Review of thermodynamics, irreversible thermodynamics, diffusion in crystals and noncrystalline materials, phase transformations via nucleation and growth, overall transformation analysis and time-temperature-transformation (TTT) diagrams, precipitation, grain growth, solidification, spinodal and order-disorder transformations, martensitic transformation.
What are the agents of developmental change in human childhood? How has the scientific community graduated from nature versus nurture, to nature
and
nurture? This course offers students an in-depth analysis of the fundamental theories in the study of cognitive and social development.
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
Prerequisites: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201, preferably) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.
Prerequisites: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201, preferably) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.
Prerequisites: STAT GU4203. At least one semester of calculus is required; two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GU4203. At least one semester of calculus is required; two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GU4204 or the equivalent, and a course in linear algebra. Theory and practice of regression analysis. Simple and multiple regression, testing, estimation, prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyse data.
Prerequisites: STAT GU4204 and GU4205 or the equivalent. Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.
Prerequisites: STAT GU4203 and two, preferably three, semesters of calculus. Review of elements of probability theory. Poisson processes. Renewal theory. Walds equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.
Prerequisites: STAT GU4203 and two, preferably three, semesters of calculus. Review of elements of probability theory. Poisson processes. Renewal theory. Walds equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.
This course explores the recording studio and Digital Audio Workstations (DAWs) as tools for diverse compositional practices. By exploring a range of recording and editing techniques to craft new musical works beyond the limitations of live performance, this class encourages a seamless blend of composition and music production. Various genres, artists, and techniques that push the boundaries of music recording will be studied, such as Jamaican dub, musique concrète, hyper-pop, jazz fusion, and more. Students will gain hands-on experience with DAWs, exploring tools like effects processing, layering, and spatial placement. They will learn to listen closely to pieces exemplifying these techniques, building a shared analytic vocabulary to describe them. Students will also create original pieces, applying and building on the techniques studied in class, while engaging in constructive feedback with peers.
This seminar engages the life and work of W.E.B. Du Bois, widely understood to be the greatest intellectual in U.S. history. Students will read and discuss Du Bois’s autobiography, and major works across his long and prolific career. Major themes include pan-Africanism, socialism, and peace.
Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approximations, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers.
Review of significant failures, civil/structural engineering design and construction practices, ethical standards and the legal positions as necessary background to forensic engineering. Discussion of standard-of-care. Study of the process of engineering evaluation of structural defects and failures in construction and in service. Examination of the roles, activities, conduct and ethics of the forensic consultant and expert witness. Students are assigned projects of actual cases of non-performance or failure of steel, concrete, masonry, geotechnical and temporary structures, in order to perform, discuss and report their own investigations under the guidance of the instructor.
Critical theory was the central practice of the Frankfurt School. Founded in Frankfurt in 1923 and later based at Columbia University, this interdisciplinary institute influenced fields like sociology, political science, film, cultural studies, media theory, and comparative literature. The course begins by examining the genealogy of the Frankfurt School in Marxism and its critique of fascism and traces its afterlife in aesthetic theory, deconstruction, and gender studies, as well as the specter of “Cultural Marxism” recently floating around right-wing circles. We read texts by key figures of the Frankfurt School such as Theodor W. Adorno, Max Horkheimer, Herbert Marcuse and Jürgen Habermas as well as works by adjacent figures like Walter Benjamin, Hannah Arendt, and Siegfried Kracauer.
Far from obvious renderings of place, maps are spatial arguments about who belongs where and how living should be defined. This course approaches place as something that is contested daily in the U.S. through the struggle of who gets to lay claim to a way of life. From the landscapes of dispossession to the alternative ways marginalized people work with and against traditional geographies, this course centers Black place-making practices as political struggle. This class will look at how power and domination become a landed project. We will critically examine how ideas about “nature” are bound up with notions of race, and the way “race” naturalizes the proper place for humans and non-human others. We will interrogate settler colonialism’s relationships to mapping who is and isn’t human, the transatlantic slave trade as a project of terraforming environments for capital, and land use as a science for determining who “owns” the earth. Centered on Black feminist, queer and trans thinkers, we will encounter space not as a something given by maps, but as a struggle over definitions of the human, geography, sovereignty, and alternative worlds. To this end, we will read from a variety of disciplines, such as Critical Black Studies, Feminist and Intersectional Science Studies, Black Geographies and Ecologies, Urban Studies and Afrofuturist literature. (Note: this class will count as an elective for the CCIS minors/concentrations in F/ISTS, ICORE/MORE, and Environmental Humanities.)
Teaching and learning in the premodern Islamic world centered around the person, rather than the
space. Entries in medieval biographical dictionaries tend to emphasize a scholar’s teachers, not the
institutions they studied at. Nonetheless knowledge had a geography: it was embodied and situated.
Where people studied, discussed, and taught determined how and what knowledge was gained and
transmitted, and to whom. At the same time, different practices and values of knowledge transmission
shaped spaces of scholarship.
This class will question the interplay between knowledge and space. We will focus on social and material
dimensions of spaces, revealing connections and separations between scholars and disciplines as we
attempt to materialize intellectual history. We will interrogate the boundaries between the informal and
formal, personal and institutional, public and private, and use these categories to analyze the teaching
and transmission of various kinds of knowledge, such as Islamic and Ancient sciences. Drawing from
biographical dictionaries, literary works, documentary and archeological evidence, we will explore the
importance of religious endowments and patronage, and examine access to scholarly spaces for the elite,
the ‘sub-elite’ and the ‘common’ people. Finally, this class will confront enduring myths, such as those
surrounding Baghdad’s Bayt al-Hikma, and the Jundishāpūr hospital, and narratives surrounding the
place of the natural sciences within the Islamic world.
Prerequisites: ECON UN3211 and ECON UN3213 and MATH UN2010 Students must register for required discussion section. Corequisites: MATH UN2500 or MATH GU4061 The course provides a rigorous introduction to microeconomics. Topics will vary with the instructor but will include consumer theory, producer theory, general equilibrium and welfare, social choice theory, game theory and information economics. This course is strongly recommended for students considering graduate work in economics. Discussion section required.
Students in the regular third-year Arabic track improve reading, writing, speaking, and listening skills through close reading, compositions, class discussions, and presentations in Arabic on topics such as cultures of the Arab world, classical and modern Arabic literature, and contemporary Arabic media. Review of grammatical and syntactic rules as needed. No P/D/F or R credit is allowed for this class.
Prerequisites: ECON UN3211 and ECON UN3213 and MATH UN2010 Students must register for lecture course ECON GU4211 Corequisites: MATH UN2500MATH GU4061 Required discussion section for ECON GU4211 Advanced Microeconomics. The course provides a rigorous introduction to microeconomics. Topics will vary with the instructor but will include consumer theory, producer theory, general equilibrium and welfare, social choice theory, game theory and information economics. This course is strongly recommended for students considering graduate work in economics. Discussion section required.
Prerequisites: MDES W4212. Through reading articles and essays by Arab thinkers and intellectuals of the Twentieth century, starting from the period called Nahda (Renaissance), such as Taha Hussein, Qasim Amin, Abdallah Laroui, Abed Al-Jabiri, Tahar Haddad, Fatima Mernissi and others, students will be able to increase their fluency and accuracy in Arabic while working on reading text and being exposed to the main
themes in Arab thought. The course works with all four skills (listening, speaking, reading and writing). Arabic is the language of instruction. No P/D/F or R credit is allowed for this class.
Static flexural response of thin, elastic, rectangular, and circular plates. Exact (series) and approximate (Ritz) solutions. Circular cylindrical shells. Axisymmetric and non-axisymmetric membrane theory. Shells of arbitrary shape.
Connects basic MEMS transduction elements to applications by analyzing the analog signal chain, sensor packaging, and sensor integration into larger systems. Underlying concepts of analog instrumentation such as filtering and digitization covered. Hands-on projects involve off-the-shelf sensors and single-board computers to create self-contained sensor systems that demonstrate relevant issues.
Review of states of stress and strain and their relations in elastic, plastic, and viscous materials. Dislocation and elastic-plastic concepts introduced to explain work hardening, various materials-strengthening mechanisms, ductility, and toughness. Macroscopic and microstructural aspects of brittle and ductile fracture mechanics, creep and fatigue phenomena. Case studies used throughout, including flow and fracture of structural alloys, polymers, hybrid materials, composite materials, ceramics, and electronic materials devices. Materials reliability and fracture prevention emphasized.
Modular Sound Synthesis is a hands-on studio class that explores contemporary techniques for synthesizers both in studio practice and performance while framing them in the historical context in which they developed. The class approaches the fundamentals of sound and synthesis through the perspective of Columbia’s Computer Music Center: vintage function generators, suitcase reel-to-reel tape machines, prototype modules, custom devices; and the first programmable music synthesizer, the RCA Mark II. Students will learn to perform and compose on both hardware devices and software emulations, utilizing them as a creative tool for recording and live performance. Topics include oscillators, modulation, sequencers, voltage processing, wave shaping, filters, and LFOs. The course will engage in listening to both historical and contemporary examples to develop critical listening skills. This class is designed as a follow-up to Intro to Digital Music for undergraduates or graduate students interested in integrating modular synthesis within their artistic practice.
Through reading and writing, students will review Arabic Grammar concepts within the context of linguistic functions such as narration, description, comparison, etc. For example, within the function of narration, students will focus on verb tenses, word order, and adverbials. Based on error analysis in the past twelve years that the Arabic Program has been using Al-Kitaab, emphasis will be placed on common and frequent grammatical errors. Within these linguistic functions and based on error analysis, the course will review the following main concepts: Types of sentence and sentence/clause structure. The Verb system, pattern meanings and verb complementation. Quadriliteral verb patterns and derivations. Weak Verbs derivations, conjugation, tense frames and negation. Case endings. Types of noun and participle: Noun of time, place, instance, stance, instrument, active and passive participles. Types of construct phrase: al-iDafa. Types of Adverbials and verb complements: Hal, Tamyiz, Maf’ul mutlaq, Maf’ul li’ajlihi, adverbs of time, frequency, place and manner. The number system and countable nouns. Types of maa.Diptotes, al-mamnu’ min-aSSarf. No P/D/F or R credit is allowed for this class.
Is the market a religious system? Can we consider "capitalism" to be a key arena in which the relationship between the religious and the secular is both negotiated and performed? In this course, students will explore the complicated relationship between faith and the market, the religious and the secular, and the evolution of vice and virtue as they relate to economic thriving in the United States. While no hard and fast rules for thinking about the relationship between right conduct and material interests cut across all religious and philosophical traditions, human agents invest real faith into currency, into markets, and into the reigning economic order to bring about increased opportunities, wealth, and freedom to people across the globe. Throughout this semester, we will chart both the long shadows and the future trajectories of these beliefs from our American perspective.
This seminar focuses on historical, sociological, and first-hand accounts of a diverse set of American non-conformist religious and spiritual groups (including MOVE, the Branch Davidians at Waco, Father Divine's International Peace Mission, the Oneida Perfectionists, and Occupy and others). Diverse in their historical origins, their activities, and their ends, each of the groups sought or seeks to offer radically news ways of living, subverting American gender, sexuality, racial, or economic norms. The title of this seminar highlights the ways that these groups explain their reasons for existing (to themselves or others) not as a choice but as a response to a system or society out of whack, at odds with the plans of the divine, or at odds with nature and survival. Likewise, it considers the numerous ways that these same groups have often found themselves the targets of state surveillance and violence.
Prerequisites: MDES UN2202 This is an introductory course to Levantine Arabic for students who have completed two years of Standard Arabic studies, at the Intermediate level. The course is designed to further develop fluency in oral communication, through building students’ familiarity with a less formal register of Arabic, namely the Levantine dialect. The course will convert and recycle some of the previous Standard Arabic knowledge to the dialect, by comparing their prior knowledge to its dialectal counterpart; while at the same time developing students’ new communicative skills in a diverse range of contexts that are essential in any conversational interaction. The course will build students abilities to interact effectively in various areas where Levantine Arabic is spoken. In addition to varied thematic topics, the course exposes students to cultural aspects specific to the region. Additionally, the course will work on both constructing students’ knowledge of dialectal diction as well as other grammatical features of the dialects. Even though the course is designed for communication in the four skills (reading, writing, listening and speaking), the emphasis will be mostly on speaking and listening. No P/D/F or R credit is allowed for this class.
The purpose of the Arabic Linguistic Tradition course is to introduce undergraduate and graduate
students to the Arabic Linguistic Tradition, starting before Islam and ending in current times. The
course maps out the context in which the Arabic language and its predecessors existed, the
history of the development of the language, its script, its geographical spread, its linguistic
influences on other languages and scripts throughout the world, as well as its own influences by
other languages. The course will also examine the importance of Arabic as a language of
religion, philosophy, sciences, and nationalism. Furthermore, the course will focus on the
classical Arabic linguistic categories and fields devised by Arab/Arabic grammarians, and how
we can situate them vis-à-vis modern western linguistic theories. The course will detail some of
the language linguistic issues, challenges and secrets, as the language stands on its own, as well
as within a euro-centric “modern” linguistic theories framework.
Prerequisites: STAT GU4205 or the equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.
Cross disciplinary interfacial engineering principles and applications in sustainable energy and material science. Surface science and systems analysis across different technology sectors - material production and processing, waste management, device manufacture, composites, coatings, ceramics, membranes, biomaterials, and microelectronics.
Prerequisites: STAT GU4204 or the equivalent. Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.
Russian ideas are familiar to the world through Tolstoy’s and Dostoevsky’s novels. In this course, we will examine key texts in the intellectual tradition that forms the backdrop to these famous works. Emphasis is on close textual readings; but also on how Russian ideas have been read and interpreted across national and cultural boundaries, including in recent English-language works like Tom Stoppard’s play,
Coast of Utopia
. Thinkers include Schellingians and Hegelians, Slavophiles, Populists and Pan-Slavists, and Vladimir Soloviev.
This seminar for advanced undergraduates and graduate students investigates the significance of dreams in multiple cultural and historical contexts with a focus on Tibetan Buddhism. Dreams and dreaming are vital aspects of Tibetan Buddhist meditative practice, visionary experience, poetry, narratives, as well as visual arts. Students in the seminar will explore a range of materials that 1) guide Buddhist practitioners to cultivate certain types of dreams, and 2) narrate dream experiences that the dreamer has deemed worth recording, and 3) situate Tibetan Buddhist examples in broader contexts of religious and psychological perspectives, with an emphasis on Freud and Jung’s treatment of dreams. According to Buddhist sources, a dream might be significant because the dreamer understands it to be revelatory, foretelling the future, or it might be recorded simply because the dreamer finds the dream in some way compelling, troubling, or funny. In life writing, dreams often highlight crucial moments in the writer’s life experience. Just as psychoanalysts make use of dreams to engage with analysands, Tibetan medical texts instruct doctors to pay close attention to patients’ dreams in the process of diagnosis. Tibetan ritual texts guide meditators in techniques for lucid dreaming. Visionary dreams are recorded in great aesthetic detail. Narratives of dreams and dreamscapes are an important part of biographies and life writing in general. We will also consider European and American treatments of dreams and lucid dreaming, including psychoanalytic, philosophical approaches to dreaming. A significant element of the course is a daily dream journal.
This course introduces the Bayesian paradigm for statistical inference. Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models; Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software.
Prerequisites: A course in the theory of statistical inference, such as STAT GU4204 a course in statistical modeling and data analysis, such as STAT GU4205.
Review of loads and structural design approaches. Material considerations in structural steel design. Behavior and design of rolled steel, welded, cold-formed light-gauge, and composite concrete/steel members. Design of multi-story buildings and space structures.
Prerequisites: ECON UN3211 and ECON UN3213 and STAT Un1201 This course takes New York as our laboratory. Economics is about individual choice subject to constraints and the ways that choices sum up to something often much more than the parts. The fundamental feature of any city is the combination of those forces that bring people together and those that push them apart. Thus both physical and social space will be central to our discussions. The underlying theoretical and empirical analysis will touch on spatial aspects of urban economics, regional, and even international economics. We will aim to see these features in New York City taken as a whole, as well as in specific neighborhoods of the city. We will match these theoretical and empirical analyses with readings that reflect close observation of specific subjects. The close observation is meant to inspire you to probe deeply into a topic in order that the tools and approaches of economics may illuminate these issues in a fresh way.
Prerequisites: COMS W3134, COMS W3136, or COMS W3137, and COMS W3203. Introduction to the design and analysis of efficient algorithms. Topics include models of computation, efficient sorting and searching, algorithms for algebraic problems, graph algorithms, dynamic programming, probabilistic methods, approximation algorithms, and NP-completeness.
Prerequisites: (COMS W3134 or COMS W3136COMS W3137) and (COMS W3203) Introduction to the design and analysis of efficient algorithms. Topics include models of computation, efficient sorting and searching, algorithms for algebraic problems, graph algorithms, dynamic programming, probabilistic methods, approximation algorithms, and NP-completeness.
This course takes an anthropological perspective on life in China today with special attention to the legacies of the country’s socialist past. We start with a brief look at the ideological and institutional frameworks employed by the Communist Party to organize the daily life of its citizens in the decades leading into the People’s Republic. We will then read about how economic and social reforms instituted since the 1980s, in particular changes to the work unit and household registration system, have resulted in dramatically different opportunities and expectations for Chinese citizens attempting to navigate career opportunities, search for romantic partners, move through communal and private spaces and engage in consumptive activities. Exploring the experiences of rural peasants, urban workers, and laborers who move between countryside and city as well as between nations, we will examine how class, gender, and sexuality come to be refigured as China integrates into the global market economy. Scholarly texts will be supplemented with political speeches, short work of fiction and essays, and films.
This seminar explores the Cold Wars impact on Eastern Europe (1940s-1980s) and Eastern Europes Cold War-era engagements with the wider world. We will address the methodologies used by historians to answer questions like these: What was the Cold War? What did it mean, and for whom? We will also look at the Cold War as something more than a series of events; we will consider its value, uses, and limits as a device for framing the second half of the twentieth century.
Prerequisites: STAT GU4205 or the equivalent. Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.
Introduces classic and modern algorithmic ideas that are central to many areas of Computer Science. The focus is on most powerful paradigms and techniques of how to design algorithms, and how to measure their efficiency. The intent is to be broad, covering a diversity of algorithmic techniques, rather than be deep. The covered topics have all been implemented and are widely used in industry. Topics include: hashing, sketching/streaming, nearest neighbor search, graph algorithms, spectral graph theory, linear programming, models for large-scale computation, and other related topics
Design of large-scale and complex bridges with emphasis on cable-supported structures. Static and dynamic loads, component design of towers, superstructures and cables; conceptual design of major bridge types including arches, cable stayed bridges and suspension bridges.
Modern challenges in the design of large-scale building structures will be studied. Tall buildings, large convention centers and major sports stadiums present major opportunities for creative solutions and leadership on the part of engineers. This course is designed to expose the students to this environment by having them undertake the complete design of a large structure from initial design concepts on through all the major design decisions. The students work as members of a design team to overcome the challenges inherent in major projects. Topics include overview of major projects, project criteria and interface with architecture, design of foundations and structural systems, design challenges in the post 9/11 environment and roles, responsibilities and legal issues.
Prerequisites: STAT GU4204 or the equivalent. Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.
Pre-requisite: At least a year of calculus and physics; basic programming experience (e.g. EESC3400 - Introduction to Computational Earth Science).
Recommended: EESC2100 (Climate System), EESC2200 (Solid Earth), EESC3201 (Solid Earth Dynamics).
The course aims to explore sea level changes that take place over a wide variety of timescales and are the result of multiple solid Earth and climatic processes. The course will step chronologically through time starting with long term sea level changes over the Phanerozoic, followed by Plio-Pleistocene ice age sea level variations and lastly modern and future sea level change. This is a cross-disciplinary course, which is aimed at students with interests in geophysics, cryosphere evolution, ocean dynamics, sedimentology, paleogeography, and past and present climate.
Urban ecology is the study of both the interactions between organisms in an urban environment and the organisms' interactions with that environment. This course facilitates learning about 1) basic principles related to ecological interactions of life on Earth, 2) the causes and consequences of biological patterns and processes in urban environments, and 3) how ecology can inform land use decisions and applied management strategies of natural resources (e.g. water, air, biodiversity), particularly in urban environments. This course aims to provide students with an understanding of the ways in which ecological perspectives can contribute to an interdisciplinary approach to solving environmental problems facing human society. Towards that end, this course covers topics ranging from applied ecology and conservation biology to sustainable development. It uses a cross disciplinary approach to understand the nature of ecology and biological conservation, as well as the social, philosophical and economic dimensions of land use strategies. Although in some ways cities may seem to be isolated from what we would otherwise call "nature," they are not, and this is a major theme of this course. This course includes discussion of biodiversity, ecosystem function, evolutionary processes, nutrient cycling, and natural resource availability in cities. Students will acquire an understanding of the ecology of human-dominated landscapes, the theory and study of urban ecology, and the application of ecological principles to building sustainable urban communities. Students will also explore timely and important urban ecology issues including ecological restoration, invasive species, and biodiversity conservation.
This course examines experiences and legacies of China’s “long 1980s” (1978-1992), a period of “reform and opening” with lasting impacts on contemporary discourses and realities. It introduces students to a wide range of primary materials (in English translation), including cinema, literature, photography, contemporary art and other social commentaries, along with theoretical readings and secondary literature from a variety of disciplines including literary and media studies, and social, economic, intellectual and art histories. Topics include politics of rehabilitation at the end of the Cultural Revolution; political and artistic movements of the Beijing Spring; cultural productions amidst rural and urban economic reforms; humanism and cybernetic imagination; extractive economies and environmental transformation; gender and financialization; and China’s integration into the world economy.
Course Overview
Often described as “twin crises,” climate change and biodiversity loss are among the most urgent sustainability challenges to be addressed in our modern era. While much focus has rightfully been placed on climate change mitigation actions at local, regional, and global scales, biodiversity loss is less often addressed by governments, institutions, industries, and individuals as a critical piece of the sustainability puzzle. In 2021, COP 15, the fifteenth meeting of the Conference of the Parties to the UN Convention on Biological Diversity, received far less media attention than COP 26, the Conference of the Parties to the UN Convention on Climate Change. Yet climate change and biodiversity loss are inextricably linked, and without biodiversity and the associated ecosystem services and biospheric resilience upon which human society relies, a sustainable world is not possible. Moreover, certain climate change mitigation actions can actually be to the detriment of biological diversity.
Unlike a traditional conservation biology course geared towards ecologists and biologists, this course will be taught through the lens of sustainability management, equipping sustainability managers with the knowledge and direction needed to begin integrating biodiversity conservation and restoration into their professions. This course will illuminate the critical importance of biodiversity to sustainability and human well-being, the science and politics behind the current biodiversity crisis, and proposals, policies, and actions for bending the curve of biodiversity loss to create more sustainable and equitable outcomes for both humans and the non-humans with which we share our planet.
Students who seek to deepen their understanding of ecological sustainability and address the biodiversity crisis through the lens of sustainability management are encouraged to take this course. This course is an on-campus (or Hy-Flex) elective offered during the Fall semester and fulfills 3 credits within the Physical Dimensions of Sustainability Management curriculum area in the Master of Science in Sustainability Management program. Cross-registration is available to students outside of the Master of Science in Sustainability Management program, space permitting.
Biodiversity, a term popularized in the 1980s, refers to the variety of life at the genetic, species, and ecosystem levels. It is crucial for sustainability, as it supports ecosystems that underpin human life, economic activities, and ecological stability. The loss of biodiversity threatens essential ecosystem services like clean air, water filtration, climate regulation, and food security. This course explores how climate change, both current and projected, impacts biodiversity and how natural ecosystems influence greenhouse gas concentrations. Human survival depends on these ecosystems, yet there is uncertainty about how much biodiversity loss can be tolerated. Climate change now poses as serious a threat to biodiversity as direct development activities. Understanding the science behind these threats is essential for sustainability students, and this course aims to provide that knowledge.
Simultaneously, tropical deforestation across the globe produces CO2 emissions equal to the total current emissions of the United States. Forest fires in Canada have produced emissions equal to the total fossil fuel based emissions of that country. Thawing of permafrost in the arctic north is one of the positive feedback loops, warming leading to more warming that has catastrophic potential. In studying biodiversity, we will examine ecosystems and species such as muskoxen, whales, penguins, primates, tree frogs, and monarch butterflies. We will also explore human practices like agriculture, forest management, hunting, and fishing, which affect both carbon and biodiversity and rely on climate stability. Students will learn how climate and natural ecosystems interact, a crucial first step toward actions needed to sustain life on Earth. While some readings may be challenging for those without an ecology background, support will be available. Students with prior ecology knowledge should find the course particularly informative.
Prerequisites: STAT GU4206. The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.
Prerequisites: (CIEN E3141) or equivalent Seismicity, earthquake intensity, propagation of seismic waves, design of earthquake motion, seismic site response analysis, in situ and laboratory evaluation of dynamic soil properties, seismic performance of underground structures, seismic performance of port and harbor facilities, evaluation and mitigation of soil liquefaction and its consequences. Seismic earth pressures, slopes stability, safety of dams and embankments, seismic code provisions and practice. To alternate with E4244.
This seminar will consider the evolution of language at the levels of the word and grammar, in each instance, phylogenetically and ontogenetically. Since humans are the only species that use language, attention will be paid to how language differs from animal communication.
Prerequisites: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will be covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.
Quantitative introduction to hydrologic and hydraulic systems, with a focus on integrated modeling and analysis of the water cycle and associated mass transport for water resources and environmental engineering. Coverage of unit hydrologic processes such as precipitation, evaporation, infiltration, runoff generation, open channel and pipe flow, subsurface flow and well hydraulics in the context of example watersheds and specific integrative problems such as risk-based design for flood control, provision of water, and assessment of environmental impact or potential for non-point source pollution. Spatial hydrologic analysis using GIS and watershed models.
Prerequisites: ECON UN3211 and ECON UN3213 The study of industrial behavior based on game-theoretic oligopoly models. Topics include pricing models, strategic aspects of business practice, vertical integration, and technological innovation.
Engineering aspects of problems involving human interaction with the natural environment. Review of fundamental principles that underlie the discipline of environmental engineering, i.e. constituent transport and transformation processes in environmental media such as water, air, and ecosystems. Engineering applications for addressing environmental problems such as water quality and treatment, air pollution emissions, and hazardous waste remediation. Presented in the context of current issues facing the practicing engineers and government agencies, including legal and regulatory framework, environmental impact assessments, and natural resource management.
Italo Calvino's imagined Marco Polo cautions in Invisible Cities (1972): "Memory's images, once they are fixed in words, are erased." How, then, can we retrieve from the vanished past the lived experiences of men and women in their built environments? This seminar invites you on a tour of a constellation of cities—as both physical sites and literary creations—from China’s pre-imperial period to the twentieth century, engaging textual, visual, and cinematic media that have shaped, and been shaped by, the palimpsests of urban life in flux.
Introduction parametric and non-parametric statistical models applied to climate and environmental data analysis. Time and space data analysis methods will be focused, including clustering, autoregressive models, trend analysis, Bayesian analysis, missing data imputation, geostatistics, principal components analysis. Application to problems of climate variation and change; hydrology; air, water and soil pollution dynamics; disease propagation; ecological change; and resource assessment. The class requires the use of R with hands-on programmings and a term project applied to a current environmental data analysis problem.
Sensor modalities and their applications in construction and facilities management. Deep learning concepts and their application in robot perception. Markov Decision Process (MDP) and its application in planning and control. Formulation of embodied AI perception and control problems as MDP. Application of classic reinforcement learning algorithms to solve MDP problems. Analysis of agents’ performance through objective and subjective metrics. Understanding the critical interactions between users/occupants and embodied AI agents. Hands-on experience with robot simulation and/or collaborative robots in controlled lab environments.
Prerequisites: STAT GU4205 or the equivalent. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.
This course will consider themes in 19th-century social and political philosophy. Central topics may include freedom, recognition, alienation, and exploitation, and the use of such concepts to critically evaluate modern social and political institutions. Figures studied may include G.W.F. Hegel, Ludwig Feuerbach, Karl Marx, Friedrich Engels, Clara Zetkin, and Lily Braun.
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: PSYC UN1010 PSYC UN1010 or equivalent; background in statistics/research methods recommended How does the human brain make sense of the acoustic world? What aspects of auditory perception do humans share with other animals? How does the brain perform the computations necessary for skills such as soundlocalization? How do we focus our auditory attention on one voice in a crowd? What acoustic cues are important for speech perception? How is music perceived? These are the types of questions we will address by studyingthe basics of auditory perception from textbook readings and reviews, and reading classic and current literatureto understand scientific progress in the field today.
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.
This course examines how digital technologies are transforming human rights advocacy, with primary emphasis on social media campaigning. Students will master hands-on social media platform practices while exploring how open source intelligence (OSINT) methodologies are used to monitor violations and present evidence online through recent case studies. The course prioritizes developing practical social media advocacy and analytic skills, examining how civil society organizations navigate platform policies, content moderation, and political pressures to drive change. Students will analyze how platform policy shifts and content governance changes constrain advocacy strategies, learning to craft campaigns and frame messages for specific audiences. They will analyze cases involving gender, immigration, and trafficking, among others. The OSINT component provides conceptual understanding through contemporary examples including forensic architecture investigations, satellite imagery documentation of mass atrocities, and open source evidence from conflicts like Ukraine. A key component of the course is a research or advocacy project of your choosing. You will develop framing strategies, map relevant networks, and create social media content that demonstrates mastery of digital advocacy techniques. The emergence of these new tools and organizations has produced new ethical dilemmas and reshaped old ones--concerning such fundamental issues as privacy vs. security, the limits of free speech, the trade-off between ethical and pragmatic messaging and fundraising strategies, topics that will be addressed at length in class discussions.
Prerequisites: For undergraduates: one course in cognitive psychology or cognitive neuroscience, or the equivalent, and the instructors permission. Metacognition and control processes in human cognition. Basic issues include the cognitive mechanisms that enable people to monitor what they know and predict what they will know, the errors and biases involved in self-monitoring, and the implications of metacognitive ability for peoples self-determined learning, behavior, and their understanding of self.
Why do we put off things until later—even things we know are important; even in cases where we know the cost of delaying; even when doing the work more gradually over time would be less unpleasant; even sometimes on tasks we anticipate enjoying? Everyone procrastinates sometimes, but why do some people seem to procrastinate a lot while others don’t have much of an issue with task delaying? This course reviews current research on selected cognitive and motivational theories of procrastination, as well as interaction of task delay with mental health and neurodiversity. We will close with an examination of some potential interventions that may help people reduce or avoid procrastination, both at the individual level and in academic settings such as course design.
Principles and practice of water treatment and utility management will be presented. Project-based class where students will work in teams to solve an issue for a water utility. Variety of external experts will lecture and serve as a resource for students for the project. Allows students to better understand the role of the water utility in providing safe drinking water in a sustainable manner. Students will become familiar with the challenges facing water utilities, gain knowledge in the design and operation of water treatment systems, and learn how to develop solutions to water supply and water quality issues which will allow them to pursue productive careers in the consulting, utility, or regulatory fields.
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.
This course will cover the development of modern social science and its relation to American history and culture. The different strands of the course are indicated by its title, where “rationalizing” refers both to attempts to understand society through rational means and to the role of social science in providing a justification or rationale for existing social structures.
Quantitative thinking and social science have become increasingly prominent in our society. But modern discussions of the political relevance of social science do not always account for the ups and downs of particular ideas. For example, Freudianism was huge in mid-century, both within psychology and in the culture at large, but has faded for both intellectual and economic reasons. The Keynesian revolution dominated economics from the 1930s through the 1960s but then was contested by later paradigms in response to the stagflation of the following decade. Trends in criminal justice policy have followed ideas from anthropology, psychology, and economics, and political theories of international relations have affected and been informed by developments in foreign policy. This course provides students with an opportunity to learn about these and other examples of the development and influence of theories in social science, and to form a larger connection between intellectual, social, and political history.
It is common for students to learn about just one or maybe two social sciences and not to see the way that different social sciences fit together intellectually and how they compete for influence. There’s a tendency to think of any field of study as being a static set of truths as laid out in textbooks or else a steady march of progress. In contrast, this course presents a series of booms and crashes: unsustainable enthusiasms for new ideas followed by disillusionment and controversies that are often never fully resolved. Through readings, class discussion and activities, and final projects, students should learn to see social science as a process that proceeds both internally and with reference to society.
By the end of the course, students should gain a broad understanding of the development of modern social science and its connection to American politics and society. They will read different sides of academic disputes involving figures from Margaret Mead to Milton Friedman and will gain a historically informed sense of how social science has been influenced by and has influence
Discussion section for POLS GU4280, Rationalizing the World: American Social Science
Discussion section for POLS GU4280, Rationalizing the World: American Social Science
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.
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.
Urbanization is inherently unequal, inscribing social, economic, environmental, and political unevenness into the spatial fabric of the city. But the distribution of such inequality is not inevitable. Urbanization is a product of the collective decisions we make (or choose not to make) in response to the shared challenges we face in our cities. And, thus, the patterns of urbanization can be changed. This is the task of urban planning and the starting point for this advanced seminar, which asks how we can reshape our cities to be more just—to alleviate inequality rather than compound it. In embarking on this effort, we face numerous “wicked” problems without clear-cut solutions. The approaches one takes in addressing urban inequality are therefore fundamentally normative—they are shaped by one’s place in the world and one’s view of it. The central challenge in addressing inequality is thus establishing a basis for collective action amongst diverse actors with differing—and sometimes conflicting—values and views. In other words, planning the just city a matter of both empathy and debate. In this course, we will endeavor to develop informed positions that can help us engage with others as a basis for taking collective action.
The course is organized into four 3-week modules, each of which addresses a dimension of the just city: equity, democracy, diversity, and sustainability. In the first week of each module, we will discuss how the issue has been understood in history and theory (with an emphasis on tradeoffs between different priorities and values); in the second week, we will apply this discussion to a global case study prepared and presented by a team of students; and in the third week, we will hold an in-class debate to determine what should be done. Specific case studies vary each year.
This course introduces the fundamental principles of corporate finance and their application to real-world business decisions. Students will examine how companies determine value, measure risk, and make financing choices, while developing the tools to analyze corporate investments and capital structures.
Intellectual Goals and Rationale
The course addresses core questions that drive business decision-making:
How do we determine what a company or investment opportunity is worth?
How do we value financial securities in an uncertain world?
What is risk? How do we measure it, and how does it affect the cost of capital?
What is the appropriate balance between debt and equity?
Course Content and Learning Approach
Through a combination of theoretical frameworks, case discussions, and Excel-based financial modeling, students will build the ability to analyze complex financial scenarios. Lectures provide the foundations of valuation and financing, while case work applies these tools to real business challenges.
Why This Course Matters
Valuation, investment evaluation, and financing decisions are central to careers in finance, consulting, entrepreneurship, and management. The skills gained—financial modeling, risk assessment, and valuation analysis—are directly relevant to roles in investment banking, private equity, corporate development, consulting, and executive leadership.
Who Should Take This Course
This introductory finance course is open to students from all academic backgrounds who seek to strengthen their financial literacy and analytical capabilities. It is particularly valuable for:
Students considering careers in finance, consulting, or general management
Entrepreneurs who need to understand funding and valuation
Students in other fields interested in how businesses create and measure value
Those planning to pursue graduate business education
Prerequisites
Economics:
ECON UN1105 Principles of Economics
Statistics (one of the following):
STAT UN1001 Intro to Statistical Reasoning
STAT UN1101 Introduction to Statistics
STAT UN1201 Calc-Based Introduction to Statistics
PSYC UN1610 Introductory Statistics for Behavioral Science
Cours
Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems.
A one-semester survey of seventeenth-century French literature, with an emphasis on the relationship between literature and the major cultural, philosophical, and religious developments of the period.
Introduction to the key concepts and issues in computational science aimed at getting students to a basic level of understanding where they can run simulations on machines aimed at a range of applications and sizes from a single workstation to modern super-computer hardware. Topics include but are not limited to basic knowledge of UNIX shells, version control systems, reproducibility, Open MP, MPI, and many-core technologies. Applications will be used throughout to demonstrate the various use cases and pitfalls of using the latest computing hardware.
Prerequisites: CHNS W3301: Classical Chinese I; completion of three years of modern Chinese at least, or four years of Japanese or Korean. Please see department. Prerequisites: CHNS W3301: Classical Chinese I; completion of three years of modern Chinese at least, or four years of Japanese or Korean.