May be repeated for credit, but no more than 3 total points may be used toward the 128-credit degree requirement. Only for MECE undergraduate students who include relevant on-campus and off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and nontechnical requirements. May not be taken for pass/fail credit or audited.
Prerequisites: approval prior to registration; see the director of undergraduate studies for details. A creative/scholarly project conducted under faculty supervision.
Prerequisites: Permission of the instructor and the chair required. Students submit, before the semester begins, a detailed proposal for independent research to a faculty sponsor.
Current topics in biomedical engineering. Subject matter will vary by year.
Aimed at understanding and testing state-of?the-art methods in machine learning applied to environmental sciences and engineering problems. Potential applications include but are not limited to remote sensing, and environmental and geophysical fluid dynamics. Includes testing "vanilla" ML algorithms, feedforward neural networks, random forests, shallow vs deep networks, and the details of machine learning techniques.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
This course offers a historical and critical overview of film and media theory from its origins up to the present.
This course is a detailed and hands-on (ears-on) exploration of the fundamental physical, physiological, and psychological aspects of sound. Topics covered include sound waves and their physical nature, the propagation and speed of sound in different mediums, geological and other non-living sound sources, animal and insect sound generating strategies, sound perception mechanisms and abilities in different species, the physiology of human hearing and the structure of the human ear, psycho-acoustics and human sound perception, sonic illusions and tricks of the ear.
In-class experiments and research make up the majority of the class. Each student will design and lead at least one experiment/demo session. Students also respond to creative weekly prompts about sound topics on courseworks.
We also have visits with a number of special guests during the term.
Genealogies of Feminism:
Course focuses on the development of a particular topic or issue in feminist, queer, and/or WGSS scholarship. Open to graduate students and advanced undergraduates, though priority will be given to students completing the ISSG graduate certificate. Topics differ by semester offered, and are reflected in the course subtitle. For a description of the current offering, please visit the link in the Class Notes.
The principal goal of this course is to examine the nature and histories of a range of early empires in a comparative context. In the process, we will examine influential theories that have been proposed to account for the emergence and trajectories of those empires. Among the theories are the core-periphery, world-systems, territorial-hegemonic, tributary-capitalist, network, and IEMP approaches. Five regions of the world have been chosen, from the many that could provide candidates: Rome (the classic empire), New Kingdom Egypt, Qin China, Aztec Mesoamerica, and Inka South America. These empires have been chosen because they represent a cross-section of polities ranging from relatively simple and early expansionist societies to the grand empires of the Classical World, and the most powerful states of the indigenous Americas. There are no prerequisites for this course, although students who have no background in Anthropology, Archaeology, History, or Classics may find the course material somewhat more challenging than students with some knowledge of the study of early societies. There will be two lectures per week, given by the professor.
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.
Physiological systems at the cellular and molecular level are examined in a highly quantitative context. Topics include chemical kinetics, molecular binding and enzymatic processes, molecular motors, biological membranes, and muscles.
Part of an accelerated consideration of the essential chemical engineering principles from the undergraduate program, including selected topics from Introduction to Chemical Engineering, Transport Phenomena I and II, and Chemical Engineering Control. While required for all M.S. students with Scientist to Engineer status, the credits from this course may not be applied toward any chemical engineering degree.
Co-requisite undergraduate discussion section for FILM GU 4000 Film & Media Theory.
Prerequisites: Calculus through multiple integration and infinite sums. A calculus-based tour of the fundamentals of probability theory and statistical inference. Probability models, random variables, useful distributions, conditioning, expectations, law of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. This course replaces SIEO 4150.
Part of an accelerated consideration of the essential chemical engineering principles from the undergraduate program, including topics from Reaction Kinetics and Reactor Design, Chemical Engineering Thermodynamics, I and II, and Chemical and Biochemical Separations. While required for all M.S. students with Scientist to Engineer status, the credits from this course may not be applied toward any chemical engineering degree.
This course is customized for 1st-year PhD and MA students in the biomedical informatics graduate program and also
open to other interested students at Columbia. It provides a detailed overview of symbolic methods.
Introduction to the economic evaluation of industrial projects. Economic equivalence and criteria. Deterministic approaches to economic analysis. Multiple projects and constraints. Analysis and choice under risk and uncertainty.
A graduate course only for MS&E, IE, and OR students. This is also required for students in the Undergraduate Advanced Track. For students who have not studied linear programming. Some of the main methods used in IEOR applications involving deterministic models: linear programming, the simplex method, nonlinear, integer and dynamic programming.
Prerequisites: Students should have completed at least one course in ecology, evolution or conservation biology. The purpose of this course is to arm emerging scientists with an understanding of conservation policy at the city, state, federal and international levels. Our focus will be on understanding the science that informs conservation policy, evaluating the efficacy of conservation policies for achieving conservation goals, and learning about the role that scientists play in forming policy.
This course is organized around a number of thematic centers or modules. Each is focused on stylistic peculiarities typical of a given functional style of the Ukrainian language. Each is designed to assist the student in acquiring an active command of lexical, grammatical, discourse, and stylistic traits that distinguish one style from the others and actively using them in real-life communicative settings in contemporary Ukraine. The styles include literary fiction, scholarly prose, and journalism, both printed and broadcast.
Fundamentals of Linear Algebra including vector and Matrix algebra, solution of linear systems, existence and uniqueness, gaussian elimination, gauss-jordan elimination, the matrix inverse, elementary matrices and the LU factorization, computational cost of solutions. Vector spaces and subspaces, linear independence, basis and dimension. The 4 fundamental subspaces of a matrix. Orthogonal projection onto a subspace and solution of Linear Least Squares problems, unitary matrices, inner products, orthogonalization algorithms and the QR factorization, applications. Determinants and applications. Eigen problems including diagonalization, symmetric matrices, positive-definite systems, eigen factorization and applications to dynamical systems and iterative maps. Introduction to the singular value decomposition and its applications.
Linear, quadratic, nonlinear, dynamic, and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering are discussed.
Prerequisites: JPNS C1202 or the equivalent. Introduction to the fundamentals of classical Japanese grammar. Trains students to read Japanese historical and literary texts from the early period up to the 20th century.
Prerequisites: advanced calculus and general physics, or the instructors permission. Basic physical processes controlling atmospheric structure: thermodynamics; radiation physics and radiative transfer; principles of atmospheric dynamics; cloud processes; applications to Earths atmospheric general circulation, climatic variations, and the atmospheres of the other planets.
Mathematical genomics synthesizes between high resolution quantitative research and molecular measurements in the context of clinical or biological analysis. This course will provide independent research experience in this field for interested students under the direction of a faculty advisor. This course is suitable for students with background in the subject matter (e.g., biology, chemistry) who wish to learn quantitative data analysis and methods development, as well as for those with technical background (e.g., biomedical informatics) who wish to apply their skills to biological research. Instructor permission is required for registration.
Prerequisites: GREK V1201 and V1202, or their equivalent. Since the content of the course changes from year to year, it may be taken in consecutive years.
Prerequisites: LATN V3012 or the equivalent. Since the content of this course changes from year to year, it may be repeated for credit.
Introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics include basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies.
Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems.
Explores a variety of ethical and political issues that arise during the conduct of basic and clinical scientific research. Course sessions include lectures, discussion periods, and analyses of case studies.
This short course surveys fundamental Microsoft Excel concepts and functionality applicable to SIPA courses and in professional settings. Topics include interacting with spreadsheets, understanding references and functions, writing formulas, building basic models, controlling formatting and presentation and creating basic charts. The course is targeted at students with limited or no prior Excel experience.
This short course surveys fundamental Microsoft Excel concepts and functionality applicable to SIPA courses and in professional settings. Topics include interacting with spreadsheets, understanding references and functions, writing formulas, building basic models, controlling formatting and presentation and creating basic charts. The course is targeted at students with limited or no prior Excel experience.
Engineering economic concepts. Basic spreadsheet analysis and programming skills. Subject to instructor's permission. Infrastructure design and systems concepts, analysis, and design under competing/conflicting objectives, transportation network models, traffic assignments, optimization, and the simplex algorithm.
This seminar course will provide a punctual survey of trends and figures in the experimental cultures of East Central Europe. Formations include the avant-gardes (first, postwar, and postcommunist); experimental Modernisms and Postmodernisms; alternative film, media, and visual culture; and formally inventive responses to exceptional historical circumstances. Proceeding roughly chronologically from early twentieth to early twenty-first centuries, we will examine expressionist/surrealistic painting and drama; zenithist hybrid genres such as cinépoetry and proto-conceptualist writing; mixed-media relief sculpture; post-conceptual art; experimental and animated film; and avant-garde classical music. In terms of theory, we will draw on regional and global approaches to artistic experimentation ranging from Marxist and other theories of value through discourses of the body and sexuality in culture to contemporary affect theory. The course will be taught in English with material drawn primarily from Poland, Yugoslavia, Czechoslovakia, and Hungary. Each session will include a lecture followed by discussion.
Application of industrial ecology to Design for Environment (DFE) of processes and products using environmental indices of resources consumption and pollution loads. Introduction of methodology for Life Cycle Assessment (LCA) of manufactured products. Analysis of several DFE and LCA case studies. Term project required on use of DFE/LCA on a specific product/process: (a) product design complete with materials and process selection, energy consumption, and waste loadings; (b) LCA of an existing industrial or consumer product using a commercially established method.
Course Description
This interdisciplinary course explores both the rights of Indigenous people in settler colonies as well as the complex historical and theoretical relationship between human rights and settler colonialism. We will pursue three lines of inquiry. The first critically explores how central political concepts of the international state system—sovereignty, property, territory, self-determination—entwine the histories of settler colonialism and human rights. The second charts the rise and mechanisms of the international Indigenous rights movement, in particular its activity at the United Nations leading to the Declaration on the Rights of Indigenous Peoples in 2007, and its contributions to ongoing debates on environmental and climate justice, group rights, natural resources and territorial autonomy, and cultural rights. The third unit interrogates settler state responses to the movement for Indigenous human rights, such as cooptation, recognition, and apology.
Through readings drawn from history, ethnography, political and critical theory, international relations, Native studies, law, and documents produced by intergovernmental organizations and NGOs, we will explore and deepen the tensions between human rights as a theory and practice and the political lives and aspirations of Indigenous peoples and activists. What technologies of rule—such as residential school systems and property law—do settler colonial states deploy to dispossess Indigenous peoples? How have Indigenous peoples used the international human rights regime to mobilize against such dispossession? How have these states resisted the global Indigenous rights movement? And can the human rights regime, rooted in the international state system, meaningfully contribute to anticolonial movements in liberal settler colonies? While we will touch on settler colonialism as it manifests around the globe, the course’s geographical focus will be on North America.
Course objectives
Throughout this course, you will:
Develop a historically-informed understanding of both international indigenous rights and settler colonialism as idea, practice, institution, and discourse;
Place the literature on human rights and settler colonialism into critical conversation in order to deepen existing conceptual problems and generate new ones;
Identify the main arguments in theoretical texts, legal and policy documents, and public debates
Prerequisites: Instructor-Managed Waitlist & Course Application.
This short course explores techniques that enable sophisticated problem solving and data analysis in Microsoft Excel. Topics include implementing advanced logic using complex formulas and intermediate calculations; managing complexity with Excel's auditing features; importing, parsing and cleaning raw data; pulling data together using lookup functions; and summarizing and analyzing data with conditional aggregate functions and PivotTables. This course does not focus on specific policy or financial applications, but instead explores general concepts and techniques that can be flexibly applied to different solutions in Excel.
The Business Chinese I course is designed to prepare students to use Chinese in a present or future work situation. Students will develop skills in the practical principles of grammar, vocabulary, and cross-cultural understanding needed in today’s business world.
How do you write literature in the midst of catastrophe? To whom do you write if you don’t know whether your readership will survive? Or that you yourself will survive? How do you theorize society when the social fabric is tearing apart? How do you develop a concept of human rights at a time when mass extermination is deemed legal? How do you write Jewish history when Jewish future seems uncertain?
This course offers a survey of the literature and intellectual history written during World War II (1939-1945) both in Nazi occupied Europe and in the free world, written primarily, but not exclusively, by Jews. We will read novels, poems, science fiction, historical fiction, legal theory and social theory and explore how intellectuals around the world responded to the extermination of European Jewry as it happened and how they changed their understanding of what it means to be a public intellectual, what it means to be Jewish, and what it means to be human.
The aim of the course is threefold. First, it offers a survey of the Jewish experience during WWII, in France, Russia, Poland, Latvia, Romania, Greece, Palestine, Morocco, Iraq, the USSR, Argentina, and the United States. Second, it introduces some of the major contemporary debates in holocaust studies. Finally, it provides a space for a methodological reflection on how literary analysis, cultural studies, and historical research intersect.
This one-day seminar, conducted by the reputable training firm Training The Street, explores best practices and efficient techniques for building finance-related spreadsheets.
The lectures will use a real company as a case study and direct participants to blend accounting, corporate finance, and Excel skills to create a dynamic, three-statement financial model. The completed product has five years of projections, three years of historical data, and supporting schedules, including working capital, debt, equity, depreciation, and amortization.
Other advanced topics include understanding and controlling circularity errors, troubleshooting, sensitivity analysis, and discounted cash flow valuations.
The course is best suited for students with exposure to basic accounting and corporate finance concepts. It stresses efficiency in using Excel and awareness of common pitfalls when developing financial models.
Prerequisites: at least 3 years of intensive Chinese language training at college level and the instructor's permission. This advanced course is designed to specifically train students' listening and speaking skills in both formal and colloquial language through various Chinese media sources. Students view and discuss excerpts of Chinese TV news broadcasts, soap operas, and movie segments on a regular basis. Close reading of newspaper and internet articles and blogs supplements the training of verbal skills.
Prerequisites: Third Year Chinese or the equivalent The course is designed to help students master formal Chinese for professional or academic purposes. It includes reading materials and discussions of selections from Chinese media on contemporary topics, Chinese literature, and modern Chinese intellectual history. The course aims to enhance students' strategies for comprehension, as well as their written and oral communication skills in formal modern Chinese.
Prerequisites: CHNS W4006 or the equivalent. This is a non-consecutive reading course designed for those whose proficiency is above 4th level. See Admission to Language Courses. Selections from contemporary Chinese authors in both traditional and simplified characters with attention to expository, journalistic, and literary styles.
Prerequisites: JPNS W4006 or the equivalent. Sections 1 & 2: Readings of advanced modern literary, historical, political, and journalistic texts, and class discussions about current issues and videos. Exercises in scanning, comprehension, and English translation. Section 3: Designed for advanced students interested in developing skills for reading and comprehending modern Japanese scholarship.