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:
CHNS W4004
or the equivalent.
Implements a wide range of reading materials to enhance the student’s speaking and writing as well as reading skills. Supplemented by television broadcast news, also provides students with strategies to increase their comprehension of formal style of modern Chinese. CC GS EN CE
This class is designed to introduce graduate students (and some advanced undergraduates) to the paleography of English vernacular manuscripts written during the period ca. 700 -1500, with brief excursions into Latin and into French as it was written on the Continent.
The purpose of the course is fourfold: (1) to teach students how to make informed judgments with regard to the date (and sometimes place) of origin, (2) to provide instruction and practice in the accurate reading and transcription of medieval scripts, (3) to learn and use the basic vocabulary of the description of scripts, and (4) to examine the manuscript book as a product of the changing society that produced it and, thus, as a primary source for the study of that society and its culture.
In order to localize manuscripts in time and place, we also examine aspects of the written page besides the script, such as the material on which it is written, its layout and ruling, the decoration and illustration of the text, the provenance, and binding. We also examine the process of manuscript production itself, whether institutional, commercial, or personal. The history of book production and of decoration and illumination are thus considered part of the study of paleography, as is the history of patronage and that of libraries. Manuscripts are among the most numerous and most reliable surviving witnesses to medieval social and intellectual change, and they will be examined as such.
To become proficient in the study of manuscripts it is necessary to look at manuscripts, as well as to read about them. The more time you are able to spend looking at manuscripts critically, in the manuals and in the Rare Book and Manuscript Library, the greater will be your first-hand experience and hence your reliable knowledge.
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.
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.
Introduces the evolution of Chinese language. It reveals the major changes in Chinese sound, writing and grammar systems, and social and linguistic factors which caused these changes. CC GS EN CE GSAS
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.
Prerequisites: (ELEN E3801) or (BIOL UN3004)
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.
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: (CIEN E3121) or equivalent.
Overview of classical indeterminate structural analysis methods (force and displacement methods), approximate methods of analysis, plastic analysis methods, collapse analysis, shakedown theorem, structural optimization.
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.
Prerequisites:
BIOL C2005
-
C2006
or equivalent.
Come discover how the union of egg and sperm triggers the complex cellular interactions that specify the diverse variety of cells present in multicellular organisms. Cellular and molecular aspects of sex determination, gametogenesis, genomic imprinting, X-chromosome inactivation, telomerase as the biological clock, stem cells, cloning, the pill and cell interactions will be explored, with an emphasis on humans. Original research articles will be discussed to further examine current research in developmental biology. SCE and TC students may register for this course, but they must first obtain the written permission of the instructor, by filling out a paper Registration Adjustment Form (Add/Drop form). The form can be downloaded at the URL below, but must be signed by the instructor and returned to the office of the registrar.
http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
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.
Designed for new Teaching Fellows. An introduction to the conceptual and practical tools of French language pedagogy.
Prerequisites: genetics or molecular biology.
The course covers techniques currently used to explore and manipulate gene function and their applications in medicine and the environment. Part I covers key laboratory manipulations, including DNA cloning, gene characterization, association of genes with disease, and methods for studying gene regulation and activities of gene products. Part II also covers commercial applications, and includes animal cell culture, production of recombinant proteins, novel diagnostics, high throughput screening, and environmental biosensors.
A survey of the Czech, German, and German-Jewish literary cultures of Prague from 1910 to 1920. Special attention to Hašek, ÄŒapek, Kafka, Werfel, and Rilke. Parallel reading lists available in English and in the original.
Prerequisites: (BMEB W4020) or (BMEE E4030) or (ECBM E4090) or (EECS E4750) or (COMS W4771) or equivalent.
Developing features & internal representations of the world, artificial neural networks, classifying handwritten digits with logistics regression, feedforward deep networks, back propagation in multilayer perceptrons, regularization of deep or distributed models, optimization for training deep models, convolutional neural networks, recurrent and recursive neural networks, deep learning in speech and object recognition.
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: one year of biology, normally
BIOL C2005-C2006
, or the equivalent.
Cell Biology 3041/4041 is an upper-division course that covers in depth all organelles of cells, how they make up tissues, secrete substances important for the organism, generate and adapt to their working environment in the body, move throughout development, and signal to each other. Because these topics were introduced in the Intro Course (taught by Mowshowitz and Chasin), this course or its equivalent is a pre-requisite for W3041/4041. Students for whom this course is useful include biology, biochem or biomedical engineering majors, those preparing to apply for medical school or graduate school, and those doing or planning to start doing research in a biology or biomedical lab. SCE and TC students may register for this course, but they must first obtain the written permission of the instructor, by filling out a paper Registration Adjustment Form (Add/Drop form). The form can be downloaded at the URL below, but must be signed by the instructor and returned to the office of the registrar.
http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
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, rings, ideals, fields, polynomials, field extensions, Galois theory.
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, rings, ideals, fields, polynomials, field extensions, Galois theory.
This course on Italian Renaissance literature and culture will pay special attention to the crossing of boundaries, whether socio-cultural, religious, linguistic, gendered, ethnic, or strictly geographical, in a range of fourteenth- to early seventeenth-century texts in a variety of genres, including travelogue, chivalric epic poetry, comedy, dialogues, and the novella, as well as political, philosophical, and scientific writing. Authors covered include Marco Polo, Leonardo Bruni, Pico della Mirandola, Boiardo, Ariosto, Machiavelli Castiglione, Beolco, Giraldi Cinzio, Tasso, Moderata Fonte, Tarabotti, and Galileo.
In English.
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.
This Workshop is linked to the Workshop on Wealth & Inequality Meetings. This is meant for graduate students, however, if you are an advanced undergraduate student you can email the professor for permission to enroll.
This course examines the avant-garde art of the fifties and sixties, including assemblage, happenings, pop art, Fluxus, and artists' forays into film. It will examine the historical precedents of artists such as Robert Rauschenberg, Jasper Johns, Allan Kaprow, Andy Warhol, Claes Oldenburg, Carolee Schneemann and others in relation to their historical precedents, development, critical and political aspects.
Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent.
Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups.
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.
Prerequisites: Course Cap 20 students. Priority given to graduate students in the natural sciences and engineering. Advanced level undergraduates may be admitted with the instructor's permission. Calculus I and Physics I & II are required for undergraduates who wish to take this course.
General introduction to fundamentals of remote sensing; electromagnetic radiation, sensors, interpretation, quantitative image analysis and modeling. Example applications in the Earth and environmental sciences are explored through the analysis of remote sensing imagery in a state-or-the-art visualization laboratory.
This course maps the origins of the Italian lyric, starting in Sicily and following its development in Tuscany, in the poets of the dolce stil nuovo and ultimately, Dante. Lectures in English; text in Italian, although comparative literature students who can follow with the help of translations are welcome.
Prerequisites: (MATH UN1202 and MATH UN2010) and rudiments of group theory (e.g., MATH GU4041). MATH UN1208 or MATH GU4061 is recommended, but not required.
Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.
Introduction to the information system paradigm of molecular biology. Representation, organization, structure, function, and manipulation of the biomolecular sequences of nucleic acids and proteins. The role of enzymes and gene regulatory elements in natural biological functions as well as in biotechnology and genetic engineering. Recombination and other macromolecular processes viewed as mathematical operations with simulation and visualization using simple computer programming.
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.
Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.
Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061
A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.
Prerequisites: (CHEM UN1403 and CHEM UN1404) or (CHEM UN1604) or (CHEM UN2045 and CHEM UN2046) , or the equivalent.
Principles governing the structure and reactivity of inorganic compounds surveyed from experimental and theoretical viewpoints. Topics include inorganic solids, aqueous and nonaqueous solutions, the chemistry of selected main group elements, transition metal chemistry, metal clusters, metal carbonyls, and organometallic chemistry, bonding and resonance, symmetry and molecular orbitals, and spectroscopy.
The course will discuss how filmmaking has been used as an instrument of power and imperial domination in the Soviet Union as well as on post-Soviet space since 1991. A body of selected films by Soviet and post-Soviet directors which exemplify the function of filmmaking as a tool of appropriation of the colonized, their cultural and political subordination by the Soviet center will be examined in terms of postcolonial theories. The course will focus both on Russian cinema and often overlooked work of Ukrainian, Georgian, Belarusian, Armenian, etc. national film schools and how they participated in the communist project of fostering a ┬źnew historic community of the Soviet people┬╗ as well as resisted it by generating, in hidden and, since 1991, overt and increasingly assertive ways their own counter-narratives. Close attention will be paid to the new Russian film as it re-invents itself within the post-Soviet imperial momentum projected on the former Soviet colonies.
Please refer to Institute for Research in African American Studies for section-by-section course descriptions.
Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010
Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sard's theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stokes' theorem.
Prerequisites: the instructor's permission.
How a society defines crime, and how it deals with the criminals tells us a lot about the moral values, and the political and economic structure of that society, as well as its internal conflicts, superstitions, and fears. Often supposed to be a barbaric community of ignorant unruly men governed by greedy kings and popes, the medieval society in the popular culture is often an inspiration to the grotesque representations of violence and torture. Even an intellectual like Michel Foucault did not hesitate to advance a theory of medieval punishment, albeit a terribly wrong one, as one that focuses on the body and spectacle. This course is designed to trace the origins of the modern criminal legislation and practices to the Middle Ages, some of which were jury trial, public persecution, and prisons. How did these practices come about, and under which social conditions? The focus of the course will be on violent crimes, such as murder, robbery, assault and suicide, and some particularly medieval crimes like sorcery, blasphemy and sodomy. The geographical scope will be limited to England, Italy and France. The class discussions are expected to take the form of collective brainstorming on how the political powers, social classes, cultural values, and religious beliefs affect the development of criminal legislation and institutions. Whenever possible the weekly readings will feature a fair share of medieval texts, including trial records, criminal laws, a manual for trying witches, and prison poetry.
Field(s): *MED
Prerequisites: (ELEN E3801)
Hands on experience with basic neural interface technologies. Recording EEG (electroencephalogram) signals using data acquisition systems (non-invasive, scalp recordings). Real-time analysis and monitoring of brain responses. Analysis of intention and perception of external visual and audio signals.
Prerequisite:
open to public. Presentations by medical informatics faculty and invited international speakers in medical informatics, computer science, nursing informatics, library science, and related fields.
Prerequisites: (APPH E3100)
Corequisites: APMA E3102
Basic theory of quantum mechanics, well and barrier problems, the harmonic oscillator, angular momentum identical particles, quantum statistics, perturbation theory and applications to the quantum physics of atoms, molecules, and solids.
The number of international migrants worldwide has continued to grow over the past decade, reaching 258 million in 2017, up from 248 million in 2015, and 220 million in 2010 (United Nations 2017). Poverty, war, and political exclusion are among the most significant reasons for the sharp rise in migration, though less distressing motivators, such as economic opportunity and family members abroad, continue to contribute to shifts in global demographics. This course examines one of the long-term outcomes of global demographic shifts – the establishment of transnational and diasporic communities throughout the world. While both the terms transnational community and diaspora remain open to scholarly debate, we will use them as broad heuristic devices to help us undertake a comparative analysis of minority communities living outside of idealized homelands from which they or their ancestors once departed.
To foster rich, focused thematic discussions, we will limit the scope of our examination to transnational and diasporic communities that were pushed to migrate by the most acute circumstances – poverty, war, and political exclusion, and that actively maintain strong collective identities predicated on connections to homeland (real or imagined). In the first section of the course, we will explore the theoretical and methodological issues underpinning recent scholarly literature on transnational migrations, nationalisms, and diasporas to develop understandings of the political and affective concepts of community and collective identity that will inform our discussions. In the second section of the course, we will examine case studies of specific transnational and diasporic communities, including Jews, Armenians, Palestinians, Africans, and Tamils. We will explore the political circumstances of the Jewish, Armenian, and African diasporas, as well as the ways that all three populations have defined the recent development of diaspora and transnational studies, becoming the standards against which scholars examine other migratory minority communities. Our examination of the less commonly studied Palestinian and Tamil diasporas will provide further comparative context to illuminate common themes of lived transnationalism, including loss, collective memory, and longing within host nations. Finally, the third section of the course will focus on the ways minority populations become diasporas and transnational communities through cultural productions, political claims, and the cultivation of inalienable connections to
An interschool course with Columbia Business School that trains engineering and business students to identify and pursue innovation opportunities that rely on intellectual property coming out of academic research. Idea generation, market research, product development, and financing. Teams develop and present business model for a technological invention. This course has limited enrollment by application, and is open to advanced undergraduate students and graduate students. Consult with department for questions on fulfillment of technical elective requirement.
Prerequisites: Understanding of single- and multi-variable calculus.
Probability simulation. Statistics, build on knowledge in probability and simulation. Point and interval estimation, hypothesis testing, regression. This course is a specialized version of IEOR E4150 for MSE and MSBA students who are exempt from the first half of IEOR E4101. Must obtain waiver for E4101.
Prerequisites: Understanding of single- and multi-variable calculus.
Probability simulation. Statistics, build on knowledge in probability and simulation. Point and interval estimation, hypothesis testing, regression. This course is a specialized version of IEOR E4150 for MSE and MSBA students who are exempt from the first half of IEOR E4101. Must obtain waiver for E4101.
In revisiting two major authors of the Italian modern novel, the course investigates the relation between fiction and the "conditions of modernity" (personal risk, anxiety and lack of control on reality, secularization, to name a few). Special attention will be paid to the response of the novelistic discourse to modernity, and to Italy's peculiarly peripheral position in the modern world. Primary texts will be read in Italian, while theoretical references will be in English.
Prerequisites: (CHEM UN1403) and (PHYS UN1403) and (APMA E2101) or equivalent.
A first course on crystallography. Crystal symmetry, Bravais lattices, point groups, space groups. Diffraction and diffracted intensities. Exposition of typical crystal structures in engineering materials, including metals, ceramics, and semiconductors. Crystalline anisotropy.
Prerequisites: (APMA E2101) and (APMA E3101)
An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications.
Prerequisites: Understanding of singe and multi-variable calculus.
MSE and MSBA students only. Basic probability theory, including independence and conditioning, discrete and continuous random variable, law of large numbers, central limit theorem, and stochastic simulation, basic statistics, including point and interval estimation, hypothesis testing, and regression; examples from business applications such as inventory management, medical treatment and finance. This course is a specialized version of IEOR E4575 for MSE and MSBA students.
Prerequisites: (MSAE E3011) or MSAE E3011 or equivalent or instructor’s permission.
A course on synthesis and processing of engineering materials. Established and novel methods to produce all types of materials (including metals, semiconductors, ceramics, polymers, and composites). Fundamental and applied topics relevant to optimizing the microstructure of the materials with desired properties. Synthesis and processing of bulk, thin-film, and nano materials for various mechanical and electronic applications.