May be repeated for credit, but no more than 3 total points may be used toward the 128-credit degree requirement. Only for SEAS computer science undergraduate students who include relevant off campus work experience as part of their approved program of study. Final report and letter of evaluation may be required. May not be used as a technical or nontechnical elective 
or as a GTE (general technical elective)
. May not be taken for pass/fail credit or audited.
                                
                            
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                                    Students must enroll for both 3998x and 3999y during their senior year. Selection of an actual problem in Earth and environmental engineering, and design of an engineering solution including technical, economic, environmental, ethical, health and safety, social issues. Use of software for design, visualization, economic analysis, and report preparation. Students may work in teams. Presentation of results in a formal report and public presentation.
Prerequisites: the departments permission. This course is open only to those who have applied and been accepted into the departments senior essay program. For information about the program, including deadline for application, please visit http://english.columbia.edu/undergraduate/senior-essay-program.
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                                Prerequisites: admission to the departmental honors program. A two-term seminar for students writing the senior honors thesis.
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                                Prerequisites: open only to qualified majors in the department; the director of undergraduate studies permission is required. An opportunity for research under the direction of an individual faculty member. Students intending to write a year-long senior thesis should plan to register for C3996 in the spring semester of their senior year and are strongly advised to consult the undergraduate studies as they plan their programs.
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                                    Current topics in biomedical engineering. Subject matter will vary by year.
Current topics in biomedical engineering. Subject matter will vary by year.
Current topics in biomedical engineering. Subject matter will vary by year.
Current topics in biomedical engineering. Subject matter will vary by year.
Current topics in biomedical engineering. Subject matter will vary by year.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
The PDL course aims to enhance and expand Columbia Engineering graduate students' interpersonal, professional, and leadership skills, through five core sessions, covering (1) in-person communication skills; (2) resume; (3) business writing; (4) social media and the job search; and (5) academic and professional ethics and integrity. ENGI E4000 also requires 5 elective sessions to further students' development based on their personal interests. Students must select at least one life management elective and one interview elective. This course is offered at the Pass/D/Fail grading option.
                                
                                Prerequisite: Successful completion of URBS UN2200 Introduction to GIS Methods, or equivalent with instructor permission.
  
With the veritable explosion of urban data alongside the continued proliferation of new tools for its consideration, this course allows students to develop specialized approaches to spatial analysis while introducing a series of common advanced techniques and nuanced methodological questions. Aimed at covering a variety of topics with immediate relevance to urbanism in practice and in research, the course operates with a two-fold mission: (1) to critically discuss the theories, concepts, and research methods involved in spatial analysis and (2) to learn the techniques necessary for engaging those theories and deploying those methods. The class will work to meet this mission with a dedicated focus on the urban environment and the spatial particularities and relationships that arise from the urban context.
  
Among others, this course takes as a foundational premise that spatial analysis within geographic information systems is an incredibly powerful and double-edged weapon: it provides both the methods for answering complex spatial questions and the means for effectively communicating the results. Like any other weapon it can serve many ends, and as such an advanced course in spatial analysis must frame its use within the developing discourse on professional practice and responsibility.
  
The course is designed with a combination format. Early weeks are predominantly lecture-style presentations supplemented with discussion and technical demonstration and exercises. Students are expected to complete these exercises outside of class (as homework), bringing their questions to our discussion. The latter half of the course is a project-based seminar. Seminar-style presentation and discussion will rely heavily on student participation and preparation to consider the variety of spatial methods available and their implications on urban research and intervention. Woven throughout the semester is the development of a self-driven research project, through which students will engage and compare the methodological advantages and disadvantages of several assumptions, approaches, analyses, and datasets.
                                
                            
Prerequisites: for undergraduates: Introductory Genetics (W3031) and the instructors permission. This seminar course provides a detailed presentation of areas in classical and molecular genetics for advanced undergraduates and beginning graduate students. Topics include transmission genetics, gain and loss of function mutations, genetic redundancy, suppressors, enhancers, epistasis, expression patterns, using transposons, and genome analysis. The course is a mixture of lectures, student presentations, seminar discussions, and readings from the original literature.
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.
Prerequisites: Medical Informatics G4001, Computer Science W3139. Survey of the methods underlying the field of medical informatics. Explores techniques in mathematics, logic, decision science, computer science, engineering, cognitive science, management science and epidemiology, and demonstrates the application to health care and biomedicine.
Students are introduced to a quantitative, engineering approach to cellular biology and mammalian physiology. Beginning with biological issues related to the cell, the course progresses to considerations of the major physiological systems of the human body (nervous, circulatory, respiratory, renal).
 
An engineering and economic analysis of past, present and future energy resources. Technological options and their role in the world energy markets. Understanding limits of energy and power density and its impact of resource adoption and feasibility. Comparison of renewable and non-renewable energy resources and analysis of the consequences of various technological choices and constraints. Economic considerations, energy availability, and the environmental consequences of large-scale, widespread use of each particular technology. Critical analysis of carbon dioxide capture and carbon dioxide disposal as a means of sustaining the fossil fuel options in comparison to dramatic increase of electrified resources.
Principles of physical chemistry applied to equilibria and kinetics of aqueous solutions in contact with minerals and anthropogenic residues. The scientific background for addressing problems of aqueous pollution, water treatment, and sustainable production of materials with minimum environmental impact. Hydrolysis, oxidation-reduction, complex formation, dissolution and precipitation, predominance diagrams; examples of natural water systems, processes for water treatment and for the production of inorganic materials from minerals.
Prerequisites: differential and integral calculus, differential equations, and PHYS UN3003 or the equivalent. Lagranges formulation of mechanics, calculus of variations and the Action Principle, Hamiltons formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics.
                                
                                For more than a century, scientists, policy makers, law enforcement, and government agencies
  
have collected, curated and analyzed data about people in order to make impactful decisions.
  
This practice has exploded along with the computational power available to these agents. Those
  
who design and deploy data collection, predictive analytics, and autonomous and intelligent
  
decision-making systems claim that these technologies will remove problematic biases from
  
consequential decisions. They aim to put a rational and objective foundation based on numbers
  
and observations made by non-human sensors in the management of public life and to equip
  
experts with insights that, they believe, will translate into better outcomes (health, economic,
  
educational, judicial) for all.
  
But these dreams and their pursuit through technology are as problematic as they are enticing.
  
Throughout American history, data has often been used to oppress minoritized communities,
  
manage populations, and institutionalize, rationalize, and naturalize systems of racial violence.
  
The impersonality of data, the same quality that makes it useful, can silence voices and
  
displace entire ways of knowing the world.
                                
                            
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.
Numerical and symbolic (algebraic) problem solving with Mathematica. Formulation for graphics application in civil, mechanical, and bioengineering. Example of two-and three-dimensional curve and surface objects in C++ and Mathematica; special projects of interest to electrical and computer science.
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.
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Prerequisites: MATH UN3007 A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.
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                                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
Advanced topics in linear algebra with applications to data analysis, algorithms, dynamics and differential equations, and more. (1) General vector spaces, linear transformations, spaces isomorphisms; (2) spectral theory - normal matrices and their spectral properties, Rayleigh quotient, Courant-Fischer Theorem, Jordan forms, eigenvalue perturbations; (3) least squares problem and the Gauss-Markov Theorem; (4) singular value decomposition, its approximation properties, matrix norms, PCA and CCA.
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Close readings of specific texts, as well as methods, skills, and tools.
Basic concepts of spatial data representation and organization, and analytical tools are introduced and applied in a form of case studies from hydrology, environmental conservation, and emergency response to natural or man-made hazards, among others. Technical content includes geographic topics (map projections, cartography, etc.), spatial statistics, database design and use, interpolation and visualization of spatial surfaces and volumes, and multi-criteria decision analysis. Students will learn the basics of ArcGIS Pro, Model Builder and Python. Elective term projects or final exams emphasize spatial information synthesis towards the solution of a specific problem.
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.
Prerequisites: GREK UN2101 - GREK UN2102 or the equivalent. Since the content of this course changes each year, it may be repeated for credit.
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                                Prerequisites: LATN UN3012 or the equivalent. Since the content of this course changes from year to year, it may be repeated for credit.
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Overview of the field of medicine for informaticians. Medical language and terminology, introduction to pathology and pathophysiology, the process of medical decision making, and an understanding of how information flows in the practice of medicine.
                                
                                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.
                                
                            
Prerequisites: two years of Chinese study at college level. This course is designed for students who have studied Chinese for two years at college level and are interested in business studies concerning China. It offers systematic descriptions of Chinese language used in business discourse. CC GS EN CE
This course is designed to help students master formal Chinese for professional or academic purposes. It includes reading materials and discussions on selections from Chinese media covering 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.
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                                Typical experiments are in the areas of plasma physics, microwaves, laser applications, optical spectroscopy physics, and superconductivity.
Prerequisites: CHNS W4017 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.
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                                Prerequisites: JPNS W4017 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.
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                                    Prerequisites: PHYS GU4021 and PHYS GU4023 or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity.
This course delves into the intersection of epidemiology and computational methods, equipping students with the tools to conduct rigorous epidemiological studies from big clinical data repositories. Students will explore techniques from informatics, computer science, machine learning, and statistics to clean, analyze, and interpret data from electronic health records (EHRs) and other large-scale datasets. Through hands-on projects and case students, students will gain practical experience in applying epidemiologic study designs to uncover patterns, identify risk factors, model disease transmission dynamics, and evaluate interventions. This interdisciplinary approach prepares students to address real-world public health challenges by leveraging the power of data-driven insights. The course is broken up into modules, each of which covers an epidemiologic study design or principle. Modules will range from 1-3 classes, and will include (i) a lecture and (ii) accompanying lab work. Students are expected to read technical texts carefully, participate actively in lecture discussion, and develop hands-on skills in labs involving real-world biomedical and health datasets. Students will curate their own analytic datasets from Observational Health Data Sciences and Informatics (OHDSI)-formatted electronic health record (SynPUF) data.
This course, taught in English, offers an in-depth exploration of the Chinese language and its historical development. Key topics include historical phonology and syntax, the Chinese script, and the classification and linguistic features of major dialects. The course also explores the emergence of modern standard Chinese and early poetic traditions. The primary goal is to deepen students’ understanding of the language’s evolution while strengthening their critical thinking skills.
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                                Second Term. Explores molecular and cellular mechanisms of nutrient action. Six major foci of modern nutritional science. These include the actions of nutrients in transcriptional regulation, in signaling pathways, on intra- and extracellular trafficking, in assuring normal development, in the maintance of antioxidant defences and nutrient/gene interations.
Prerequisites: PHYS GU4021. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.
This advanced lecture course is intended for students with little or no background in medieval art of Latin (“Western”) Europe. It provides a comprehensive introduction to a period spanning roughly one millennium, from Pope Gregory the Great’s defense of art ca. 600 to rising antagonism against it on the eve of the Protestant Reformation. Themes under consideration include Christianity and colonialism, pilgrimage and the cult of saints, archaism versus Gothic modernism, the drama of the liturgy, somatic and affective piety, political ideology against “others,” the development of the winged altarpiece, and pre-Reformation iconophobia. We will survey many aspects of artistic production, from illuminated manuscripts, portable and monumental sculpture, stained glass, sumptuous metalworks, drawings, and reliquaries to the earliest examples of oil paintings and prints. While this course is conceived as a pendant to Medieval Art I: From Late Antiquity to the End of the Byzantine Empire (AHIS GU4021), each can be taken independently of one another. In addition to section meetings, museum visits to the Metropolitan Museum of Art, The Cloisters, and The Morgan Library are a required component to the course. Students must register for a mandatory discussion section.
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                                This course provides an introduction to semantics, the study of meaning in language. We will explore a range of semantic phenomena, and students will learn the tools and techniques of formal semantic analysis as well as core concepts, goals, and findings of the field.
Designed for new Teaching Fellows. An introduction to the conceptual and practical tools of French language pedagogy.
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                                The seminar prioritizes a particular branch of French-language film theory and criticism that broadly deals with aesthetics, at the expense of reception and apparatus theories. We follow its history from the silent film-era writings of Germaine Dulac and Jean Epstein to the intersection of film aesthetics and French theory in the work of Barthes, Deleuze, Lyotard, and Rancière, to the most recent inquiries into such notions as montage, découpage, and mise en scène (Aumont, Barnard, Kessler). Weekly films will accompany the readings in order to put pressure on theory, but also to help dissipate its excessive maleness. Because French film aesthetics has been influential around the world and—vice versa—because world cinema has been crucial for the development of French film aesthetics, we will also see American, Italian, Soviet, Japanese, Iranian, Malian, and Taiwanese films, in addition to French films.
  
All films will be presented with English subtitles. There are no prerequisites for the course, but students wanting to enroll must be committed to attending the Tuesday night 6–9pm screenings, in addition to the 12:10–2pm seminars on Wednesdays.
                                
                            
                                
                                This class aims to introduce the students to the field of Bible and Literature, with special attention to the Hebrew Bible and to Literary Theory. We will read portions of 
Genesis, Numbers, Jonah, Hosea, Ezekiel, Esther, Mark, 
and
 Revelations
, and discuss it in tandem with literary theory as well as 20th Century literary texts. Literary theory, this class will argue, is central for our understanding of the Bible, and, at the same time, the Biblical text is essential for the manner in which we theorize literature. Our discussion will be guided by four loosely interconnected questions: What insights can we gain about the theology of the Biblical text from a literary analysis? What happens to theological ideas once they are dramatized and narrativized? In what way can modern literary adaptations of the Bible contribute to our understanding of the Biblical text? How does the Bible challenge and trouble some of the perceived ideas of literary theory?
  
The syllabus is divided into three units. The first unit —
Bible and Literature in Theory,
 offers a survey of some of the scholarly approaches to the intersection of literature and theology. We will read theory that interrogates the intersection of theological and literary concepts, focusing on omniscience, authorship, temporality, characterization, and plot. The second unit —
Literature as Biblical Exegesis, 
shifts the focus to a reading of Biblical texts in tandem with their modern literary and cinematic interpretations, focusing on 
Job 
and 
Esther
.  What, we will ask, happen to the Biblical world once it is being refracted through a modern sensibility? How can we take literature seriously as Biblical hermeneutics? The third unit —
Recent Directions, 
introduces some of the recent directions in the field, focusing on how literature imagines the relationship between Bible, archeology, and modernity, as well as on the intersection of Biblical literature, fantasy, and science fiction.
                                
                            
In one sense, Pragmatics is concerned with how we use the language, why and how the speakers communicate in social interactions. The interpretation of meaning in context is probably the main field of study of this multidiscipline, considering the speaker-meaning as the central point of departure. The term Pragmatics refers to a broad perspective on different aspects of communication, including linguistics, but also cognitive psychology, cultural anthropology, philosophy, sociology and rhetoric among others. Through this course we will study chronologically and apply in specific cases of study of the Spanish language the most meaningful pragmatic theories, such as: Context, Deixis, Speech acts, Implicature, Cooperative Principle, Politeness, Relevance, Pragmatic markers, Metaphors and Cross-cultural pragmatics. Pragmatics, as we know, is a most helpful criterion in the interpretation of many different types of texts. As a course within our Departments curriculum this instrument of rhetoric analysis is a basic tool in the comprehension of our students discourse in their literary, cultural, and critical papers. This discipline goes beyond the analysis of strictly forms or verbal utterances, hence its multidisciplinary applicability to a wide range of fields of studies in Spanish. Whichever the students field of study might be, Pragmatics provides a valuable and accurate vocabulary that can be applied to any textual interpretation. In this course, the pragmatic perspective is a starting point to delve into the processes of communication in Spanish. After this first approach, the student will gain an insight into new aspects of the linguistics of language use in general and the use of Spanish in particular.
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                                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.
This course studies the renaissance in Ukrainian culture of the 1920s - a period of revolution, experimentation, vibrant expression and polemics. Focusing on the most important developments in literature, as well as on the intellectual debates they inspired, the course will also examine the major achievements in Ukrainian theater, visual art and film as integral components of the cultural spirit that defined the era. Additionally, the course also looks at the subsequent implementation of the socialist realism and its impact on Ukrainian culture and on the cultural leaders of the renaissance. The course treats one of the most important periods of Ukrainian culture and examines it lasting impact on today's Ukraine. This period produced several world-renowned cultural figures, whose connections with the 1920s Ukraine have only recently begun to be discussed. The course will be complemented by film screenings, presentations of visual art and rare publications from this period. Entirely in English with a parallel reading list for those who read Ukrainian.
                                
                                We will explore Anton Chekhov’s work on its own terms, in its cultural context, and in relation to the work of others, especially Anglophone writers who responded, directly or indirectly, to Chekhov and his work. Readings by Chekhov include selected stories (short and long), his four major plays, and 
Sakhalin Island, 
his study of the Russian penal colony.
  
There are no prerequisites.  Knowledge of Russian is not required; all readings in English.
  
Students who know Russian are encouraged to read Chekhov’s work in Russian.
  
The course will be comparative as it addresses Chekhov on his own and in relation to anglophone writers.
  
The course is open to undergraduates (CC, GS, BC) and graduates in GSAS and other schools. The attention to 
how 
Chekhov writes may interest students in the School of the Arts.
                                
                            
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                                Prerequisites: PHYS UN3003 and PHYS UN3007 or the equivalent. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Groups, homomorphisms, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, finitely generated abelian groups.
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Rings, homomorphisms, ideals, integral and Euclidean domains, the division algorithm, principal ideal and unique factorization domains, fields, algebraic and transcendental extensions, splitting fields, finite fields, Galois theory.
Prerequisites: MATH GU4041 and MATH GU4042 or the equivalent Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function.
Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.
Intensive study of a philosophical issue or topic, or of a philosopher, group of philosophers, or philosophical school or movement. Open only to Barnard senior philosophy majors.
Course Summary: Water, one of humankind’s first power sources, remains critically important to the task of maintaining a sustainable energy supply, in the United States and elsewhere. Conversely, the need to provide safe drinking water and keep America’s rivers clean cannot be met without access to reliable energy supplies. As the impact of climate disruption and other resource constraints begins to mount, the water/energy nexus is growing increasingly complex and conflict-prone. Essential Connections begins by examining the development of America’s water and energy policies over the past century and how such policies helped to shape present-day environmental law and regulation. Our focus then turns to the current state of US water and energy resources and policy, covering issues such as oil and gas exploration, nuclear energy, hydroelectric power and renewables. We also examine questions of inclusion and equity in connection with the ways in which communities allocate their water and energy resources and burdens along racial, ethnic and socioeconomic lines. The third and final section of the course addresses the prospects for establishing water and energy policies that can withstand climate disruption, scarcity and, perhaps most importantly, America’s seemingly endless appetite for political dysfunction. By semester’s end, students will better understand the state of America’s energy and water supply systems and current efforts to cope with depletion, climate change and related threats affecting these critical, highly-interdependent systems. As a final project, students will utilize the knowledge gained during the semester to create specific proposals for preserving and enhancing the sustainability of US water and energy resources.