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.
INDEPENDENT STUDY
Current topics in biomedical engineering. Subject matter will vary by year. Instructors may impose prerequisites depending on the topic.
Current topics in biomedical engineering. Subject matter will vary by year. Instructors may impose prerequisites depending on the topic.
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 Russian Revolution and Civil War displaced over a million people who took refuge all over Europe. It also prompted the origins of what is now known as the modern refugee regime as the continent faced issues such as refugees’ legal status, mobility, the provision of humanitarian assistance, and burden-sharing by states. Starting with events in Russia, the first half of this course will look at major episodes of displacement across the Eurasian space that have shaped this regime. It will also trace other important episodes, including displacement after World War II, the wars of succession in the former Yugoslavia, the wars in Chechnya, and, more recently, the so-called European Refugee ‘Crisis.’ This course will feature scholarship from the fields of human rights, law, political science, history, and anthropology, in addition to policy papers. It will chart the evolution of law and institutions and look at how refugees understand these bodies and their experiences of exile and belonging. This course features a scholarly conversation with these interdisciplinary works and a practicum with practitioners working in the field today. In the second half of the course, practitioners with specializations in the region and experience working in the field in numerous global settings will give guest lectures. They will address policy debates and the challenges of meeting the needs of forced migrants today amidst an environment of closed borders, externalization measures, austerity, and populism.
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: 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.
This course has three interrelated goals:
(i)
to develop an intuitive understanding of the thermodynamic forces that control the structure of biological macromolecules and the evolution of life,
(ii)
to learn how to apply that understanding to experimental analyses of macromolecular interactions, and
(iii)
to master the use of molecular graphics software for understanding and interpreting macromolecular structures and interactions. The lectures develop the essential thermodynamic theory from the ground up, starting from a review of the relevant physical forces (Newton's and Coulomb's Laws) and culminating with an intuitive explanation of how complex biological organisms can evolve spontaneously, in a universe in which all natural processes are driven by increasing randomness or entropy, as specified by the 2nd Law of Thermodynamics. Subsequent lectures elaborate how these thermodynamic principles govern the formation and interaction of macromolecular structures, which represent the physical foundation for the evolution of life, and how the same principles are applied to analyze related experimental data. The problem sets for the course focus on practical applications of these principles to the analysis of data from common experiments used by molecular biologists to characterize macromolecular interactions. Extensive use is made of molecular graphics software throughout the semester, including in the problem sets, based on instruction provided in both the lectures and recitation sections. The course is designed to develop a deep understanding of the physical mechanisms controlling macromolecular interactions while simultaneously empowering students to critically read related literature and rigorously design and analyze related experiments themselves.
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).
Staring in the 1980s, ‘French theory,’ an eclectic corpus of philosophy, political theory, psychoanalytic and feminist thought, became a catalyzing force in North-American intellectual culture. But while ‘theory’ came to be associated with France, it was in reality a product of transcontinental colonial and postcolonial intellectual encounters and exchanges. Seminal thinkers such as Althusser, Cixous, Derrida, Fanon, Glissant, Balibar, Bourdieu and Rancière were either born or began their careers in Algeria or the Francophone Caribbean. Others, such as Kristeva and Todorov, were immigrants from Eastern Europe. This course approaches ‘French theory’ from a decolonial perspective resituating its leading thinkers, intellectual contributions and political interventions in light of colonial hybridity, postcolonial migration, the global circulation of Marxism and psychoanalysis, and American branding and marketing. The course is divided into five units, each organized around a pair of complementary terms. Neither these categories nor the readings associated with them are in any way exhaustive; rather, they introduce a few important theoretical conversations, notably at the intersections of literary and historical studies, the two fields in which the instructors of this course are trained. During the semester we explore questions about authorship and reading, canonicity and the worlding of literature, documents and emotions, and the boundedness and/or fluidity of selves and others.
From the late 1950s to the late 1990s, Latin America has experienced a wave of violent and non-violent revolutionary movements that attempted to change economic inequalities and create a more just society. An important dimension of these movements was the participation of Indigenous groups—whether taking the shape of collaboration, resistance, or self-defense. Why did ethnic groups participate in such avowedly class-based revolutions? How did the revolutionary leaders address the ethnic, race, and gender questions? How about the role of women? Furthermore, what role did the United States play in preventing or fomenting violence and atrocities? This seminar explores the roots and internal dynamics of revolutions and counterrevolutions and their ideological positionalities about ethnicity, race, and gender issues, focusing on Guatemala, Cuba, Chile, and Peru.
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.
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.
Prerequisites: Any programming language and linear algebra. 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.
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: 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.
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.
Discrete optimization problems. Mathematical techniques and testing strengths and limits in practice on relevant applications. Transportation (travelling salesman and vehicle routing) and matching (online advertisement and school allocation) problems.
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.
This course will examine geological problems from a standpoint of thermodynamic and kinetic theory. Theoretical thermodynamic concepts will be used to derive the crystallization depth and temperature of metamorphic and magmatic minerals, describe the solubility of volatile species in magmas, predict the composition of volcanic gas mixtures, model the nucleation and growth of crystals and bubbles in a melt and determine the chemical interaction between water and rock at the Earth’s surface. Kinetic treatments on the diffusion of heat and matter through crystals and melts will be used to constrain the timing of geological processes. Recommended preparation: Knowledge of mathematics at the level of partial differential equations; mineralogy (EESC 4113); and petrology (EESC 4701); or permission of the instructor.
Prerequisites: CHEN E4230 or equivalent, or instructors permission. 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.
This course looks at nighttime as an object of inquiry from an experiential, historical, religious, literary, and cultural perspectives, introducing the students with the growing field of night studies. It covers the Early Modern and the Modern Periods and centers primarily on Eastern Europe and East Central Europe, with a secondary focus on Jewish Literature and Culture in these regions. The course caters for students who are interested in in night studies, in the history and culture of Eastern Europe, students who are interested in Jewish (Hebrew and Yiddish) Studies, as well as students who are interested in the intersection of history and literature.
Full details on course curriculum, syllabus, schedule, speakers, policies, etc.: https://www.gsas.cuimc.columbia.edu/responsi ble-conduct-research-and-related-policy- issues
Prerequisites: GREK UN2101 - GREK UN2102 or the equivalent. Since the content of this course changes each year, it may be repeated for credit.
Prerequisites: LATN UN3012 or the equivalent. Since the content of this course changes from year to year, it may be repeated for credit.
This year-long course introduces students to important conversations within and about oral history through a series of curated public lectures. We will meet for six events a semester, plus one session to orient you to the class. From 5:00 – 6:00, students will meet with the speaker for an informal conversation about their career path and research process. The public portion of the event will be from 6:10 to 7:30 PM. You should plan to be in class until 8 in case an event runs slightly over, and so that you can stick around after the event to chat with the speaker or have a glass of wine.
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
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: (PHYS UN1403 or PHYS UN2601 or PHYS UN2802) and (MATH UN1202 or MATH UN1208) students are recommended but not required to have taken PHYS UN3003 and PHYS UN3007. An introduction to the basics of particle astrophysics and cosmology. Particle physics - introduction to the Standard Model and supersymmetry/higher dimension theories; Cosmology – Friedmann-Robertson-Walker line element and equation for expansion of universe; time evolution of energy/matter density from the Big Bang; inflationary cosmology; microwave background theory and observation; structure formation; dark energy; observational tests of geometry of universe and expansion; observational evidence for dark matter; motivation for existence of dark matter from particle physics; experimental searches of dark matter; evaporating and primordial black holes; ultra-high energy phenomena (gamma-rays and cosmic-rays).
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.
This is a course in Spanish conversation. Students will study and practice features of social interaction in Spanish that are crucial to participate in the new culture. This means the course has two learning objectives: One is learning to engage in regular conversations in Spanish; the other is to understand how conversation works. We will cover conversational issues such as gesture, narratives, intonation, opening and closing interactions, turn taking, etc. both in linguistics and social terms. Practice and analysis will be connected: Every week we will consider an aspect of oral interaction in Spanish. We will study those features in naturally occurring conversations among native speakers and we will practice in actual conversations inside and outside the classroom, by means of role play, simulation, film making, debates and interviews. We will use topics of conversation to provide a meaningful environment for the conversation practice.
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: 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 Level 4 Chinese language class engages students in reading and discussion of current events. Course materials consist of news stories, commentaries and documentary films. Topics covered for the summer term include US-China relations, China’s economic development, China's rise, Chinese dissidents, and public health.
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 Level 4 Chinese language course emphasizes systematic development of lexical knowledge and the enhancement of reading and writing skills. Through an in-depth exploration of video clips, expository essays and short stories, students will expand their vocabulary, learn to analyze syntactically and semantically complicated texts, and develop their narrative and summary writing skills.
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.
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.
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.
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.
Survey of the major topics in basic immunology with an emphasis on the molecular basis for immune recognition and regulation.
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: (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: (CIEN E3125) or equivalent. Bridge design history, methods of analysis, loads: static, live, dynamic. Design: allowable stress, ultimate strength, load resistance factor, supply/demand. Steel and concrete superstructures: suspension, cable stayed, prestressed, arches. Management of the assets, life-cycle cost, expected useful life, inspection, maintenance, repair, reconstruction. Bridge inventories, condition assessments, data acquisition and analysis, forecasts. Selected case histories and field visits.
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 course examines a broad array of topics related to the nature of women in Buddhism, both as presented in historical and religious texts as well as in the lives of female Buddhist practitioners. Our aim will be to consider these rules and traditions within the context of their creation as well as their subsequent use. We will also look to the words and examples of women Buddhist practitioners directly, including in modern Western Buddhism.
This course will study building practice, sculpture, and architectural ornamentation in Western Europe during the Middle Ages. The monuments selected belong to a period that starts when architecture moved away from Roman antique models and ends just before the re-adoption of Classical standards in the Renaissance. In this course the originality of medieval architecture, its relationship with earlier and later monuments, and the dramatic effort involved in its creation will be discussed. Major themes of medieval society such as pilgrimages, crusades, piety, the cult of relics, and the social and intellectual context of the Middle Ages are also part of this lecture. The course will also introduce students on how to harness digital technologies such as laser scanning or photogrammetry for the study of medieval art. No preliminary knowledge of medieval history or architectural history is needed and no knowledge of digital technologies or specific computer skills is expected. (Virtual) Museum visits will complement the regular lectures.
Required for first-year Genetics and Development students. Open to students from all departments, but students from outside the Genetics Department should consult the instructor before registering. The course emphasizes the molecular control of vertebrate embryogenesis. Divided into three main areas: early embryogenesis, developmental neurobiology, and the development and differentiation of specialized organs or lineages. A combination of faculty lectures and presentations by participating students.
This course is a survey of the art of Italy from the early fourteenth century until the onset of the Reformation. It will cover the major artists and cultural centers of the peninsula, examining them in the context of broader artistic currents and conventions of the period. Special attention will be paid to the social, political, and historical factors that led to changes in the visual arts as well as the impact of cultures beyond classical antiquity on the form and iconography of paintings and sculptures in the Early Renaissance. The lectures will provide students with a deeper understanding of the canonical works of Italian artists from Cimabue and Giotto to Leonardo da Vinci and Giovanni Bellini, of the development of new criteria for assessing the visual arts, of the relationship between artists, patrons, and audiences in the period. The readings, in turn, will familiarize them with key primary sources of the fourteenth and fifteenth century, as well as the writings of distinguished Renaissance scholars from the nineteenth century until the present.
The course explores the unique period in Czech film and literature during the 1960s that emerged as a reaction to the imposed socialist realism. The new generation of writers (Kundera, Skvorecky, Havel, Hrabal) in turn had an influence on young emerging film makers, all of whom were part of the Czech new wave.
Whether you’re in the early stages of your career or an experienced professional navigating a career change, pursuing your next position requires a compelling, marketable professional profile. This course will cover the essential strategies and tools you will need to present yourself effectively to prospective employers. Topics include career assessment and its value to your self-marketing tools; your “pitch” and why it’s critical to your candidacy; constructing a resume that’s right for your industry and experience; and the value of LinkedIn as a professional network. Like all Professional Development courses in 2020-2021, Building Your Professional Profile is a single-class course. Students may attend only the section for which they are registered. This course is a required component of the two-course (0.5 point, total) SIPA Professional Development requirement; the other component may be chosen from among a menu of four electives (see SIPA U4041 through SIPA U4044). Students should complete both components of the PD sequence in their first semester.
Whether you’re in the early stages of your career or an experienced professional navigating a career change, pursuing your next position requires a compelling, marketable professional profile. This course will cover the essential strategies and tools you will need to present yourself effectively to prospective employers. Topics include career assessment and its value to your self-marketing tools; your “pitch” and why it’s critical to your candidacy; constructing a resume that’s right for your industry and experience; and the value of LinkedIn as a professional network. Like all Professional Development courses in 2020-2021, Building Your Professional Profile is a single-class course. Students may attend only the section for which they are registered. This course is a required component of the two-course (0.5 point, total) SIPA Professional Development requirement; the other component may be chosen from among a menu of four electives (see SIPA U4041 through SIPA U4044). Students should complete both components of the PD sequence in their first semester.