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

A general introduction to computer science concepts, algorithmic problem-solving capabilities, and programming skills in C. Columbia University students may receive credit for only one of the following three courses: 1003, 1004, and 1005.

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 three courses: 1003, 1004, and 1005.

Prerequisites: None
Corequisites: None

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 three courses: 1003, 1004, and 1005.

An interdisciplinary course in computing intended for first year SEAS students. Introduces computational thinking, algorithmic problem solving and Python programming with applications in science and engineering. Assumes no prior programming background.

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.

Corequisites: COMS W1004/1007 or ENGI 1006. Enrollment with
instructor permission only.

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.

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.

Prerequisites: COMS W1003 or knowledge of C.

Not intended for computer science majors. 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 C. Note: Due to significant overlap, students may receive credit for only one of the following four courses: COMS W3133, W3134, W3137, and W3139.

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 four courses: COMS W3134, COMS W3136, COMS W3137

Prerequisites: 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 four courses: COMS W3133, W3134, W3137.

Prerequisites: COMS W1007

Practical, hands-on introduction to programming techniques and tools for professional software construction, including learning how to write code to given specifications as well as document the results. Provides introductory overview of C and C++ in a UNIX environment, for students with Java background. Also introduces scripting languages (perl) and basic web programming. UNIX programming utilities are also covered.

Lab Required.

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).

Prerequisites: two terms of calculus.

Computational linear algebra, solution of linear systems, sparse linear systems, least squares, eigenvalue problems, and numerical solution of other multivariate problems as time permits.

Prerequisites: COMS W3203
Corequisites: 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.

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.

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.

Introduction to the information system paradigm of molecular biology. Representation, organization, structure, function, and manipulation of the biomolecular sequences of nucleic acids and proteins. The role of enzymes and gene regulatory elements in natural biological functions as well as in biotechnology and genetic engineering. Recombination and other macromolecular processes viewed as mathematical operations with simulation and visualization using simple computer programming. This course shares lectures with ECBM E3060, but the work requirements differ somewhat.

Prerequisites: COMS W3137 or W3134, fluency in Java; or permission of the instructor.

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.

Prerequisites: COMS W3137 or equivalent, W3261, and CSEE W3827, 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.

Prerequisites: COMS W4115 or the instructor's permission.

Continuation of COMS W4115, with broader and deeper investigation into the design and implementation of contemporary language translators, be they compilers or interpreters. Topics include: parsing, semantic analysis, code generation and optimization, run-time environments, and compiler-compilers. A programming project is required.

Prerequisites: CSEE W3827 and knowledge of C and programming tools as covered in 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.

Corequisites: SIEO E3658 or W3600 or equivalent

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.

Prerequisites: Experience in Java, basic understanding of analysis of algorithms. COMS W1004 and COMS W3137 (or equivalent).

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.

Prerequisites: CSEE 4119 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 proctocols 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 Protocal (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).

Prerequisites: Substantial software development experience in Java, C++ or C# beyond the level of COMS W3157.
Corequisites: Recommended COMS W4111

Software lifecycle from the viewpoint of designing and implementing N-tier applications (typically utilizing web browser, web server, application server, database). Major emphasis on quality assurance (code inspection, unit and integration testing, security and stress testing). Centers on a student-designed team project that leverages component services (e.g., transactions, resource pooling, publish/subscribe) for an interactive multi-user application such as a simple game.

Prerequisites: COMS W3137 or W3139, 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.

Prerequisites: COMS W4160 or equivalent, or 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.

Prerequisites: 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.

Prerequisites: COMS W3137 and W4119, or the instructor's permission.

Introduction to network security concepts and mechanisms. Foundations of network security and an in-depth review of commonly-used security mechanisms and techniques, security threats and network-based attacks, applications of cryptography, authentication, access control, intrusion detection and response, security protocols (IPsec, SSL, Kerberos), denial of service, viruses and worms, software vulnerabilities, web security, wireless security, and privacy.

Prerequisites: COMS W4118; W4180 and/or W4119 recommended.

Secure programming. Cryptograhic engineering and key handling. Access controls. Tradeoffs in security design. Design for security.

Prerequisites: COMS W3203 and a 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.

Prerequisites: COMS W3137 or W3139, and 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.

Prerequisites: CSOR W4231 or COMS W4236 or (COMS W3203 and permission of instructor) or (COMS W3261 and permission of instructor).

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.

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.

Prerequisites: 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.

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 backgroud 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 health care 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 health care providers and patients, developing interventions using computer technology, and evaluating the impact of those interventions.

Prerequisites: COMS W3137.

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.

Prerequisites: COMS W3133, or W3134, or W3137, or W3139, 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.

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 will be paid to design tradeoffs between language expressiveness and reasoning complexity, and issues relating to the use of KR systems in larger applications.

Prerequisites: The 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, 2-D and 3-D object representation, object recognition, vision systems and applications.

Prerequisites: COMS 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.

Prerequisites: 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.

Prerequisites: A background at the sophomore level in computer science, engineering, or like discipline.
Corequisites: None

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.

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.

Prerequisites: CSEE 3827, 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.

Prerequisites: CSEE W3827 or the 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.

Prerequisites: The 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.

Prerequisites: The instructor's permission.

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

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.

Prerequisites: COMS W4115 or instructor's permission.

Concentration on the design and implementation of programming languages, and tools focused on advanced applications in new areas in software verification, distributed systems, programming in the large, and web computing. A substantial project is typically required. May be repeated for credit.

Prerequisites: At least one COMS W41xx or COMS E61xx course and/or COMS W4444, or the instructor's permission. Strongly recommended: COMS W4156.

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.

Prerequisites: COMS W4160 or instructor's permission.

An advanced graduate course, involving study of an advanced research topic in Computer Graphics. Content varies between offerings, and the course may be repeated for credit. Recent offerings have included appearance models in graphics, and high quality real-time rendering.

Prerequisites: COMS W4118 and SIEO W4150

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.

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.

Prerequisites: COMS W4180, CSEE 4119 and COMS W4261 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.

Prerequisites: COMS W4203 or instructor's permission.

Content varies from year to year. This course may be repeated for credit. Concentration on some aspect of graph theory, such as topological graph theory, algebraic graph theory, enumerative graph theory, graphical optimization problems, or matroids.

Prerequisites: COMS W4203 or W4205, or instructor's permission.

Concentration on some aspect of combinatorial theory. Content varies form year to year. This course may be repeated for credit.

Prerequisites: CSOR W4231.

Continuation of CSOR W4231.

Prerequisites: Instructor's permission.

Concentration on some theoretical aspect of computer science. Content varies from year to year. May be repeated for credit.

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 art in computational imaging. Review of recent papers on: omni directional 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.

Prerequisites: Experience with at least one of the following topics: Computer Graphics, Computer Vision, Pixel Processing, Robotics or Computer Aided Design, or permission of the instructor. Programming proficiency in C, C++ or JAVA.

Programming proficiency in C, C++ or JAVA. 3D Photography - the process of automatically creating 3D, texture-mapped models of objects in detail. Applications include robotics, medicine, graphics, virtual reality, entertainment and digital movies etc. Topics include 3D data acquisition devices, 3D modeling systems and algorithms to acquire, create, augment, manipulate, render, animate and physically build such models.

Prerequisites: A background at the sophomore level in computer science, engineering, or like discipline.
Corequisites: None

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 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 and not both.

Prerequisites: CSEE W3827 or any introduction to logic circuits.

A list of topics for each offering of the course is available in the department office one month before registration. May be taken more than once if topics are different Iterative logic circuits applied to pattern recognition. Finite state machines; alternative representations, information loss, linear circuits, structure theory. Reliability and testability of digital systems.

Prerequisites: Basic probability and statistics

Theory and practice of contemporary automatic speech recognition. Gaussian mixture distributions, hidden Markov models, pronunciation modeling, decision trees, finite-state transducers, and language modeling. Selected advanced topics will be covered in more depth.

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

A general introduction to computer science concepts, algorithmic problem-solving capabilities, and programming skills in C. Columbia University students may receive credit for only one of the following three courses: 1003, 1004, and 1005.

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 three courses: 1003, 1004, and 1005.

Prerequisites: None
Corequisites: None

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 three courses: 1003, 1004, and 1005.

An interdisciplinary course in computing intended for first year SEAS students. Introduces computational thinking, algorithmic problem solving and Python programming with applications in science and engineering. Assumes no prior programming background.

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.

Corequisites: COMS W1004/1007 or ENGI 1006. Enrollment with
instructor permission only.

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.

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.

Prerequisites: COMS W1003 or knowledge of C.

Not intended for computer science majors. 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 C. Note: Due to significant overlap, students may receive credit for only one of the following four courses: COMS W3133, W3134, W3137, and W3139.

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 four courses: COMS W3134, COMS W3136, COMS W3137

Prerequisites: COMS W1004, W1005, W1006, or W1007

A second programming course intended for non-majors with at least one semester of introductory programming experience. Basic elements of programming in C and C++, array-based data structures, heaps, linked lists, C programming in UNIX environment, object-oriented programming in C++, trees, graphs, generic programming, hash tables.

Prerequisites: 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 four courses: COMS W3133, W3134, W3137.

Prerequisites: COMS W1007

Practical, hands-on introduction to programming techniques and tools for professional software construction, including learning how to write code to given specifications as well as document the results. Provides introductory overview of C and C++ in a UNIX environment, for students with Java background. Also introduces scripting languages (perl) and basic web programming. UNIX programming utilities are also covered.

Lab Required.

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).

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.

Prerequisites: COMS W3203
Corequisites: 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.

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.

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.

Prerequisites: COMS W3137 or W3134, fluency in Java; or permission of the instructor.

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.

Prerequisites: COMS W4111; 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.

Prerequisites: COMS W3137 or equivalent, W3261, and CSEE W3827, 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.

Prerequisites: COMS W4115 or the instructor's permission.

Continuation of COMS W4115, with broader and deeper investigation into the design and implementation of contemporary language translators, be they compilers or interpreters. Topics include: parsing, semantic analysis, code generation and optimization, run-time environments, and compiler-compilers. A programming project is required.

Prerequisites: CSEE W3827 and knowledge of C and programming tools as covered in 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.

Corequisites: SIEO E3658 or W3600 or equivalent

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.

Prerequisites: CSEE 4119 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 proctocols 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 Protocal (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).

Prerequisites: COMS W3137 or W3139, 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.

Prerequisites: COMS W4160 or equivalent, or 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.

Prerequisites: COMS W3137 and W4119, or the instructor's permission.

Introduction to network security concepts and mechanisms. Foundations of network security and an in-depth review of commonly-used security mechanisms and techniques, security threats and network-based attacks, applications of cryptography, authentication, access control, intrusion detection and response, security protocols (IPsec, SSL, Kerberos), denial of service, viruses and worms, software vulnerabilities, web security, wireless security, and privacy.

Prerequisites: COMS W4118; W4180 and/or W4119 recommended.

Secure programming. Cryptograhic engineering and key handling. Access controls. Tradeoffs in security design. Design for security.

Prerequisites: COMS W3137 or W3139, and 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.

Prerequisites: COMS W3261.

Develops a quantitative theory of the computational difficulty of problems in terms of the resources (eg. 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.

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.

Prerequisites: CSOR W4231 or COMS W4236 or (COMS W3203 and permission of instructor) or (COMS W3261 and permission of instructor).

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.

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.

Prerequisites: COMS W3134, W3137 or equivalent or permission of instructor.

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

Prerequisites: COMS W3137.

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.

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 will be paid to design tradeoffs between language expressiveness and reasoning complexity, and issues relating to the use of KR systems in larger applications.

Prerequisites: The 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, 2-D and 3-D object representation, object recognition, vision systems and applications.

Prerequisites: COMS 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.

Prerequisites: 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.

Prerequisites: A background at the sophomore level in computer science, engineering, or like discipline.
Corequisites: None

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.

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.

Prerequisites: CSEE 3827, 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.

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.

Lab Required.

Prerequisites: The 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.

Prerequisites: The instructor's permission.

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

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.

Prerequisites: COMS W4115 or instructor's permission.

Concentration on the design and implementation of programming languages, and tools focused on advanced applications in new areas in software verification, distributed systems, programming in the large, and web computing. A substantial project is typically required. May be repeated for credit.

Prerequisites: At least one COMS W41xx or COMS E61xx course and/or COMS W4444, or the instructor's permission. Strongly recommended: COMS W4156.

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.

Prerequisites: COMS W4160 or instructor's permission.

An advanced graduate course, involving study of an advanced research topic in Computer Graphics. Content varies between offerings, and the course may be repeated for credit. Recent offerings have included appearance models in graphics, and high quality real-time rendering.

Prerequisites: COMS W4118 and SIEO W4150

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.

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.

Prerequisites: COMS W4180, CSEE 4119 and COMS W4261 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.

Prerequisites: COMS W4203 or instructor's permission.

Content varies from year to year. This course may be repeated for credit. Concentration on some aspect of graph theory, such as topological graph theory, algebraic graph theory, enumerative graph theory, graphical optimization problems, or matroids.

Prerequisites: COMS W4203 or W4205, or instructor's permission.

Concentration on some aspect of combinatorial theory. Content varies form year to year. This course may be repeated for credit.

Prerequisites: CSOR W4231.

Continuation of CSOR W4231.

Prerequisites: Instructor's permission.

Concentration on some theoretical aspect of computer science. Content varies from year to year. May be repeated for credit.

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 art in computational imaging. Review of recent papers on: omni directional 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.

Prerequisites: Experience with at least one of the following topics: Computer Graphics, Computer Vision, Pixel Processing, Robotics or Computer Aided Design, or permission of the instructor. Programming proficiency in C, C++ or JAVA.

Programming proficiency in C, C++ or JAVA. 3D Photography - the process of automatically creating 3D, texture-mapped models of objects in detail. Applications include robotics, medicine, graphics, virtual reality, entertainment and digital movies etc. Topics include 3D data acquisition devices, 3D modeling systems and algorithms to acquire, create, augment, manipulate, render, animate and physically build such models.

Prerequisites: COMS W4160, COMS W4731, or a working knowledge of photography are 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.

Prerequisites: A background at the sophomore level in computer science, engineering, or like discipline.
Corequisites: None

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 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 and not both.

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.

Prerequisites: CSEE W3827 or any introduction to logic circuits.

A list of topics for each offering of the course is available in the department office one month before registration. May be taken more than once if topics are different Iterative logic circuits applied to pattern recognition. Finite state machines; alternative representations, information loss, linear circuits, structure theory. Reliability and testability of digital systems.

Prerequisites: (i) one semester of advanced digital logic (CSEE4823 or equivalent, or instructor�s permission); and (ii) a basic course in data structures and algorithms (CS3133, 3134, 3137, 3139 or 3157, or equivalent, and familiarity with programming.

Introduction to modern digital CAD synthesis and optimization techniques. Topics include: modern digital system design (high-level synthesis, register-transfer 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 multi-level 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.

Prerequisites: Basic probability and statistics

Theory and practice of contemporary automatic speech recognition. Gaussian mixture distributions, hidden Markov models, pronunciation modeling, decision trees, finite-state transducers, and language modeling. Selected advanced topics will be covered in more depth.