Computer Science

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.

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.

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

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).

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.

Mathematical foundations of machine learning: Linear algebra, multivariable calculus,
and probability and statistics. Comprehensive review and additional treatment of
relevant topics used in the analysis and design of machine learning models. Preliminary
exposure to core algorithms such as linear regression, gradient descent, principal
component analysis, low-rank approximations, and kernel methods.

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.

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.

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.

Computational approaches to the analysis, understanding, and generation of natural language text at scale. Emphasis on machine learning techniques for NLP, including deep learning and large language models. Applications may include information extraction, sentiment analysis, question answering, summarization, machine translation, and conversational AI. Discussion of datasets, benchmarking and evaluation, interpretability, and ethical considerations.
Due to significant overlap in content, only one of COMS 4705 or Barnard COMS 3705BC may be taken for credit.

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.

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.

Selected topics in computer science. Content and prerequisites vary between sections and semesters. May be repeated for credit. Check “topics course” webpage on the department website for more information on each section.

Selected topics in computer science. Content and prerequisites vary between sections and semesters. May be repeated for credit. Check “topics course” webpage on the department website for more information on each section.

Selected topics in computer science. Content and prerequisites vary between sections and semesters. May be repeated for credit. Check “topics course” webpage on the department website for more information on each section.

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.

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.

DATA SCIENCE: Decoding the Secrets of Data

How (not) to bet: Demystifying probability

Math in Action: Operations Research for Social Good

Product Studio: From Idea to Prototype

Product Studio: From Idea to Prototype

Sustainable Engineering

Sustainable Engineering

Program components include experience in working on genuine engineering research projects, research skills and college prep workshops, science communications workshops, and additional supplemental seminars and opportunities. 

Enrollment in this course acknowledges the student’s participation in an industry project. 

Working with a mentor (alumni, adjunct faculty, or industry partner) in relevant industry, students will work with a team of 3-5 students on an identified project. The career placement officer can assist in administering the advertisement, selection and recruitment processes.  Students can enroll in ENGI E4700 for zero credit, zero fees; students who wish to earn academic credit can enroll in Fieldwork. The specific requirements for the project is defined by the mentor.  Groups should meet with their mentor on a weekly basis for at least 30 minutes. Students are also encouraged to submit bi-weekly progress reports to the mentor.  Upon completion of the project (end of July/beginning of August), each team will participate in an industry project showcase to present their project and deliverables.  Students will receive coaching on presentation skills from the professional development and leadership and the career placement officer teams.

Working with a faculty member and a team of 3-5 graduate or undergraduate students, students will have the opportunity to work on a small research project. Students can enroll ENGI E3900/4900 for zero credit, zero fees; students who wish to earn academic credit can enroll in the faculty member’s independent research course or Fieldwork. Specific requirements for the project are defined by the faculty members.  Research groups meet weekly with their faculty member. Students are also encouraged to submit bi-weekly progress reports to the faculty member.  Upon completion of the research project (end of July/beginning of August), each research team will participate in a research symposium to present their research and deliverables. Note: Enrollment in this course acknowledges the student’s participation in research with an Engineering faculty member.

Working with a faculty member and a team of 3-5 graduate or undergraduate students, students will have the opportunity to work on a small research project. Students can enroll ENGI E3900/4900 for zero credit, zero fees; students who wish to earn academic credit can enroll in the faculty member’s independent research course or Fieldwork. Specific requirements for the project are defined by the faculty members.  Research groups meet weekly with their faculty member. Students are also encouraged to submit bi-weekly progress reports to the faculty member.  Upon completion of the research project (end of July/beginning of August), each research team will participate in a research symposium to present their research and deliverables. Note: Enrollment in this course acknowledges the student’s participation in research with an Engineering faculty member.

Working with a faculty member and a team of 3-5 graduate or undergraduate students, students will have the opportunity to work on a small research project. Students can enroll ENGI E3900/4900 for zero credit, zero fees; students who wish to earn academic credit can enroll in the faculty member’s independent research course or Fieldwork. Specific requirements for the project are defined by the faculty members.  Research groups meet weekly with their faculty member. Students are also encouraged to submit bi-weekly progress reports to the faculty member.  Upon completion of the research project (end of July/beginning of August), each research team will participate in a research symposium to present their research and deliverables. Note: Enrollment in this course acknowledges the student’s participation in research with an Engineering faculty member.

English communication proficiency is important for academic achievement and career success. Columbia Engineering provides English communication instruction for students who would like to improve their communication skills in English. In a small group setting (15-20 students), enrollees will obtain opportunities to interact with the instructor and fellow classmates to improve communication skills.

English communication proficiency is important for academic achievement and career success. Columbia Engineering provides English communication instruction for students who would like to improve their communication skills in English. In a small group setting (15-20 students), enrollees will obtain opportunities to interact with the instructor and fellow classmates to improve communication skills.