Physiological systems at the cellular and molecular level are examined in a highly quantitative context. Topics include chemical kinetics, molecular binding and enzymatic processes, molecular motors, biological membranes, and muscles.
Part of an accelerated consideration of the essential chemical engineering principles from the undergraduate program, including selected topics from Introduction to Chemical Engineering, Transport Phenomena I and II, and Chemical Engineering Control. While required for all M.S. students with Scientist to Engineer status, the credits from this course may not be applied toward any chemical engineering degree.
Co-requisite undergraduate discussion section for FILM GU 4000 Film & Media Theory.
Prerequisites: Calculus through multiple integration and infinite sums. A calculus-based tour of the fundamentals of probability theory and statistical inference. Probability models, random variables, useful distributions, conditioning, expectations, law of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. This course replaces SIEO 4150.
Part of an accelerated consideration of the essential chemical engineering principles from the undergraduate program, including topics from Reaction Kinetics and Reactor Design, Chemical Engineering Thermodynamics, I and II, and Chemical and Biochemical Separations. While required for all M.S. students with Scientist to Engineer status, the credits from this course may not be applied toward any chemical engineering degree.
This course is customized for 1st-year PhD and MA students in the biomedical informatics graduate program and also
open to other interested students at Columbia. It provides a detailed overview of symbolic methods.
Introduction to the economic evaluation of industrial projects. Economic equivalence and criteria. Deterministic approaches to economic analysis. Multiple projects and constraints. Analysis and choice under risk and uncertainty.
Prerequisites: one year of biology; a course in physics is highly recommended. Lecture and recitation. This is an advanced course intended for majors providing an in depth survey of the cellular and molecular aspects of nerve cell function. Topics include the cell biology and biochemistry of neurons, ionic and molecular basis of electrical signals, synaptic transmission and its modulation, function of sensory receptors. Although not required, it is intended to be followed by Neurobiology II (see below). The recitation meets once per week in smaller groups and emphasizes readings from the primary literature.
A graduate course only for MS&E, IE, and OR students. This is also required for students in the Undergraduate Advanced Track. For students who have not studied linear programming. Some of the main methods used in IEOR applications involving deterministic models: linear programming, the simplex method, nonlinear, integer and dynamic programming.
A graduate course only for MS&E, IE, and OR students. This is also required for students in the Undergraduate Advanced Track. For students who have not studied linear programming. Some of the main methods used in IEOR applications involving deterministic models: linear programming, the simplex method, nonlinear, integer and dynamic programming.
Ukrainians’ response to Russia’s full-scale invasion of the country in February 2022 has attracted global attention. Ukraine is also known to many for mass protests in Kyiv 2004 and 2013-14. However, fewer people know that Ukraine has a rich history of activism and protest throughout the country, going back decades. This course is designed to help students cultivate a deeper understanding of Ukraine’s nationwide history of activism, from the late Soviet period to present-day. This knowledge will also help us better contextualize and analyze key episodes of resistance, protest and revolution in Ukraine, including the current war. Moreover, via the lens of activism and protest, this course intends to provide students with a more nuanced understanding of regional variation in Ukraine, empowering them to question simplistic narratives about Ukraine as a divided county. The multidisciplinary nature of this course also aims to encourage students to engage with Ukrainian art and cultural objects that relate to social and political themes.
For graduate students and others who need to develop their reading knowledge of Italian. Open to undergraduate students as well, who want a compact survey/review of Italian structures and an approach to translation. Grammar, syntax, and vocabulary review; practice in reading and translating Italian texts of increasing complexity from a variety of fields, depending on the needs of the students. No previous knowledge of Italian is required. Note: this course may not be used to satisfy the language requirement or to fulfill major or concentration requirements.
The transition from the protected status of childhood into adulthood in the United States varies across class, age, socioeconomic, and legal status, but how does law intersect with rites of passage in coming of age experiences with youths in Latin America? How have societies in the Americas define the shifting notions of childhood and adolescence and how have youths experience coming of age? This course will familiarize students with how legal regimes in Latin America and the United States define the fluid parameters of childhood, adolescence and adulthood. Students will learn to recognize the role of law and the contradictions in how youths experience the emotional, legal, political, and cultural transition of coming of age.
This course is organized around a number of thematic centers or modules. Each is focused on stylistic peculiarities typical of a given functional style of the Ukrainian language. Each is designed to assist the student in acquiring an active command of lexical, grammatical, discourse, and stylistic traits that distinguish one style from the others and actively using them in real-life communicative settings in contemporary Ukraine. The styles include literary fiction, scholarly prose, and journalism, both printed and broadcast.
Fundamentals of Linear Algebra including vector and Matrix algebra, solution of linear systems, existence and uniqueness, gaussian elimination, gauss-jordan elimination, the matrix inverse, elementary matrices and the LU factorization, computational cost of solutions. Vector spaces and subspaces, linear independence, basis and dimension. The 4 fundamental subspaces of a matrix. Orthogonal projection onto a subspace and solution of Linear Least Squares problems, unitary matrices, inner products, orthogonalization algorithms and the QR factorization, applications. Determinants and applications. Eigen problems including diagonalization, symmetric matrices, positive-definite systems, eigen factorization and applications to dynamical systems and iterative maps. Introduction to the singular value decomposition and its applications.
This course explores national case studies of environmental and racial injustice in Latinx communities and their connection to climate change. Students in the course will analyze, interpret, and evaluate cultural symbols and arguments from migrant farmworkers; Black Indigenous in cities; Afro-Latina women in rural, island contexts; and others who confront the most serious consequences of environmental degradation and climate disruption. It addresses theories and concepts of environmental racism and environmental justice, underscoring how Latinx groups have challenged, expanded, and contributed to the environmental justice discourse in struggles over public parks and beaches, clean air, clean water, pesticide exposure, lead poisoning, and high environmental risks since the 1960s. The course will examine distinct Latinx histories and geographies through the lens of essays, art and sound installations, short stories, documentaries, poetry, short films, and digital multimedia projects to understand better the environmental attitudes and issues that impact Latinx groups in the historical and increasingly urgent challenges of climate change and environmental injustice.
Linear, quadratic, nonlinear, dynamic, and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering are discussed.
Linear, quadratic, nonlinear, dynamic, and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering are discussed.
Prerequisites: JPNS C1202 or the equivalent. Introduction to the fundamentals of classical Japanese grammar. Trains students to read Japanese historical and literary texts from the early period up to the 20th century.
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Prerequisites: advanced calculus and general physics, or the instructors permission. Basic physical processes controlling atmospheric structure: thermodynamics; radiation physics and radiative transfer; principles of atmospheric dynamics; cloud processes; applications to Earths atmospheric general circulation, climatic variations, and the atmospheres of the other planets.
Prerequisites: GREK V1201 and V1202, or their equivalent. Since the content of the course changes from year to year, it may be taken in consecutive years.
Prerequisites: LATN V3012 or the equivalent. Since the content of this course changes from year to year, it may be repeated for credit.
Introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics include basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies.
Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems.
Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems.
Explores a variety of ethical and political issues that arise during the conduct of basic and clinical scientific research. Course sessions include lectures, discussion periods, and analyses of case studies.
This introductory course surveys fundamental Microsoft Excel concepts and functionality applicable to SIPA courses and in professional settings. Topics include understanding references and functions, writing formulas, interacting with spreadsheets, building basic models, controlling formatting and presentation and creating basic charts. The course is targeted at students with limited or no prior Excel experience. The course is open to SIPA students only. Note: A laptop is required for this course
Prerequisites: Intermediate reading knowledge of Spanish This course considers how language has traditionally shaped constructs of national identity in the Caribbean vis-à-vis the US. By focusing on language ‘crossings’ in Latinx Caribbean cultural production, we critically explore how various sorts of texts–narrative, drama, performance, poetry, animated TV series, and songs–contest conventional notions of mainstream American, US Latinx, and Caribbean discourses of politics and identities. Taking 20th-century social and historical context into account, we will analyze those contemporary styles and uses of language that challenge monolingual and monolithic visions of national and ethnolinguistic identities, examining societal attitudes, cultural imaginaries, and popular assumptions about the Spanish language in the Greater Caribbean and the US.
Engineering economic concepts. Basic spreadsheet analysis and programming skills. Subject to instructor's permission. Infrastructure design and systems concepts, analysis, and design under competing/conflicting objectives, transportation network models, traffic assignments, optimization, and the simplex algorithm.
A close reading of works by Dostoevsky (Netochka Nezvanova; The Idiot; A Gentle Creature) and Tolstoy (Childhood, Boyhood, Youth; Family Happiness; Anna Karenina; The Kreutzer Sonata) in conjunction with related English novels (Bronte's Jane Eyre, Eliot's Middlemarch, Woolf's Mrs. Dalloway). No knowledge of Russian is required.
A close reading of works by Dostoevsky (Netochka Nezvanova; The Idiot; A Gentle Creature) and Tolstoy (Childhood, Boyhood, Youth; Family Happiness; Anna Karenina; The Kreutzer Sonata) in conjunction with related English novels (Bronte's Jane Eyre, Eliot's Middlemarch, Woolf's Mrs. Dalloway). No knowledge of Russian is required.
Application of industrial ecology to Design for Environment (DFE) of processes and products using environmental indices of resources consumption and pollution loads. Introduction of methodology for Life Cycle Assessment (LCA) of manufactured products. Analysis of several DFE and LCA case studies. Term project required on use of DFE/LCA on a specific product/process: (a) product design complete with materials and process selection, energy consumption, and waste loadings; (b) LCA of an existing industrial or consumer product using a commercially established method.
Prerequisites: SIPA U4010 or equivalent experience This course explores skills needed for sophisticated spreadsheet development and problem solving in Microsoft Excel. Topics include implementing advanced logic using complex formulas, managing complexity with Excel's auditing features, leveraging lookup functions leveraging and calculated references, parsing and cleaning raw data, refining data structure, and constructing and leveraging PivotTables. The course does not focus on specific models or applications, but instead explores general concepts and techniques that can be flexibly applied to different solutions in Excel. The course is open to SIPA students only. Instructor approval is required: students will be waitlisted in SSOL and contacted by the instructor. Part of the Excel at SIPA course series. Deadline to drop this course is one week prior to the start date of the course. A notation of "W" will be assigned if requests to drop are not made by this deadline.
The Business Chinese I course is designed to prepare students to use Chinese in a present or future work situation. Students will develop skills in the practical principles of grammar, vocabulary, and cross-cultural understanding needed in today’s business world.
How do you write literature in the midst of catastrophe? To whom do you write if you don’t know whether your readership will survive? Or that you yourself will survive? How do you theorize society when the social fabric is tearing apart? How do you develop a concept of human rights at a time when mass extermination is deemed legal? How do you write Jewish history when Jewish future seems uncertain?
This course offers a survey of the literature and intellectual history written during World War II (1939-1945) both in Nazi occupied Europe and in the free world, written primarily, but not exclusively, by Jews. We will read novels, poems, science fiction, historical fiction, legal theory and social theory and explore how intellectuals around the world responded to the extermination of European Jewry as it happened and how they changed their understanding of what it means to be a public intellectual, what it means to be Jewish, and what it means to be human.
The aim of the course is threefold. First, it offers a survey of the Jewish experience during WWII, in France, Russia, Poland, Latvia, Romania, Greece, Palestine, Morocco, Iraq, the USSR, Argentina, and the United States. Second, it introduces some of the major contemporary debates in holocaust studies. Finally, it provides a space for a methodological reflection on how literary analysis, cultural studies, and historical research intersect.
This intensive one-day workshop develops financial modeling skills through the hands-on construction of an interactive financial model. Using a real company as a case study, the lectures will direct participants to blend accounting, corporate finance and Excel skills to create a dynamic, three-statement financial model. The completed product has five years of projections, three years of historical data and supporting schedules including working capital, debt, equity, depreciation and amortization. Other advanced topics include understanding and controlling circularity errors, troubleshooting, sensitivity analysis and discounted cash flow valuations.
Prerequisites: at least 3 years of intensive Chinese language training at college level and the instructor's permission. This advanced course is designed to specifically train students' listening and speaking skills in both formal and colloquial language through various Chinese media sources. Students view and discuss excerpts of Chinese TV news broadcasts, soap operas, and movie segments on a regular basis. Close reading of newspaper and internet articles and blogs supplements the training of verbal skills.
Prerequisites: Third Year Chinese or the equivalent The course is designed to help students master formal Chinese for professional or academic purposes. It includes reading materials and discussions of selections from Chinese media on contemporary topics, Chinese literature, and modern Chinese intellectual history. The course aims to enhance students' strategies for comprehension, as well as their written and oral communication skills in formal modern Chinese.
This seminar examines the many meanings of food in Italian culture and tradition; how values and peculiarities are transmitted, preserved, reinvented and rethought through a lens that is internationally known as ;Made in Italy;; how the symbolic meanings and ideological interpretations are connected to creation, production, presentation, distribution, and consumption of food. Based on an anthropological perspective and framework, this interdisciplinary course will analyze ways in which we can understand the Italian taste through the intersections of many different levels: political, economic, aesthetic, symbolic, religious, etc. The course will study how food can help us understand the ways in which tradition and innovation, creativity and technology, localism and globalization, identity and diversity, power and body, are elaborated and interpreted in contemporary Italian society, in relation to the European context and a globalized world. Short videos that can be watched on the computer and alternative readings for those fluent in Italian will be assigned. In English.
This course researches the potentiality and development of a Socialist World Literature. Students will learn about the more contemporary constructions of World Literature in the West, and then look at how the Soviet Union and its satellites potentially crafted an alternative to the contemporary construction. The class will then examine whether the Soviet version addressed some of the criticism of the contemporary definitions of World Literature, particularly through addressing the colonialism and nationalism.
Students will learn about the complex history of World Literature and its definitions, reading the major theorists of the concept as well as the major critics. They will also create their own arguments about World Literature in a highly-scaffolded major project due at the end of the term.
All readings will be provided online.
Prerequisites: CHNS W4006 or the equivalent. This is a non-consecutive reading course designed for those whose proficiency is above 4th level. See Admission to Language Courses. Selections from contemporary Chinese authors in both traditional and simplified characters with attention to expository, journalistic, and literary styles.
Central Europe is home to large number of authors, artists, and directors who made use of the critical power of the grotesque. Beginning from the
fin-de-siecle
and moving to the contemporary moment, students will get to know a wide range of grotesque art from Central Europe as well as several of the critical approaches to the subject. The course should be of interest to anyone studying Central European culture, as well as students interested in cultural studies more generally.
Students will learn to identify and analyze examples of the grotesque through a variety of theoretical lenses. They will also enrich their knowledge of Central European literature and culture.
Prerequisites: JPNS W4006 or the equivalent. Sections 1 & 2: Readings of advanced modern literary, historical, political, and journalistic texts, and class discussions about current issues and videos. Exercises in scanning, comprehension, and English translation. Section 3: Designed for advanced students interested in developing skills for reading and comprehending modern Japanese scholarship.
This course aims to provide a comprehensive understanding of computational approaches in the microbiome field. Through the discussion of state-of-the-art methods and algorithms, we will review key methodological challenges in microbiome data analysis, such as taxonomic inference, compositional data analysis, reference-free metagenomic reconstructions, and applications of machine learning. To understand the role of these challenges and methods in the wider context of biological research in the field, we will discuss major high-impact controversies among researchers as well as impactful areas of clinical and biological investigations. The course will comprise of lectures, short weekly assignments, a midterm, and a final presentation. Each week will comprise a lecture on computational methods and another on clinical impact and controversies. By the end of the course, students will have a deep understanding of the current state of microbiome research and potential future directions, and will be able to dissect and analyze different computational approaches for their advantages and disadvantages in the context of progress in the field.
This course is suitable for: biology-oriented students who wish to obtain a better understanding of computational challenges in the field; CS/engineering students who wish to get exposure to applications of computational methods in biology; microbiome enthusiasts.
Prerequisites:
A prior introductory class in mathematics or statistics.
The evolution of the Chinese language. Topics include historical phonology, the Chinese script, the classical and literary languages, the standard language and major dialects, language and society, etc.
Prerequisites: PHYS UN3003 and PHYS UN3007 and differential and integral calculus; linear algebra; or the instructor's permission. This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: ordinary and partial differential equations; generalized functions; integral transforms; Green’s functions; nonlinear equations, chaos, and solitons; Hilbert space and linear operators; Feynman path integrals; Riemannian manifolds; tensor analysis; probability and statistics. There will also be a discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity.
The biophysics of computation: modeling biological neurons, the Hodgkin-Huxley neuron, modeling channel conductances and synapses as memristive systems, bursting neurons and central pattern generators, I/O equivalence and spiking neuron models. Information representation and neural encoding: stimulus representation with time encoding machines, the geometry of time encoding, encoding with neural circuits with feedback, population time encoding machines. Dendritic computation: elements of spike processing and neural computation, synaptic plasticity and learning algorithms, unsupervised learning and spike time-dependent plasticity, basic dendritic integration. Projects in MATLAB.
To expose engineers, scientists and technology managers to areas of the law they are most likely to be in contact with during their career. Principles are illustrated with various case studies together with active student participation.
To expose engineers, scientists and technology managers to areas of the law they are most likely to be in contact with during their career. Principles are illustrated with various case studies together with active student participation.
Prerequisites: ECON UN3211 and ECON UN3213 and STAT UN1201 Topics include behavior uncertainty, expected utility hypothesis, insurance, portfolio choice, principle agent problems, screening and signaling, and information theories of financial intermediation.
Prerequisites: PHYS UN3003 and PHYS UN3007 Formulation of quantum mechanics in terms of state vectors and linear operators. Three dimensional spherically symmetric potentials. The theory of angular momentum and spin. Identical particles and the exclusion principle. Methods of approximation. Multi-electron atoms.
This course introduces the students to a growing subfield of both literary studies and sociology as well as history: sociology of literature. It is particularly developed in the French-speaking countries: The course and discussions will be in French, and many of the texts will be in French when an English version is not available.
After two classes centered around theories that form the basis of most of current sociology of literature, the course will explore empirical case studies, which all have also a theoretical aspect. This will be organized into three parts. Part one will be dedicated to the social conditions of literary production and of being a writer. Part two will focus on inequalities in the literary field, depending on “identity” factors (gender, race, nation, language). Part three will be centered around the reception of the literary text and its afterlife, in particular its process of consecration.
Typically, one class consists of a discussion around two texts (chapters of a book, and one article). It is introduced by a student who will compare both texts: they will also introduce the other students to a text that they would have picked within the “additional texts” (they can also propose a text outside of this list). Each class will bring together empirical case studies that have a temporal and/or geographical scope: in general, one will concern the Francophone world, and another one will concern another linguistic area. Sociology of literature always try to go beyond the particular to try and find patterns across time and space: this course is henceforth also a class of comparative literature.
Prerequisites: PHYS GU4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism.
This course will offer an account of the multiple migrations out, in and through Italy since 1800. By combining history, literature, and film, and by approaching the topic through the lens of transnationalism, we will study different topics of Italian mobility, such as Exile and the Risorgimento, The Mediterranean in Motion, Migrants’ Experiences at Sea, The Great Italian “Exodus” to the Americas, Mobile Italy and its Colonies, The Lost Italian “Cosmopolitanisms” of the Middle East, Postwar Italian “National Refugees”, and Contemporary Migration to Italy. We will read masterpieces of Italian literature both by Italian-American authors and by contemporary migrants to Italy. We will watch some of the most important films and documentaries on these topics. And we will think about how such phenomena as Italian mass emigration in the long nineteenth century, Fascist colonialism and resettlement of populations in the twentieth century, postwar refugees, and contemporary immigrants to Italy are all intrinsically interconnected and make part of the same story. Overall, the aim of this course is to turn our gaze away from the territorially defined Italy, towards a view of Italy as a space on the move.
This course will offer an account of the multiple migrations out, in and through Italy since 1800. By combining history, literature, and film, and by approaching the topic through the lens of transnationalism, we will study different topics of Italian mobility, such as Exile and the Risorgimento, The Mediterranean in Motion, Migrants’ Experiences at Sea, The Great Italian “Exodus” to the Americas, Mobile Italy and its Colonies, The Lost Italian “Cosmopolitanisms” of the Middle East, Postwar Italian “National Refugees”, and Contemporary Migration to Italy. We will read masterpieces of Italian literature both by Italian-American authors and by contemporary migrants to Italy. We will watch some of the most important films and documentaries on these topics. And we will think about how such phenomena as Italian mass emigration in the long nineteenth century, Fascist colonialism and resettlement of populations in the twentieth century, postwar refugees, and contemporary immigrants to Italy are all intrinsically interconnected and make part of the same story. Overall, the aim of this course is to turn our gaze away from the territorially defined Italy, towards a view of Italy as a space on the move.
Designed for new Teaching Fellows. An introduction to the conceptual and practical tools of French language pedagogy.
The city has historically served to gather and leverage what the hinterland has produced: urban crafts guilds added value to raw materials, crops and piecework were monetized, knowledge was assembled and disseminated in cities. Within sustainability studies, cities are often cited for the efficiency of their transportation, housing and supply or refuse infrastructures, but the nature of their relationship to their hinterlands in a globalized world may be underplayed. Nothing – whether a living creature or a settlement – can have a metabolic rate of zero. This course will look to the knowledge base of urban metabolism to ask questions about how cities supply and off-load their metabolic processes. We will also engage with experts in food supply, public health, water, energy and other basic components of urban metabolism.
Prerequisites: three terms of calculus and linear algebra or four terms of calculus. Prerequisite: three terms of calculus and linear algebra or four terms of calculus. Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines.
This course investigates representations of gender and sexuality in the Portuguese-speaking world in a variety of media, such as cinema, comics, and music through a queer perspective aligned with understandings of language and representation. Taking the term “Lusofonia”—a concept coined to designate a sense of cultural coherence shared among Portuguese-speaking countries worldwide—as point of departure, we will investigate how one deals with questions of gender identity and sexual orientation in the Lusophone world.
This course aims at understanding how language shapes our perceptions of gender identities and sexual orientations. Also, this course intends to develop the idea of Mapping Queerness using technology for mapping language in regards to sexual identities representations.
The idea of inclusive language permeates the discussions proposed in this course. However, it is intended to observe points of exclusion in our daily communications as well.
Therefore, this course aims at discussing these complex issues in regards to gender and sexual identity in Brazil and in other Lusophone countries taking into consideration cultural productions such as cinema and music.