Prerequisites: Any introductory course in linear algebra and any introductory course in statistics are both required. Highly recommended: COMS W4701 or knowledge of Artificial Intelligence.
Topics from generative and discriminative machine learning including least squares methods, support vector machines, kernel methods, neural networks, Gaussian distributions, linear classification, linear regression, maximum likelihood, exponential family distributions, Bayesian networks, Bayesian inference, mixture models, the EM algorithm, graphical models and hidden Markov models. Algorithms implemented in MATLAB.
This course will introduce some of the most fascinating texts of the first eight hundred years of English literature, from the period of Anglo-Saxon rule through the Hundred Years’ War and beyond—roughly, 700–1500 CE. We will proceed by exploring the role of some crucial figures in medieval writing: heroes, lovers, and visionaries. These key players relate in complex ways to the major genres of the Middle Ages, such as epic, romance, and spiritual writing; part of our work will be disentangling these relationships. We’ll hit on some texts you’ve heard of –
Beowulf
and selections from Chaucer’s
Canterbury Tales
– while leaving time for some you may not have encountered – Marie de France’s
Lais
and Margery of Kempe’s
Book
. Along the way, we’ll also hone skills of reading, writing, and oral expression crucial to appreciating and discussing literature in nuanced, supple ways.
If you take this course, you’ll discover how medieval literature is both a mirror and a foil to modern literature. You’ll explore the plurilingual and cross-cultural nature of medieval literary production and improve (or acquire!) your knowledge of Middle English. You’ll discover sources for famous texts, like
King Lear,
and see the posterity of other famous texts, like the
Aeneid.
Plus, you’ll flex your writing muscles with two short textual analyses (2-4 pp.) and one longer research paper (8-10pp).
Prerequisites: (ELEN E3801)
Digital filtering in time and frequency domain, including properties of discrete-time signals and systems, sampling theory, transform analysis, system structures, IIR and FIR filter design techniques, the discrete Fourier transform, fast Fourier transforms.
This course engages with approaches from anthropology, geography, and indigenous studies to analyze contemporary urban transitions on the Tibetan plateau.
Religious claims to political power are a global phenomenon, and Tibetan Buddhism once offered a divine means to power and legitimacy to rule. This class will explore the intersection of politics, religion, and art in Tibetan Buddhism--the force of religion to claim political power. Images were one of the primary means of political propagation, integral to magical tantric rites, and embodiments of power.
The European novel in the era of its cultural dominance. Key concerns: the modern metropolis (London, Paris, St. Petersburg); the figures of bourgeois narrative (
parvenus
, adulterers, adolescents, consumers) and bourgeois consciousness (nostalgia,
ressentiment
, sentimentalism, ennui); the impact of journalism, science, economics. Authors to be drawn from: Goethe, Stendhal, Balzac, Dickens, Tolstoy, Dostoevsky, Flaubert, Turgenev, Zola.
Prerequisites: (CSEE W3827) or a half semester introduction to digital logic, or the equivalent.
An introduction to modern digital system design. Advanced topics in digital logic: controller synthesis (Mealy and Moore machines); adders and multipliers; structured logic blocks (PLDs, PALs, ROMs); iterative circuits. Modern design methodology: register transfer level modelling (RTL); algorithmic state machines (ASMs); introduction to hardware description languages (VHDL or Verilog); system-level modelling and simulation; design examples.
Prerequisites: (CSEE W3827) or equivalent.
Focuses on advanced topics in computer architecture, illustrated by case studies from classic and modern processors. Fundamentals of quantitative analysis. Pipelining. Memory hierarchy design. Instruction-level and thread-level parallelism. Data-level parallelism and graphics processing units. Multiprocessors. Cache coherence. Interconnection networks. Multi-core processors and systems-on-chip. Platform architectures for embedded, mobile, and cloud computing.
Prerequisites: introductory biology or chemistry, or the instructor's permission.
Analysis of modern wetland dynamics and the important ecological, biogeochemical, and hydrological functions taking place in marshes, bogs, fens, and swamps, with a field emphasis. Wetlands as fossil repositories, the paleoenvironmental history they provide, and their role in the carbon cycle. Current wetland destruction, remediation attempts, and valuation. Laboratory analysis and field trips.
A recent American newspaper headline announced that China has become “the most materialistic country the world.” Globally circulating narratives often interpret Chinese consumers’ demand for commodities as an attempt to fill a void left by the absence of the Maoist state, traditional religious life, and Western-style democracy. But things aren’t as simple as they appear. This course explores the intertwined questions of “Chinese” desire and the desire for China. Avoiding reductionist understandings of desire as either a universal natural human attribute or a particular Chinese cultural trait, we will track the production and management of desire within a complex global field. Drawing on ethnographies, films, short stories, and psychoanalytic and postcolonial theory, this course will explore the shifting figure of desire across the Maoist and post-Maoist eras by examining how academics, government officials, intellectuals, and artists have represented Chinese needs, wants and fantasies. From state leaders’ attempts to improve the “quality” of the country’s population to citizens’ dreams of home ownership, from sexualized desire to hunger for food, drugs and other commodities, we will attend to the continuities and disjunctures of recent Chinese history by tracking how desire in China has been conceptualized and refracted through local and global encounters.
Prerequisites: ECON UN3211 and ECON UN3213 and STAT UN1201
Standard economic theory seeks to explain human behavior (especially in "economic" settings, such as markets) in terms of rational choice, which means that the choices that are made can be predicted on the basis of what would best serve some coherent objective, under an objectively correct understanding of the predictable consequences of alternative actions. Observed behavior often seems difficult to reconcile with a strong form of this theory, even if incentives clearly have some influence on behavior; and the course will discuss empirical evidence (both from laboratory experiments and observations "in the field") for some well-established "anomalies." But beyond simply cataloguing anomalies for the standard theory, the course will consider the extent to which departures from a strong version of rational choice theory can be understood as reflecting cognitive processes that are also evident in other domains such as sensory perception; examples from visual perception will receive particular attention. And in addition to describing what is known about how the underlying mechanisms work (something that is understood in more detail in sensory contexts than in the case of value-based decision making), the course will consider the extent to which such mechanisms --- while "suboptimal" from a normative standpoint that treats perfect knowledge of one's situation as costless and automatic --- might actually represent efficient uses of the limited information and bounded information-processing resources available to actual people (or other organisms). Thus the course will consider both ways in which the realism of economic analysis may be improved by taking into account cognitive processes, and ways in which understanding of cognitive processes might be advanced by considering the "economic" problem of efficient use of limited (cognitive) resources.
Prerequisites: (COMS W3157) and (CSEE W3827)
Design and programming of System-on-Chip (SoC) platforms. Topics include: overview of technology and economic trends, methodologies and supporting CAD tools for system-level design, models of computation, the SystemC language, transaction-level modeling, software simulation and virtual platforms, hardware-software partitioning, high-level synthesis, system programming and device drivers, on-chip communication, memory organization, power management and optimization, integration of programmable processor cores and specialized accelerators. Case studies of modern SoC platforms for various classes of applications.
China’s transformation under its last imperial rulers, with special emphasis on economic, legal, political, and cultural change.
This course covers image formation, methods of analysis, and representation of digital images. Measures of qualitative performance in the context of clinical imaging. Algorithms fundamental to the construction of medical images via methods of computed tomography, magnetic resonance, and ultrasound. Algorithms and methods for the enhancement and quantification of specific features of clinical importance in each of these modalities.
This course is 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.
This course is 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 instructor's permission.
Topics chosen in consultation between members of the staff and students.
(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.
For 4 pts. credit, term paper required. This course is required for all applied mathematics majors in the senior year. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studies per term.
This course is 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.
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.
Prerequisites: four years of college Russian or the equivalent.
Workshop in literary translation from Russian into English focusing on the practical problems of the craft. Each student submits a translation of a literary text for group study and criticism. The aim is to produce translations of publishable quality.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in microeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in macroeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in macroeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in macroeconomics. Selected topics will be posted on the department's webpage.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 Registration information is posted on the department's Seminar Sign-up webpage.
Selected topics in macroeconomics. Selected topics will be posted on the department's 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.
Based upon the most current understanding of our planet and our impact on it and how we make decisions about the threats we face, a new knowledge-based "green" framework is developed for our relationship to our planet and to each other as well as its general implications for human stewardship of our planet and meeting the needs of 8 billion humans. This new framework is explored using case studies, class participation, and term papers on specific current scientific and policy issues like global warming, renewable energy, carbon dioxide removal and their impact on the sustainability and resilience of our planet and ourselves.
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.
This course introduces students to the emerging methodologies that combine geographic information systems (GIS) with historical thinking. Students will study and evaluate the benefits and limitations of key works in historical GIS, become familiar with basic principles of cartographic design, and learn technical skills to create their own HGIS project.
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.
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: course in solid earth geology or geophysics; solid background in math and physics
Development of a comprehensive understanding of deformation and evolution of Earth's surface through cross-disciplinary analysis of the plate-tectonic cycle. Topics include the thermal and chemical evolution of mid-ocean ridges, the deep-ocean basins, subduction zones, continental rifts and collisions, and hot spots; driving forces of plate motion and mantle convection; magmatism and volcanism; and faulting and earthquakes. Emphasizes integration of geophysical, geological and geochemical observations and processes, with a particular focus on observations from the ocean basins.
,
Prerequisites: (EAEE E4901) and (EAEE E4003) and (CIEE E4252) or EAEE E4901, E4003, CIEE E4252 or the instructor's approval.
Qualitative and quantitative considerations in engineered environmental biochemical processes. Characterization of multiple microbial reactions in a community and techniques for determining associated kinetic and stoichiometric parameters. Engineering design of several bioreactor configurations employed for biochemical waste treatment. Mathematical modeling of engineered biological reactors using state-of-the-art simulation packages.
Prerequisites: the instructor's 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.
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 we'll 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 course highlights the process of diversification of platforms, forms, and voices through which film, television, and the internet have taken part in what might perhaps be called the most democratic period in the history of this highly unequal Southern country. The idea is to discuss the diversification of the audio-visual scene, and the emergence of new political and social cultural voices in a process that started in the mid-eighties, and that has intensified, with the advent of cable television, the internet, YouTube, VOD, and with the emergence of specific public policies to finance film.
Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.
This course 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.
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.
This is a required course for undergraduate students majoring in OR:EMS.
Focus on the management and consequences of technology-based innovation. Explores how new industries are created, how existing industries can be transformed by new technologies, the linkages between technological development and the creation of wealth and the management challenges of pursuing strategic innovation.