Prerequisites: STAT GU4204 or the equivalent. STAT GU4205 is recommended. Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering. This is a core course in the MS program in mathematical finance.
Prerequisites: STAT GU4203. STAT GU4207 is recommended. Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
Prerequisites: STAT GU4264. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates. This is a core course in the MS program in mathematical finance.
Can the words “trauma” and “pleasure” be put in the same sentence? If trauma epitomizes suffering and pleasure represents enjoyment, is there any relation between these experiences? And yet, how else to explain that people seem endlessly addicted to negative experiences, or that traumatized people often try to recreate the damage they endured?
We are living in an age of endless trauma, and everywhere we go, we hear that trauma is destructive, anathema to pleasure, that it destroys our sense of self, our security, our stability, and identity. We are taught to avoid trauma at all costs because it is harmful and inimical to flourishing. New statistics routinely confirm that we are living through a trauma epidemic in which ordinary people experience symptoms of extreme distress, flashbacks, intrusive thoughts, nightmares, and difficulty sleeping. Every year, new memoirs are published in which protagonists detail their endless battles with traumatic adversity and most television shows, across a variety of genres, include trauma as a subplot to character development (
Ted Lasso
,
Euphoria
,
True Detective
, to name a few). Referring to its growing pervasiveness, the
New Yorker
critic Parul Sehgal wrote a controversial essay, “The Case Against the Trauma Plot” (2021) in which she criticizes our culture’s overreliance on trauma as a primary trope of character development, forcing us to ask: is trauma really as widespread as we think? how did trauma become such a popular ‘identity’? what work is trauma doing for us, as individuals and as a culture? Is it possible to recognize the ubiquity of trauma while also acknowledging that we often seek situations which are harmful, even traumatizing, that we might be attracted to suffering for reasons we don’t yet understand?
This course examines the complex relationship between trauma and pleasure by familiarizing students with the clinical and theoretical concepts at the core of contemporary trauma and critical theory. We will focus specifically on the topics of: sexuality, perversion, trauma, identity, relationality, narcissism, gender and attachment in order to explore how these concepts work today. Delving into theoretical writing by Foucault, Bersani, Edelman, Berlant, Butler, Dean and Preciado, as well as clinical writing by major psychoanalysts, Freud, Laplanche, Loewald, Lacan, Laplanche and Winnicott, we will redefine contemporary debates by exploring their clinica
Narrative competence is a crucial dimension of health-care delivery, the capacity to attend and respond to stories of illness, and the narrative skills to reflect critically on the scene of care and its contexts. Narrative Medicine explores and builds the clinical applications of literary knowledge.
The objectives of this foundations course include furthering close reading skills, and exploring theories of self-telling and relationality. At the center of this project is the medical encounter. In examining the complexities of this exchange, to help clinicians to fulfill their "receiving" duties more effectively, we will turn to narrative theory, autobiographical theory, psychoanalytic theory, trauma scholarship and witnessing literature. Classwork integrates didactic and experiential methodologies to develop a heightened awareness of self and others and build a practical set of narrative competencies.
Readings will include works by Toni Morrison, W.G. Sebald, Lucy Grealy, Kazuo Ishiguro, Alison Bechdel, Arthur Frank, Paul Ricoeur, Jonathan Shay and Jens Brockmeier.
Prerequisites: ECON UN3211 and ECON UN3213 and STAT UN1201 An introduction to the economics principles underlying the financial decisions of firms. The topics covered include bond and stock valuations, capital budgeting, dividend policy, market efficiency, risk valuation, and risk management. For information regarding REGISTRATION for this course, go to: http://econ.columbia.edu/registration-information.
Prerequisites: PSYC UN1001 or equivalent introductory psychology course What is curiosity and how do we study it? How does curiosity facilitate learning? This course will explore the various conceptual and methodological approaches to studying curiosity and curiosity-driven learning, including animal and human studies of brain and behavior.
Prerequisites: STAT GU4205 and at least one statistics course numbered between GU4221 and GU4261. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and non-standard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.
What did it mean to be queer in the francophone Middle Ages? Was there such a thing? The term ‘sodomy’ was used in the period to describe a wide variety of acts (not all sexual), and the term would seem to foreclose the possibility of female same-sex eroticism. In an era in which all non-procreative sex was conceived as sinful, does the opposition between homosexual and heterosexual still hold? Was male and female homosexuality conceived symmetrically? Topics include the construction of gender (binary vs. spectral, natural vs. cultural), gender variance (transgender and nonbinary people), sodomy and the contours of “sex,” and sadomasochism. Our readings will take us through a broad range of genres—from penance manuals to lyric poetry to romance. Texts include selected
lais
by Marie de France, troubadour songs, Alan of Lille’s
Plaint of Nature
, the
Roman d’Enéas
(a medieval French rewriting of the
Aeneid
that makes Aeneas gay), Heldris of Cornwall’s
Le Roman de Silence
and selected saints’ lives. Class taught in English, although some readings may be available only in modern French translation (reading knowledge of French required).
Latina/o/x populations constitute over 19% of the U.S. population as of 2020, one of the fastest
growing groups in the U.S. with a long and rich history in the U.S while maintaining transnational ties.
In this course students are invited to critically analyze the social histories of and contemporary
experiences of a diverse range of Latino/a/x populations from across the Americas. Over the course of
the semester, we will discuss how Latino/a/x populations come to reside in and transform New York
City, how Latina/o/x populations contend with everyday life and, how they shape and reshape the
communities they resettle in. Although the focus is on New York City, we will also examine the
movement of peoples from the Caribbean and Latin America. Topics include histories of migration,
labor recruitment, citizenship, coloniality and racialization, neoliberalism and the rise of
financialization in NYC, environmental racism, community formation and Latino/a/x political
activism. We will critically examine a variety of text and genres ranging from anthropological,
historical, poetry, documentary, films, media, and art to shift away from homogeneous categorization
of Latino/a/x populations to understanding populations as dynamic and complex. Students are
invited to bring their stories to class as this is a collaborative learning environment.
Programming experience in Python extremely useful. Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODEs. All programming exercises will be in Python.
Overview of properties and interactions of static electric and magnetic fields. Study of phenomena of time dependent electric and magnetic fields including induction, waves, and radiation as well as special relativity. Applications are emphasized.
Prerequisites: four semesters of biology with a firm foundation in molecular and cellular biology. Introduces students to the current understanding of human diseases, novel therapeutic approaches and drug development process. Selected topics will be covered in order to give students a feeling of the field of biotechnology in health science. This course also aims to strengthen students’ skills in literature comprehension and critical thinking.
Ordinary differential equations including Laplace transforms. Reactor Design. An introduction to process control applied to chemical engineering through lecture and laboratory. Concepts include the dynamic behavior of chemical engineering systems, feedback control, controller tuning, and process stability.
Introduction to natural and anthropogenic carbon cycle, and carbon - climate. Rationale and need to manage carbon and tools with which to do so (basic science, psychology, economics and policy background, negotiations - society; emphasis on interdisciplinary and inter-dependent approach). Simple carbon emission model to estimate the impacts of a specific intervention with regards to national, per capita and global emissions. Student-led case studies (e.g. reforestation, biofuels, CCS, efficiency, alternative energy) to illustrate necessary systems approach required to tackle global challenges.
This course examines the historical and theoretical issues concerning the representation of African Americans in film and media. The course will provide a historical overview while focusing on key themes, concepts, and texts.
This course seeks to build upon (or expand) skills learned in sculpture I. This workshop based course allows students more access to the shops to continue to develop those introductory skills while focusing on specific materials and processes. In this course students will complete one self directed project and a number of inclass short assignments and exercises providing a greater exposure to sculptural practice and processes. Acting as both a bridge to and support for more advanced inquiry into making.
Prerequisites: completion of three years of modern Chinese at least, or four years of Japanese or Korean.
This course is intended to provide a quantitative introduction to storage of carbon derived from greenhouse gases, mainly CO2, with a focus on geological carbon storage and mineralization in saline aquifers, depleted hydrocarbon reservoirs, and “reactive” subsurface formations (rocks rich in Fe, Ca, and Mg) as well and other natural and engineered storage reservoirs (e.g., terrestrial storage, ocean storage, building materials). Course modules cover fundamental processes such as geochemical fluid-rock interactions and fluid flow, transport, and trapping of supercritical and/or dissolved CO2 in the context of pore-scale properties to field-scale example storage reservoirs and specific integrative problems such as reservoir characterization and modeling techniques, estimating storage capacity, and regulations and monitoring.
Prerequisites: ECON UN3211 and ECON UN3213 Empirical findings on economic development, theoretical development models; problems of efficient resource allocation in a growing economy; balanced and unbalanced growth in closed and open economic systems; the role of capital accumulation and innovation in economic growth.
This course examines the historical and theoretical issues concerning the representation of African Americans in film and media. The course will provide a historical overview while focusing on key themes, concepts, and texts.
General experimental techniques in materials science, including X-ray diffraction, scanning electron microscopies, atomic force microscopy, materials synthesis and thermodynamics, characterization of material properties (mechanical, electrochemical, magnetic, electronic). Additional experiments at discretion of instructor.
Biomechanics of orthopaedic soft tissues (cartilage, tendon, ligament, meniscus, etc.). Basic and advanced viscoelasticity applied to the muscoskeletal system. Topics include mechanical properties, applied viscoelasticity theory, and biology of orthopaedic soft tissues.
This seminar introduces students to architectural and environmental histories of abolition through constructed environments, spatial practices, and texts from the eighteenth century to the present. The course locates abolition in social movements and historical discourses, examining the roles that both reform and radical refusal have played in struggles for spatial justice by considering debates around enslavement, prisons, and borders. The course situates abolition as a significant intersectional feminist problem, and conceptually core to the consideration of race in global architectural history. We examine individual and collective works of architecture, art, landscape, and material culture, which highlight incarceration and the production of enclosure within the institutions that have shaped them in various parts of the world, and as elements of the formation of space, power, and knowledge in colonial and postcolonial contexts.
The seminar is structured around multiple full-book engagements. We will closely read three texts that are foundational to the literature on abolition and architecture:
Are Prisons Obsolete?
by Angela Y. Davis;
Golden Gulag: Prisons, Surplus, Crisis, and Opposition in Globalizing California
by Ruth Wilson Gilmore; and
Marking Time: Art in the Age of Mass Incarceration
by Nicole Fleetwood. These readings are complemented by articles and other shorter texts, and works of art and architecture, which help to contextualize and draw out the themes of the course. Each student leads seminars on the readings and builds on this foundation by engaging in independent research, culminating in a long-format paper that intervenes in the discourse or frames a narrative, presenting an architectural history of abolition.
This advanced seminar examines historical, social, cultural, and theoretical propositions for decolonizing praxis and their complex relations to feminist critique. How do we understand Western European colonialism and coloniality as modes, conditions, and institutions of power, dispossession, subjugation, and subjection continuing into the present? What are the methods, practices, and vision enacted and proposed by the colonized for undoing and radically transforming the determinate logics, instruments, and structures of colonialism as these persist in the present moment? We will consider how gender and sexuality as well as race – as technologies of social organization, codes of valuation, and modes of survival – shape colonialism and the struggles against it. We will inquire into their significance to projects of decolonization. How might decolonization envision and make possible other ways of life?
Descriptive statistics, central limit theorem, parameter estimation, sufficient statistics, hypothesis testing, regression, logistic regression, goodness-of-fit tests, applications to operations research models.
In recent decades, the study of the so-called “Buddho-Daoism” has become a burgeoning field that breaks down the traditional boundary lines drawn between the two Chinese religious traditions. In this course we will read secondary scholarship in English that probes the complex relationships between Buddhism and Daoism in the past two millennia. Students are required not only to be aware of the tensions and complementarity between them, but to be alert to the nature of claims to either religious purity or mixing and the ways those claims were put forward under specific religio-historical circumstances. The course is organized thematically rather than chronologically. We will address topics on terminology, doctrine, cosmology, eschatology, soteriology, exorcism, scriptural productions, ritual performance, miracle tales and visual representations that arose in the interactions of the two religions, with particular attention paid to critiquing terms such as “influence,” “encounter,” “dialogue,” “hybridity,” “syncretism,” and “repertoire.” The course is designed for both advanced undergraduate and graduate students in the fields of East Asian religion, literature, history, art history, sociology and anthropology. One course on Buddhism or Chinese religious traditions is recommended, but not required, as background.
Applications of continuum mechanics to the understanding of various biological tissues properties. The structure, function, and mechanical properties of various tissues in biolgical systems, such as blood vessels, muscle, skin, brain tissue, bone, tendon, cartilage, ligaments, etc. are examined. The establishment of basic governing mechanical principles and constitutive relations for each tissue. Experimental determination of various tissue properties. Medical and clinical implications of tissue mechanical behavior.
This course examines historical narratives and record-keeping in premodern Korea, focusing on the Chosŏn dynasty (1392–1910). It explores writing as a medium of power that shaped politics, social order, gender relations, and cultural identity. Through diverse texts, including official chronicles, didactic texts, memoirs, and (auto)biographies, students will analyze how individuals and institutions used writing to assert authority, express dissent, and document their lives.
Advanced instruction in the Armenian dialect. No P/D/F or R credit is allowed for this class.
This course deals with a fundamental question of sustainability management: how to change organizations and more complex systems, such as communities, industries, and markets, by integrating sustainability concerns in the way that they operate. The course poses this question to a dozen leading sustainability practitioners, who answer it by discussing management strategies that they use in their own work. Through these guest lectures, extensive class discussion, readings, and writing assignments, students identify and simulate applying practical ways for transforming how organizations and complex systems work. The practitioners, who work in the public, private, and nonprofit sectors and in a wide variety of organizations, make presentations in the first hour of the course. Students then have time to ask questions and speak informally with the guest practitioners, and will participate in an instructor-led class discussion, geared toward identifying management strategies, better understanding their application, and considering their effectiveness. By the end of the course, the students gain an understanding of management tools and strategies that they, themselves, would use to integrate sustainability in organizations.
The course complements the M.S. in Sustainability Management program’s required course, Sustainability Management (SUMA K4100). In that course, students study management and organization theory. In the Practicum, students learn directly from leading practitioners, who confront sustainability management issues daily.
Prerequisites: VIAR UN2300 (Formerly R3302) Laboratory in Relational Art; Sculpture without Objects The purpose of this class will be to explore the function of Relational Aesthetics in contemporary art practice and to develop ideas about the role of context in art, as the students develop their own site-specific works and research historical precedents for art designed to be exhibited in non-traditional venues. This course will also prepare students for professional work preparing art for venues of that type. This class will be structured around studio work, with an emphasis on the development and production of a final site-specific project. In order to foster students’ growth and ongoing investigation into the nature of contemporary sculpture, the class will also be comprised of slide lectures, visits to local artists’ studios, and galleries, as well as various public art projects throughout the city. As the semester progresses, the emphasis will gradually be shifted from research to intensive studio work on a final project, often a proposal for a site-specific work in a non-traditional venue. Generally, the first half of each class session will be dedicated to lecture and discussion, while the second half will be dedicated to individual studio work and critique.
Prerequisites: (CHEM UN2443 and CHEM UN2444) and (CHEM UN3079 and CHEM UN3080) and (BIOC UN3501) , or the equivalent. Development and application of chemical methods for understanding the molecular mechanisms of cellular processes. Review of the biosynthesis, chemical synthesis, and structure and function of proteins and nucleic acids. Application of chemical methods--including structural biology, enzymology, chemical genetics, and the synthesis of modified biological molecules--to the study of cellular processes--including transcription, translation, and signal transduction.
Differential and multistage amplifiers; small-signal analysis; biasing techniques; frequency response; negative feedback; stability criteria; frequency compensation techniques. Analog layout techniques. An extensive design project is an integral part of the course.
Thermodynamics and kinetics of reacting flows; chemical kinetic mechanisms for fuel oxidation and pollutant formation; transport phenomena; conservation equations for reacting flows; laminar nonpremixed flames (including droplet vaporization and burning); laminar premixed flames; flame stabilization, quenching, ignition, extinction, and other limit phenomena; detonations; flame aerodynamics and turbulent flames.
Prerequisites: ECON UN3211 and ECON UN3213 Historical comparative examination of the economic development problems of the less developed countries; the roles of social institutions and human resource development; the functions of urbanization, rural development, and international trade.
Design and analysis of high speed logic and memory. Digital CMOS and BiCMOS device modeling. Integrated circuit fabrication and layout. Interconnect and parasitic elements. Static and dynamic techniques. Worst-case design. Heat removal and I/O. Yield and circuit reliability. Logic gates, pass logic, latches, PLAs, ROMs, RAMs, receivers, drivers, repeaters, sense amplifiers.
Tragedy is a compact form that poses monumental questions. As a dramatic genre, it purports to help us make sense of mourning, justice, sacrifice, acts of bearing witness, citizenship, tyranny, suffering, and grief. Following its emergence in ancient Athens, tragic drama – and, more diffusely, the idea of the “tragic” – has shaped European theater stages for millennia, while also giving rise to a potent philosophical tradition. This seminar picks up with conversations on tragedy around the year 1800, focusing especially on European and American drama of the long twentieth century. In modernity, as we will find, the role of tragedy was fiercely contested: some dramatists and theorists claimed that tragedy could not (or should not) be “modern,” while others assigned it pride of place in the emergent cultures and politics of modernity. Together we will explore these tensions in the works of such playwrights as Goethe, Ibsen, Treadwell, Brecht, Soyinka, and Churchill, as we consider whether tragedy is best understood as form, function, or feeling. In tracing the stories of this genre through many of its canonical modern formations, we will crystallize an understanding of modern tragedy’s affordances, aims, audiences, and effects. Students will engage closely with theories of tragedy in an initial short paper; in addition to this assignment, they will have the option of writing two shorter essays or one longer seminar paper. Students at all levels are welcome to apply. Prior experience reading drama critically is welcome but is not required.
This advanced seminar examines important approaches, issues, perspectives, and themes related to planetary concerns of environmental crisis, climate change, life sustainability, and multi-species flourishing, with a focus on feminist, postcolonial, anti-racist, and queer perspectives. Topics for discussion and study include the global pandemic, histories of colonialism, slavery, and capitalism,
Prereqs: BOTH 1 WMST Intro course PLUS any WGSS 'Foundation' course, OR instructor permission.
This course provides a rigorous introduction to the theory underlying widely used biophysical methods, which will be illustrated by practical applications to contemporary biomedical research problems. The course has two equally important goals. The first goal is to explain the fundamental approaches used by physical chemists to understand the behavior of molecules and to develop related analytical tools. The second goal is to prepare students to apply these methods themselves to their own molecular biology research projects. The course will be divided into seven modules: (i) solution thermodynamics with an emphasis on application to analysis of protein structure, folding, and binding interactions; (ii) hydrodynamic methods; (iii) statistical analysis of experimental data; (iv) molecular dynamics calculations; (v) optical spectroscopy with an emphasis on fluorescence; (vi) nuclear magnetic resonance spectroscopy; and (vii) light-scattering and diffraction methods including an overview of cryogenic electron microscopy reconstruction methods. In each module, the underlying physical theories and models will be presented and used to derive the mathematical equations applied to the analysis of experimental data. Weekly recitations will emphasize the analysis of real experimental data and understanding the applications of biophysical experimentation in published research papers. The problem sets emphasize use of PyMOL for analysis of macromolecular structures and use of standard curve-fitting software for analysis of protein binding data; detailed tutorials on the related methods are provided in the recitation sections. The first three modules will be covered in Biophysical Chemistry I during the fall term, while the final three will be covered in Biophysical Chemistry II during the spring term, and treatment of molecular dynamics calculations will be divided between the two terms.
In 1935, WEB Dubois wrote about abolition democracy: an idea based not only on breaking down unjust systems, but on building up new, antiracist social structures. Scholar activists like Angela Davis, Ruth Gilmore and Mariame Kaba have long contended that the abolition of slavery was but one first step in ongoing abolitionist practices dismantling racialized systems of policing, surveillance and incarceration. The possibilities of prison and police abolition have recently come into the mainstream national consciousness during the 2020 resurgence of nationwide Black Lives Matters (BLM) protests. As we collectively imagine what nonpunitive and supportive community reinvestment in employment, education, childcare, mental health, and housing might look like, medicine must be a part of these conversations. Indeed, if racist violence is a public health emergency, and we are trying to bring forth a “public health approach to public safety” – what are medicine’s responsibilities to these social and institutional reinventions?
Medicine has a long and fraught history of racial violence. It was, after all, medicine and pseudoscientific inquiry that helped establish what we know as the racial categorizations of today: ways of separating human beings based on things like skin color and hair texture that were used (and often continue to be used) to justify the enslavement, exclusion, or genocide of one group of people by another. Additionally, the history of the professionalization of U.S. medicine, through the formation of medical schools and professional organizations as well as and the certification of trained physicians, is a history of exclusion, with a solidification of the identity of “physician” around upper middle class white masculinity. Indeed, the 1910 Flexner Report, whose aim was to make consistent training across the country’s medical schools, was explicit in its racism. From practices of eugenic sterilization, to histories of experimentation upon bodies of color, medicine is unfortunately built upon racist, sexist and able-ist practices.
This course is built on the premise that a socially just practice of medicine is a bioethical imperative. Such a practice cannot be achieved, however, without examining medicine’s histories of racism, as well as learning from and building upon histories of anti-racist health practice. The first half of the semester will be dedicated to learning about histories of medical racism: from eugenics and racist experiment
Interface between clinical practice and quantitative radiation biology. Microdosimetry, dose-rate effects and biological effectiveness thereof; radiation biology data, radiation action at the cellular and tissue level; radiation effects on human populations, carcinogenesis, genetic effects; radiation protection; tumor control, normal-tissue complication probabilities; treatment plan optimization.
Explores cutting-edge field of cellular bioengineering and applications of cell therapies. Comprehensive understanding of the principles, techniques, and ethical considerations involved in cells for medical applications studied.
Complex reactive systems. Catalysis. Heterogeneous systems, with an emphasis on coupled chemical kinetics and transport phenomena. Reactions at interfaces (surfaces, aerosols, bubbles). Reactions in solution.
Fundamentals of catalyst design and characterization, kinetic modeling and interpretation, and reactor design for CO2 utilization technologies. Topics include tandem catalysis, fundamentals of electrocatalysis, heterogeneous catalysis, catalytic processes for the activation of CO2, and reactive capture. Course grades are based on evaluating case studies, quizzes, and the final project design, where students apply concepts learned in class to propose solutions for practical, real-world CO2 utilization challenges.
Direct stiffness approach for trusses. Strong and weak forms for one-dimensional problems. Galerkin finite element formulation, shape functions, Gauss quadrature, convergence. Multidimensional scalar field problems (heat conduction), triangular and rectangular elements, Isoparametric formulation. Multidimensional vector field problems (linear elasticity). Practical FE modeling with commercial software (ABAQUS). Computer implementation of the finite element method. Advanced topics. Not open to undergraduate students.
Prerequisites: two years of college Czech or the equivalent. A close study in the original of representative works of Czech literature. Discussion and writing assignments in Czech aimed at developing advanced language proficiency.
See syllabus attached
Guiding ideals in American architecture from the centennial to around 1960. The evolution of modernism in America is contrasted with European developments and related to local variants.
Prerequisites: RUSS UN3101 and RUSS UN3102 Third-Year Russian I and II, or placement test. Systematic study of problems in Russian syntax; written exercises, translations into Russian, and compositions. Conducted entirely in Russian.
Exploring philosophies of history from the ancient Greeks to the present.
Developments in architectural history during the modern period. Emphasis on moments of significant change in architecture (theoretical, economic, technological, and institutional). Themes include positive versus arbitrary beauty, enlightenment urban planning, historicism, structural rationalism, the housing reform movement, iron and glass technology, changes generated by developments external or internal to architecture itself and transformations in Western architecture.
Developments in architectural history during the modern period. Emphasis on moments of significant change in architecture (theoretical, economic, technological, and institutional). Themes include positive versus arbitrary beauty, enlightenment urban planning, historicism, structural rationalism, the housing reform movement, iron and glass technology, changes generated by developments external or internal to architecture itself and transformations in Western architecture.
Introduction to runoff and drainage systems in an urban setting, including hydrologic and hydraulic analyses, flow and water quality monitoring, common regulatory issues, and mathematical modeling. Applications to problems of climate variation, land use changes, infrastructure operation and receiving water quality, developed using statistical packages, public-domain models, and Geographical Information Systems (GIS). Team projects that can lead to publication quality analyses in relevant fields of interest. Emphasis on the unique technical, regulatory, fiscal, policy, and other interdisciplinary issues that pose a challenge to effective planning and management of urban hydrologic systems.
Review of building energy modeling techniques for simulating time-varying demand. Detailed Physics-based models, gray-box and black-box modeling. Static and dynamic models of building energy systems. Deterministic and Stochastic occupancy modeling. Modeling of control and dispatch of HVAC and local energy systems. Implementation of models in Energyplus and Modelica platforms. Modeling of low and net-zero carbon buildings and local energy systems.
This seminar, which focuses on Montaigne’s
Essays
, is one of a series on the history of the modern self. The series has included seminars on figures like Pascal, Rousseau, and Tocqueville, and will continue to expand.
Introduction to multiscale analysis. Information-passing bridging techniques: among them, generalized mathematical homogenization theory, the heterogeneous multiscale method, variational multiscale method, the discontinuous Galerkin method and the kinetic Monte Carlo–based methods. Concurrent multiscale techniques: domain bridging, local enrichment, and multigrid-based concurrent multiscale methods. Analysis of multiscale systems.
Premodern Chinese literati have long been regarded as active historical agents who shaped “This Culture of Ours”—a metonym for civilization in the premodern Sinitic context—while they also fed from, partook in, and influenced popular and foreign cultures. Besides “literary writings” like poetry and prose, literati also engaged in calligraphy, painting, and antiquarianism under the umbrella term of “literary or cultural arts.” In turn, the creation and appreciation of artwork were intrinsic to the aesthetic life of literati community and further established their self-identity. At the same time, social exclusivity, (self-)doubt and identity crises, along with the looming threat of cultural decline, have continually haunted this literati community throughout the ages.
Covering the long trajectory of imperial China, this course reveals the birth and development of literati culture. In particular, we take an interdisciplinary approach, introducing intellectual and poetic discourses, socio-historical contexts, literary criticism, visual and material culture, to envision a “common ground” for their civil world. Textual, visual sources plus material objects are meant to have conversations with each other in this course. Important issues include historical transformations of the elite class, cultural geography in different eras, materiality and visuality of elite calligraphy and painting, literati self-expression through aesthetic practice, the roles of the court and literati in producing and preserving art, as well as other relevant issues such as gender studies, vernacular literature, and commodity society.
This course is cross-listed in AMEC and CPLT. For undergraduates, no background in Chinese language is required in this course, and all reading materials—either translation of primary sources or secondary scholarship—are accessible in English.
The objective of this course is to develop understanding of how political institutions and behavior shape economic outcomes, and vice versa. Starting from the micro level study of political behavior, we will build up to analyze the internal workings of institutions and ultimately macro level economic and political outcomes. During the course we will cover the following topics
• Limits and potential of markets
• Public goods provision
• Voting
• Redistribution
Prerequisites: LING UN3101 An investigation of the sounds of human language, from the perspective of phonetics (articulation and acoustics, including computer-aided acoustic analysis) and phonology (the distribution and function of sounds in individual languages).
In this course we will examine the New Testament canon and the twenty-seven texts that comprise it in light of their respective literary genres, their Jewish antecedents and Greco-Roman influences, which will include their historical, social, cultural, political and economic contexts, and the ways these factors impinged upon their various dimensions of meaning. Various modes of biblical interpretation, both ancient and contemporary, will be explored. A major emphasis will be on the ways select texts are utilized, misconstrued and weaponized in the public sphere in this contemporary moment.
How does one live with sound and move within worlds of sound? In pursuit of this question the course explores: soundscapes and sound arts; echoes of audible pasts and resonances of auditory cultures; sound and the uncanny; repetitive listening in the age of electronic reproduction, ethereal transmissions, and audio-vision; sounds at the edges of listening with experimental music and sonic installations. Sound, chambers, noise, feedback, voice, resonance, silence: from the sirens of the Odyssey, to compositional figures ala John Cage, to contemporary everyday acoustical encounters, if one were to really listen, closely, how might one write about sound? How might one rethink the ties between sound and image? How then might one think with sound, and through sound?
Following the trials of the immediate postwar, and the
Historikerstreit
of the 1980s, the study of the Holocaust has another significant turn with the opening of the Soviet archives beginning in the 1990s. The Holocaust in the USSR expands our knowledge of the catastrophe, situating the latter phases of emblematic extermination camps like Auschwitz-Birkenau against a longer continuum of personalized, individual violence. The “Holocaust by Bullets” as coined by Father Desbois has parallels to other colonial violence and further explains the genocidal process from dehumanization to militarily crafted murder to institutions of extermination. This course specifically addresses the Holocaust in the USSR with a focus on historical research methods, expanded victim groups, testimony, archival research, denial, and rigorous historiographical grounding. Materials include testimonies from the USC Shoah Foundation and Fortunoff Archives, historiographical surveys like Wachsmann’s
KL
and
Friedländer’s
Years of Extermination
, and important books with new turns in Holocaust scholarship specifically on the USSR like Lower’s
Hitler’s Furies
and Snyder’s
Black Earth
. Our class will be supplemented by field trips to YIVO, the Bukharian Jewish Center, and the Museum of Jewish Heritage, giving students hands-on experience with archival materials and research methods. Together, diverse research methods and materials present students with a more complete understanding of the Holocaust and an excellent foundation to continue research in atrocity studies.
This course serves as an introduction to key texts, concepts, and thinkers in Media and Cultural Studies. Rather than presenting a reductionist, linear narrative that uncritically traces the triumphs of Western technological innovations and genius individuals, this course instead explores media as organizational and management devices that produce particular kinds of knowledge and power, including by influencing our understanding of social issues and social justice.
We will explore how media, as vehicles of knowledge production, are intimately connected to meaning-making, policing, and exclusion practices. At the same time, media can be repurposed as instruments for liberation struggles and emancipatory imaginaries of all kinds. Throughout the course, we will learn about these themes both through the lens of a critical history of the present, emphasizing the long-standing value struggles that underpin media environments and inform practices of re-mediation and cultural production, and also through being in conversation with recent trends in media studies and contemporary social issues.
“Wall Street is a disaster area”—so declared a real estate lawyer in a 1974
New York Times
story on the pitiful state of lower Manhattan. The World Trade Center had been inaugurated in 1973 as a beacon of global capitalism with a mandate to lease only to international firms. A year later, much of the Twin Towers went unoccupied. Some eight million square feet of financial district office space sat empty, brokerage houses were shuttering at a rate of more than one per day, and the surrounding city was hurtling towards a full-blown fiscal crisis. The New York of the mid-1970s did not appear destined to become the model global city we know today. Within a decade, however, the city had transformed into a central node—arguably
the
central node—in the ballooning global financial industry and its accompanying class and cultural formations. But this outcome was never guaranteed. How did New York go from “Fear City” to “Capital of the World”? What historical structures, contingencies, and policy decisions produced Global New York?
This course examines New York City’s long history as a site of globalization. Since European colonization, New York has served as a hub in world-spanning networks of capital, goods, and people.
At the same time, the city’s reinvention in the late-20th century as a “global city”—defined in large part by its deep embeddedness in world financial markets—represented a fundamental shift in the city’s economy, governance, demography, cultural life, and social relations.
We will interrogate how this came to be by exploring New York’s historical role in global business, culture, and immigration, with attention to how local and national conditions have shaped the city’s relationship to the world. While critically analyzing how elites both in and outside New York have wielded power over its politics and institutions, readings and discussions will also center the voices of New Yorkers drawn from the numerous and diverse communities that make up this complex city.
Chemical engineering fundamentals as applied to process research, development, and manufacturing of pharmaceutical products. Course topics include: comprehensive overview of the biopharmaceutical business (therapeutic areas, markets, drug discovery, clinical development, commercialization), process research, creation, development, optimization, sustainability, green chemistry and engineering, safety (patient, process, and personnel), unit operations and associated calculations relevant to pharmaceutical processes, process scale-up, implementation, assessment, technology transfer, new technologies, economic analysis, drug product formulation and manufacturing, and regulatory considerations. Case studies and real-life examples are presented throughout the course.
The history of the Bronx is a history of the struggles, political coalitions, and creative contributions of the dispossessed. To tell the story of the Bronx is to tell the story of how historically marginalized communities have survived and made a home in environments forsaken by the state. And yet, in the popular imagination, the Bronx often circulates simply as a symbol of urban abjection, as the necessary foil against which prosperous urban spaces define themselves. Many of these "Bronx tales" invariably relegate the borough both materially and imaginatively to the past—infused with either white ethnic nostalgia of a lost Bronx innocence or with battle-scar bravado won on its mean streets. This interdisciplinary course invites students to interrogate these long-standing narratives about the Bronx through a critical study of the borough’s rich history and enduring cultural, political, and artistic traditions during the past century. This course explores a variety of movements and artifacts that have been central to the making of the Bronx such as: efforts to establish affordable housing, public art-making, the literary tradition of Bronx coming-of-age stories, grassroots organizing for immigrant rights, struggles against gentrification and environmental racism, and the inter-ethnic collaborations that led to the emergence of hip hop. Students will have the opportunity to embark on field trips and will undertake a wide array of methods including oral histories, performance analysis, archival research, ethnography, mapping, as well as opportunities to engage in creative art-making. By the end of the semester, students will gain a nuanced understanding of the central role that Bronx communities have played in the making of modern New York City.
Interpret financial statements, build cash flow models, value projects, value companies, and make Corporate Finance decisions. Additional topics include: cost of capital, dividend policy, debt policy, impact of taxes, Shareholder/Debtholder agency costs, dual-class shares, using option pricing theory to analyze management behavior, investment banking activities, including equity underwriting, syndicated lending, venture capital, private equity investing and private equity secondaries. Application of theory in real-world situations: analyzing financial activities of companies such as General Electric, Google, Snapchat, Spotify, and Tesla.
Generation of random numbers from given distributions; variance reduction; statistical output analysis; introduction to simulation languages; application to financial, telecommunications, computer, and production systems. Graduate students must register for 3 points. Undergraduate students must register for 4 points. Note: Students who have taken IEOR E4703 Monte Carlo simulation may not register for this course for credit. Recitation section required.
Required for undergraduate students majoring in OR:FE and OR. A mathematically rigorous study of game theory and auctions, and their application to operations management. Topics include introductory game theory, private value auction, revenue equivalence, mechanism design, optimal auction, multiple-unit auctions, combinatorial auctions, incentives, and supply chain coordination with contracts. No previous knowledge of game theory is required.
Fourier analysis. Physics of diagnostic ultrasound and principles of ultrasound imaging instrumentation. Propagation of plane waves in lossless medium; ultrasound propagation through biological tissues; single-element and array transducer design; pulse-echo and Doppler ultrasound instrumentation, performance evaluation of ultrasound imaging systems using tissue-mimicking phantoms, ultrasound tissue characterization; ultrasound nonlinearity and bubble activity; harmonic imaging; acoustic output of ultrasound systems; biological effects of ultrasound.
Planar resonators. Photons and photon streams. Photons and atoms: energy levels and band structure; interactions of photons with matter; absorption, stimulated and spontaneous emission; thermal light, luminescence light. Laser amplifiers: gain, saturation, and phase shift; rate equations; pumping. Lasers: theory of oscillation; laser output characteristics. Photons in semiconductors: generation, recombination, and injection; heterostructures; absorption and gain coefficients. Semiconductor photon sources: LEDs; semiconductor optical amplifiers; homojunction and heterojunction laser diodes. Semiconductor photon detectors: p-n, p-i-n, and heterostructure photo diodes; avalanche photodiodes.
Prerequisites: ECON UN3211 and ECON UN3213 and ECON UN3412 and MATH UN2010 Students must register for required discussion section. The linear regression model will be presented in matrix form and basic asymptotic theory will be introduced. The course will also introduce students to basic time series methods for forecasting and analyzing economic data. Students will be expected to apply the tools to real data.
Prerequisites: ECON UN3211 and ECON UN3213 Introduction to the systematic treatment of game theory and its applications in economic analysis.
Transportation, primarily focused on the movement of people, and logistics, primarily focused on the movement of goods, are two of the most fundamental challenges to modern society. To address many problems in these areas, a wide array of mathematical models and analytics tools have been developed. This class will introduce many of the foundational tools used in transportation and logistics problems, relying on ideas from linear optimization, integer optimization, stochastic processes, statistics, and simulation. We will address problems such as optimizing the routes of cars and delivery trucks, positioning emergency vehicles, and controlling traffic behavior. Moreover, we will discuss modern issues such as bicycle sharing, on-demand car and delivery services, humanitarian logistics, and autonomous vehicles. Concepts will be reinforced with technical content as well as real-world data and examples.
No place or period in American history has ignited more passion or brought into being a richer trove of first-rate scholarship than the South during the years before the Civil War. On the other hand, no place or period in American history has generated more misguided scholarship or more propaganda. In this course, students will sample historical literature and primary sources about the Old South, evaluating the interpretations historians have offered and scrutinizing some of the documents on which historians of the Old South have based their conclusions.
Generalized dynamic system modeling and simulation. Fluid, thermal, mechanical, diffusive, electrical, and hybrid systems are considered. Nonlinear and high order systems. System identification problem and Linear Least Squares method. State-space and noise representation. Kalman filter. Parameter estimation via prediction-error and subspace approaches. Iterative and bootstrap methods. Fit criteria. Wide applicability: medical, energy, others. MATLAB and Simulink environments.
Hands-on introduction to solving open-ended computational problems. Emphasis on creativity, cooperation, and collaboration. Projects spanning a variety of areas within computer science, typically requiring the development of computer programs. Generalization of solutions to broader problems, and specialization of complex problems to make them manageable. Team-oriented projects, student presentations, and in-class participation required.
Introduces students to technological innovations that are helping cities around the world create healthier, safer, more equitable, and more resilient futures. Focus on architecture, urban design, real estate development, structural, civil and mechanical engineering, data analytics, and smart communication technologies. Course covers five distinct sectors in the field of urban infrastructure, including transportation and mobility, buildings, power, sanitation, and communications. A Columbia Cross-Disciplinary Course.
This course offers a comparative exploration of women music practitioners from cross-cultural perspectives, examining their music, oral histories, and lived experiences as well as the impact of these experiences on their music-making in a global context. By tracing the journeys and analyzing the music of specific selected women musicians from various regions, the course investigates their participation in art music, traditional music, popular music, and sacred music from women’s perspectives. Engaging primarily with their music and interviews, the course particularly examines the comparative roles of women as active creators, performers, sponsors, and consumers of music, highlighting how their lived experiences shape their musical contributions. Students will be introduced to critical concepts for analyzing representations of gender, class, ethnicity, nationalism, race, and globalization in music while exploring these women’s sounds, identities, and performances.
Team project centered course focused on principles of planning, creating, and growing a technology venture. Topics include: identifying and analyzing opportunities created by technology paradigm shifts, designing innovative products, protecting intellectual property, engineering innovative business models.