Prerequisite(s): Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Required for, and can be taken only by, all applied mathematics majors in the junior year. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operation research, etc.
Required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly.
Prerequisites: the instructors permission. Topics chosen in consultation between members of the staff and students.
Prerequisites: Approval by a faculty member who agrees to supervise the work. A second-level independent project involving laboratory work, computer programming, analytical investigation, or engineering design. May be repeated for credit, but not for a total of more than 3 points of degree credit. Consult the department for section assignment.
Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 4900 to 4909.
(Lecture). A survey of the history of the English language from before Old English to 21st Century Modern English, with no background in linguistics required. Grammar, dialectal variety, and social history will be covered to roughly equal extents. Requirements include three examinations, one of them an extended take-home exercise. Lecture format with some discussion depending on the topic.
Required for all applied mathematics majors in the senior year. Term paper required. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studied per term.
Required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly.
Prerequisites: LING UN3101 Syntax - the combination of words - has been at the center of the Chomskyan revolution in Linguistics. This is a technical course which examines modern formal theories of syntax, focusing on later versions of generative syntax (Government and Binding) with secondary attention to alternative models (HPSG, Categorial Grammar).
For more than forty years, second language acquisition (SLA) has been emerging as an independent field of inquiry with its own research agenda and theoretical paradigms. The study of SLA is inherently interdisciplinary, as it draws on scholarship from the fields of linguistics, psychology, education, and sociology. This course explores how Chinese is acquired by non-native speakers. Students will learn about general phenomena and patterns during the process of acquiring a new language. They will become familiar with important core concepts, theoretical frameworks, and research practices of the field of SLA, with Chinese as the linguistic focus.
This advanced seminar examines materialist conceptions of labor and life as approached through feminist, black, anti-racist, indigenous, queer, postcolonial, and Marxist perspectives. We will trace the ways that labor and life as well as their constitutive relations have been understood in historical and contemporary radical critiques of capitalism, with a focus on gender, race and sexuality as analytical categories for understanding their shifting roles in structures and practices of social reproduction, the production and expropriation of value, the logic and exercise of violence, the organization of sociality and culture, and the practice and imagination of freedom, justice, and new forms and potentials of collective existence. Finally, we will consider the limits and possibilities of different conceptions of “material life” for understanding politics today.
Prerequisites: introductory biology sequence, including organismal biology. A survey of vascular plants with emphasis on features of greatest utility in identifying plants in the field to the family level. This will be coupled with a survey of the major plant communities of northeastern North America and the characteristic species found in each. The course will consist of one lecture and one laboratory per week with several lab sessions extended to accommodate field trips to local and regional natural areas.
Advanced Turkish I is designed to use authentic Turkish materials around projects that are chosen by the student in a research seminar format where students conduct their own research and share it in class in a friendly atmosphere. No P/D/F or R credit is allowed for this class.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Selected topics in microeconomics.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the departments Seminar Sign-up webpage. Selected topics in macroeconomics. Selected topics will be posted on the departments webpage.
The course will explore the often-contested terrain of urban contexts, looking at cities fron architectural, sociological, historical, and political positions. What do rights have to do with the city? Can the ancient idea of a right to the city tell us something fundamental about both rights and cities? Our notion of citizenship is based in the understanding of a city as a community, and yet today why do millions of people live in cities without citizenship? The course will be organized thematically in order to discuss such issues as the consequences of cities developments in relation to their peripheries beginning with the normative idea of urban boundaries deriving from fortifying walls, debates around the public sphere, nomadic architecture and urbanism, informal settlements such as slums and shantytowns, surveillance and control in urban centers, refugees and the places they live, catastrophes natural and man-made and reconstruction, and sovereign areas within cities the United Nations, War Crimes Tribunals. At the heart of our inquiry will be an investigation of the ways in which rights within urban contexts are either granted or withheld.
An advanced film theory "workshop" in which we shall avoid reading film theory in favor of a selection of other texts, taken mainly from the domains of art history, philosophy, and literature. Our central question will be: What can we, who have grown up in the age of cinema and digital media, learn from discourses about vision and its relation to narrative that pre-date the cinema, or that consider the cinema only marginally? In this course, we shall begin to approach some of the major topics of contemporary film theory -- narrativity, subject-construction, the relation of words to images -- through the lens of texts that have remained largely outside the network of citations and references we normally associate with the work of professional media theory. We might begin the groundwork for an "opening up" or critique of some of the blind spots of current theory; at the very least, we shall be reading works that challenge our usual ways of theorizing.
Prerequisites: Recommended preparation: a solid background in mathematics, physics, and chemistry. Physical properties of seawater, water masses and their distribution, sea-air interaction influence on the ocean structure, basic ocean circulation pattern, relation of diffusion and advection with respect to distribution of ocean properties, ocean tides and waves, turbulence, and introduction to ocean dynamics.
Intended for junior and senior undergraduate and graduate students interested in gaining hands-on experience in biopharmaceutical processing. Processes and unit operations applied widely in the biopharmaceutical industry, including tableting, dissolution, disintegration, fermentation, chromatography, tangential flow filtration, mixing, and crystallization. Process parameters, chemical and molecular properties, process performance, and product attributes. Includes a combination of lectures (given during lab time), experiments, and report writing.
Fundamentals of human brain imaging is a new advanced course open to undergraduates students from the Psychology, Neuroscience, Engineering, and Statistics Departments, that traces the key steps of the recent “neuroimaging revolution”, and introduces the various methodologies and associated analytic approaches that are now available in the field of cognitive neuroscience. Specifically, the course develops around three main questions, currently under-represented in our undergraduate curriculum:
1) What is the advantage to study human cognition using correlational methodologies (e.g., EEG, MEG, fMRI)? 2) Which is the particular contribution of each method in the understanding of brain/behavior relationship? 3) Which are the most common ways to approach the analyze the neuroimaging data?
By promoting an inclusive environment and implementing active learning strategies, this course stimulates critical thinking and fosters collaboration among students from different departments.
This seminar serves as an introduction to the British literature and culture of the long eighteenth century through the lens of the medical humanities. In the period roughly defined as 1688-1815, the progress of medicine was shaped by a new strain of Enlightenment thinking, which held that reason and empiricism could lead to accurate scientific knowledge about the body. Yet the period also saw the lingering presence of other ways of knowing about fundamental bodily concepts, like illness, disease, health, and disability—from the humors of Galenic medicine to the notion of maternal imagination, which explained how a woman could give birth to rabbits. This course explores the collision of medical epistemologies in this period of change by reading eighteenth-century novels, poetry, drama, memoirs, and medical writing. Literary writers were deeply engaged in the period’s medical discoveries, and their writing served as a testing-ground for working out ideas about the competing roles of bodies in the complex sociocultural world of the eighteenth century. In reading works by authors such as Molière, Frances Burney, Daniel Defoe, Olaudah Equiano, Mary Wortley Montagu, Laurence Sterne, and Mary Wollstonecraft, we will also study medical topics, including the history of epidemic and inoculation; sexuality, pregnancy and disease; humoral theories of the body and of satire; the patient’s narrative; and the rise of autopsy and the clinical gaze. Ultimately, the course traces how “wonder becomes error,” in Rosemarie Garland Thomson’s terms, as Enlightenment literature “moves from a narrative of the marvelous to a narrative of the deviant.” The seminar will particularly suit students who are interested in British literature, literature pre-1800, and the medical humanities. To apply, write to the instructor with a brief statement of interest.
Science and technology of conventional and advanced microfabrication techniques for electronics, integrated and discrete components. Topics include diffusion; ion implantation, thin-film growth including oxides and metals, molecular beam and liquid-phase epitaxy; optical and advanced lithography; and plasma and wet etching.
Prerequisites: the instructors permission. Please e-mail the instructor at bc14@columbia.edu. This course will examine the tension between two contradictory trends in world politics. On the one hand, we have emerged from a century that has seen some of the most brutal practices ever perpetrated by states against their populations in the form of genocide, systematic torture, mass murder and ethnic cleansing. Many of these abuses occurred after the Holocaust, even though the mantra never again was viewed by many as a pledge never to allow a repeat of these practices. Events in the new century suggest that these trends will not end anytime soon. At the same time, since the middle of the twentieth century, for the first time in human history there has been a growing global consensus that all individuals are entitled to at least some level of protection from abuse by their governments. This concept of human rights has been institutionalized through international law, diplomacy, international discourse, transnational activism, and the foreign policies of many states. Over the past two decades, international organizations, non-governmental organizations, and international tribunals have gone further than any institutions in human history to try to stem state abuses. This seminar will try to make sense of these contradictions.
This class is designed for the beginner student to gain working level knowledge of basic Spanish vocabulary, verb conjugation, and medical terminology for use in a clinical setting. In addition to short lectures to facilitate grammar and usage patterns, class time will be used for intensive speaking practice to improve pronunciation, enhance comprehension, and build confidence in using Spanish through the use of hypothetical scenarios, student presentations, and small group discussions to improve Spanish language and Spanish language proficiency.
The rapid democratization of technology has led to a new wave of immersive storytelling that spills off screens into the real world and back again. These works defy traditional constraints as they shift away from a one-to-many to a many-to-many paradigm, transforming those formerly known as the audience from passive viewers into storytellers in their own right. New opportunities and limitations offered by emergent technologies are augmenting the grammar of storytelling, as creators wrestle with an ever-shifting digital landscape. New Media Art pulls back the curtain on transmedial works of fiction, non-fiction, and emergent forms that defy definition. Throughout the semester well explore projects that utilize Artificial Intelligence, Virtual Reality, Augmented Reality and the Internet of Things, alongside a heavy-hitting selection of new media thinkers, theorists, and critics. The course will be co-taught as a dialogue between artistic practice and new media theory. Lance Weiler, a new media artist and founder of Columbia’s Digital Storytelling Lab, selected the media artworks; Rob King, a film and media historian, selected the scholarly readings. It is in the interaction between these two perspectives that the course will explore the parameters of emerging frontiers in media art and the challenges these pose for existing critical vocabularies.
This class is designed for the intermediate student to gain a more advanced level knowledge of Spanish vocabulary, verb conjugation, and medical terminology for use in a clinical setting. In addition to short lectures to facilitate grammar and usage patterns, class time will be used for intensive speaking practice to improve pronunciation, enhance comprehension, and build confidence in using Spanish through the use of hypothetical scenarios, student presentations, and small group discussions to improve Spanish language and Spanish language proficiency.
This course introduces undergraduate and graduate students to the materials, techniques, contexts, and meanings of skilled craft and artistic practices in early modern Europe (1350-1750), in order to reflect upon a series of topics, including craft knowledge and artisanal epistemology; the intersections between craft and science; and questions of historical methodology in reconstructing the material world of the past. The course will be run as a “Laboratory Seminar,” with discussions of primary and secondary materials, as well as hands-on work in a laboratory. The first semester long course to use the published Edition of Fr. 640 as its focus, it will test the use of the Edition in a higher education classroom to inform the development of the Companion. This course is associated with the Making and Knowing Project of the Center for Science and Society at Columbia University.The first semester-long course to use the published Edition of Fr. 640 as its focus, it will test the use of the Edition in a higher education classroom to inform the development of Phase II of the Making and Knowing Project - a Research and Teaching Companion. Students’ final projects (exploratory and experimental work in the form of digital/textual analysis of Ms. Fr. 640, reconstruction insight reports, videos for the Companion, or a combination) will be published as part of the Companion or the Sandbox depending on content and long-term maintenance considerations.
The term 'gendercide' highlights a range of distinct and specific forms of violence executed against human beings based on their own gender self-identification as well as patriarchal assumptions about their gender. In this course, we will examine research discerning, movements challenging, and the adjudication, and/or lack thereof, of Gender Based Violence (GBV) in several major categories traversing spatial, temporal, and ideological contexts, including: reproductive rights and health; trafficking and migration; and disaster and pandemics. It is critical to: interrogate the ideologies that drive and sustain GBV; examine in detail the harm it presents to human beings; explore what can be done to protect the security of those experiencing GBV; and to think about measures of prevention to guard additional human beings from experiencing it. The heart of the course will involve an intersectional analysis of specific case studies; highlighting the GBV associated with each case; examining the impact of GBV on human rights; and how GBV has been addressed in society. The close study of each case will assist students in illuminating intricacies, complexities, and challenges to human security in specific contexts.
May be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, biological sciences, and other fields. Examples of topics include multi-scale analysis and Applied Harmonic Analysis.
May be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, biological sciences, and other fields. Examples of topics include multi-scale analysis and Applied Harmonic Analysis.
Research Course for Master's Students.
Research Course for Master's Students.
Research Course for Master's Students.
This course approaches Jewish Studies from theoretical and pedagogical standpoints. In addition to looking back at ancient, medieval and Early Modern approaches to the study of Jewish topics and examining the theoretical, historical and religious underpinnings of Jewish Studies as a modern discipline, we will also read theoretical writings from related disciplines. The course will balance these materials with pedagogical materials and exercises. Faculty from disciplines related to Jewish Studies will visit the seminar to offer perspectives on current approaches to the field, and the class will visit the Rare Book and Manuscript Library with Jewish Studies Librarian Michelle Chesner. This course is required for students in the Jewish Studies MA program. It is open to graduate students, and advanced undergraduates may register with permission from the instructor. Please note that faculty visits will be added to the syllabus as they are scheduled.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: Instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment.
Prerequisites: the director of undergraduate studies permission. Provides students with the experience of participating in the research process by matching them to a faculty mentor who will put them to work on one of his or her current research projects. A list of available research positions is distributed each semester on the major listserv.
Prerequisites: the director of undergraduate studies permission.
May be repeated for credit, but no more than 3 total points may be used for degree credit. Substantial independent project involving laboratory work, computer programming, analytical investigation, or engineering design.