Prerequisites: Open to majors who have fulfilled basic major requirements or written permission of the staff member who will supervise the project. Specialized reading and research projects planned in consultation with members of the Asian and Middle Eastern Cultures teaching staff.
Provides work experience on chemical engineering in relevant intern or fieldwork experience as part of their program of study as determined by the instructor. Written application must be made prior to registration outlining proposed internship/study program. A written report describing the experience and how it relates to the chemical engineering core curriculum is required. Employer feedback on student performance and the quality of the report are the basis of the grade. This course may not be taken for pass/fail or audited. May not be used as a technical or nontechnical elective. May be repeated for credit, but no more than 3 points total of CHEN E3999 may be used for degree credit.
CEEM undergraduate students only. Written application must be made prior to registration outlining proposed internship/study program. Final reports required. May not be taken for pass/fail credit or audited. International students must also consult with the International Students and Scholars Office.
Introduces students to research and writing techniques and requires the preparation of a senior thesis proposal. Required for majors and concentrators in the East Asian studies major in the spring term of the junior year.
Prerequisites: Permission of the chair required. Does not provide major credit. Advanced projects for students who have adequate backgrounds to work independently with guidance from a member of the faculty.
Application required:
https://english.barnard.edu/english/independent-studies
. Senior majors who wish to substitute Independent Study for one of the two required senior seminars should consult the chair. Permission is given rarely and only to students who present a clear and well-defined topic of study, who have a department sponsor, and who submit their proposals well in advance of the semester in which they will register. There is no independent study for screenwriting or film production.
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.
INDEPENDENT STUDY
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.
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.
History and development of aviation and spaceflight; application of fundamental physics to analyze atmospheric and space flight; core principles of aerodynamics, propulsion, and flight mechanics; basic aircraft performance and stability characteristics; influence of space and atmospheric environment on vehicles; key lightweight materials and structural design considerations in aerospace applications. Course intended for graduate students. Students who have previously taken AERO E3001 may not take AERO E4001.
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.
This course offers a comprehensive introduction to the core computational methods driving modern biomedical research and health data science. As biological and clinical datasets grow in scale and complexity—from genomic sequences and molecular profiles to electronic health records (EHRs) and consumer health data—this course equips students with the essential computational foundations to model, analyze, and interpret high-dimensional biomedical data.
Organized around key algorithmic challenges spanning Clinical Informatics, Consumer Health Informatics, and Bioinformatics, the course focuses on the design and application of algorithms and statistical models to solve real-world biomedical problems. Lectures emphasize practical techniques and showcase their use across diverse biomedical data types.
Designed for advanced undergraduates and graduate students in biomedical informatics, computer science, biomedical engineering, applied mathematics, and related fields, this course builds a rigorous understanding of computational biomedicine. It serves as a core requirement for the Biomedical Informatics PhD and master’s programs and is cross-listed with Computer Science. Students interested in careers in bioinformatics, health data science, computational biology, or biomedical AI will find this course especially valuable.
As biomedical data continue to expand in size, diversity, and impact, this course provides a critical foundation in the algorithmic, statistical, and computational tools needed to advance the future of research at the intersection of computation and human health.
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.
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.
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 course is an advanced seminar that will review current knowledge about the computation carried out by microcircuits present in the mammalian CNS. This year the seminar will focus on dendritic integration and in the function of dendritic spines. The class will run as a seminar discussion, where it is assumed that every student will have studied the reading material ahead of time and will be knowledgeable enough to explain it. Students should expect a minimum of 9 hours of work / week (classroom + work at home combined).
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.
A close reading of works by Dostoevsky (Netochka Nezvanova; The Idiot; A Gentle Creature) and Tolstoy (Childhood, Boyhood, Youth; Family Happiness; Anna Karenina; The Kreutzer Sonata) in conjunction with related English novels (Bronte's Jane Eyre, Eliot's Middlemarch, Woolf's Mrs. Dalloway). No knowledge of Russian is required.
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
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.
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.
This seminar examines the many meanings of food in Italian culture and tradition; how values and peculiarities are transmitted, preserved, reinvented and rethought through a lens that is internationally known as ;Made in Italy;; how the symbolic meanings and ideological interpretations are connected to creation, production, presentation, distribution, and consumption of food. Based on an anthropological perspective and framework, this interdisciplinary course will analyze ways in which we can understand the Italian taste through the intersections of many different levels: political, economic, aesthetic, symbolic, religious, etc. The course will study how food can help us understand the ways in which tradition and innovation, creativity and technology, localism and globalization, identity and diversity, power and body, are elaborated and interpreted in contemporary Italian society, in relation to the European context and a globalized world. Short videos that can be watched on the computer and alternative readings for those fluent in Italian will be assigned. In English.
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.
This course offers an overview of twentieth-century literary modernism through the lens of the Harlem Renaissance, a movement of Black artistic and intellectual flourishing loosely concentrated in New York City. Formal innovation, explorations of interiority, the autonomy of the artist, and political radicalism were all hallmarks of the works of Black Americans in the 1920s and 1930s, as they similarly came to define those of artists across the U.K. and Europe. We will begin by foregrounding the emergence of the Harlem Renaissance, reading manifestos, retrospective overviews, and signal texts of the period. In what ways—either complementary or competing—did Black artists conceptualize cultural modernity and political legibility? How did Black women understand themselves within these fraught, often masculine frameworks? We will then turn our attention abroad to consider surprising resonances between such authors as Nella Larsen and Virginia Woolf; Langston Hughes and T.S. Eliot; Wallace Thurman and James Joyce. In the final third of the semester, we will discuss continuities and departures between the Harlem Renaissance and the
Négritude
movement in Paris, a city sometimes referred to as the capital of the Black Atlantic. The course ultimately invites students to think about modernist literatures from a transatlantic, multiracial, and diasporic perspective, appreciating similarities without glossing over important points of tension and conflict.
What was History in the Renaissance? This class tries to answer this question by focusing on three great historians and political philosophers of the fifteenth and sixteenth century: Leonardo Bruni, Niccolò Machiavelli, and Francesco Guicciardini. Analyzing their local and peninsular histories, we will learn how Renaissance scholars read, learned from, and rewrote Greek and especially Roman History. We will dive into Bruni’s reading of Florence’s distant and recent past, including historical events discussed in Dante’s
Divine Comedy
. Also, we will learn how Machiavelli transformed his reading of Livy in a laboratory to understand the tragic events of Renaissance Italy, and how Guicciardini narrates and analyzes contemporary Italian history. Dialoguing with Renaissance Historians, we will learn how creative and problematic is the reading of the past for the understanding of the present. We will discuss the many functions of History and reflect upon big ideas such as fortune, virtue, tyranny, freedom, and truth.
In English.
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.