such as CISCO routers and end systems. A set of laboratory experiments will provide hands-on experience with engineering wide-area networks and will familiarize students with the Internet Protocol (IP), Address Resolution Protocol (ARP), Internet Control Message Protocol (ICMP), User Datagram Protocol (UDP) and Transmission Control Protocol (TCP), the Domain Name System (DNS), routing protocols (RIP, OSPF, BGP), network management protocols (SNMP, and application-level protocols (FTP, TELNET, SMTP)

CSEE W4823 Advanced Logic Design. 3 points.

Lect: 3.

Prerequisites: (CSEE W3827) or a half semester introduction to digital logic, or the equivalent.

An introduction to modern digital system design. Advanced topics in digital logic: controller synthesis (Mealy and Moore machines); adders and multipliers; structured logic blocks (PLDs, PALs, ROMs); iterative circuits. Modern design methodology: register transfer level modelling (RTL); algorithmic state machines (ASMs); introduction to hardware description languages (VHDL or Verilog); system-level modelling and simulation; design examples.

CSEE W4824 Computer Architecture. 3 points.

Lect: 3.

Prerequisites: (CSEE W3827) or equivalent.

Focuses on advanced topics in computer architecture, illustrated by case studies from classic and modern processors. Fundamentals of quantitative analysis. Pipelining. Memory hierarchy design. Instruction-level and thread-level parallelism. Data-level parallelism and graphics processing units. Multiprocessors. Cache coherence. Interconnection networks. Multi-core processors and systems-on-chip. Platform architectures for embedded, mobile, and cloud computing.

CSEE W4840 Embedded Systems. 3 points.

Lect: 3.

Prerequisites: (CSEE W4823)

Embedded system design and implementation combining hardware and software. I/O, interfacing, and peripherals. Weekly laboratory sessions and term project on design of a microprocessor-based embedded system including at least one custom peripheral. Knowledge of C programming and digital logic required.

CSEE W4868 System-on-chip platforms. 3 points.

Prerequisites: (COMS W3157) and (CSEE W3827)

Design and programming of System-on-Chip (SoC) platforms. Topics include: overview of technology and economic trends, methodologies and supporting CAD tools for system-level design, models of computation, the SystemC language, transaction-level modeling, software simulation and virtual platforms, hardware-software partitioning, high-level synthesis, system programming and device drivers, on-chip communication, memory organization, power management and optimization, integration of programmable processor cores and specialized accelerators. Case studies of modern SoC platforms for various classes of applications.

CSEE W6600 From Data to Solutions. 3 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: Ability to study research solutions and write a coherent weekly report in English that summarizes problems involving large-scale data sets and solutions based on data science methods and tools

Introduces students interested in data science and interdisciplinary research to a wide variety of problems in medical research, journalism, history, economics, business, English, psychology, and other areas which might benefit from computational approaches.

COSA E9800 Data Science Doctoral Seminar. 1 point.

Not offered during 2022-23 academic year.

The Data Science Doctoral Seminar is a 1-credit course that meets weekly. The purpose is to expose the doctoral students to a breadth of ideas in data science across disciplinary domains. The syllabus combines guest lectures from academic data scientists in the greater NYC area and faculty at Columbia, along with a selection of related readings chosen by the guest lecturers. As part of this seminar, students will be expected to engage in active open discussion about the topics and readings covered in class, as well as discuss how such topics apply to their own respective research areas.

CSOR E4010 GRAPH THEORY: COMBINATL VIEW. 3.00 points.

Lect: 3.Not offered during 2022-23 academic year.

Prerequisites: Linear Algebra, or instructor's permission.
An introductory course in graph theory with emphasis on its combinatorial aspects. Basic definitions, and some fundamental topics in graph theory and its applications. Topics include trees and forests graph coloring, connectivity, matching theory and others

CSOR E4200 Data-driven Decision Modeling. 3.00 points.

Introduction to modeling, estimating, and solving decision-making problems in the context of artificial intelligence and analytics. Potential topics include choice models, quantity models, online learning using multi-armed bandits, dynamic decision modeling, dynamic games, and Bayesian learning theory. Practice both theory and applications using Python programming

CSOR E4231 ANALYSIS OF ALGORITHMS I. 3.00 points.

Prerequisites: COMS W3134, COMS W3136, or COMS W3137, and COMS W3203. Introduction to the design and analysis of efficient algorithms. Topics include models of computation, efficient sorting and searching, algorithms for algebraic problems, graph algorithms, dynamic programming, probabilistic methods, approximation algorithms, and NP-completeness

CSOR W4231 Analysis of Algorithms I. 3 points.

Lect: 3.

Prerequisites: (COMS W3134 or COMS W3136COMS W3137) and (COMS W3203)

Introduction to the design and analysis of efficient algorithms. Topics include models of computation, efficient sorting and searching, algorithms for algebraic problems, graph algorithms, dynamic programming, probabilistic methods, approximation algorithms, and NP-completeness.

CBMF W4761 Computational Genomics. 3 points.

Lect: 3.

Prerequisites: Working knowledge of at least one programming language, and some background in probability and statistics.

Computational techniques for analyzing genomic data including DNA, RNA, protein and gene expression data. Basic concepts in molecular biology relevant to these analyses. Emphasis on techniques from artificial intelligence and machine learning. String-matching algorithms, dynamic programming, hidden Markov models, expectation-maximization, neural networks, clustering algorithms, support vector machines. Students with life sciences backgrounds who satisfy the prerequisites are encouraged to enroll. 

AMCS E4302 PARALLEL SCI COMPUTING. 3.00 points.