Prerequisites: PHYS W3008 or its equivalent. Fundamentals of electromagnetism from an advanced perspective with emphasis on electromagnetic fields in vaccum with no bounding surfaces present. A thorough understanding of Maxwells equations and their application to a wide variety of phenomena. Maxwells equations (in vacuum) and the Lorentz force law - noncovariant form. Scalar and vector potentials, gauge transformations. Generalized functions (delta functions and their derivatives), point changes. Fourier transforms, longitutdinal ad transverse vector fields. Solution of Maxwells equations in unbounded space for electrostatics and magnetostatics with given charge and current sources. Special relativity, Loretnz transformations, 4-momentum, relativistic reactions. Index mechanics of Cartesian tensor notation. Covariatn formulation of Maxwells equations and the Lorentz force law, Lorentz transformation properties of E and B. Lagrangian density for the electromagnetic field, Langrangian density for the Proca field. Symmetries and conservation laws, Noethers theorem. Field conservation laws (energy, linear momentum, angular momentum, stress tensor). Monochromatic plane wave solutions of the time-dependent source-free Maxwell equations, elliptical polarization, partially-polarized electromagnetgic waves, Stokes parameters. Solution of the time-dependent Maxwell equations in unbounded space with given chare and current sources (retarded and advanced solutions). Properties of electromagnetic fields in the radiaion zone, angular distribution of radiated power, frequency distribution of radiated energy, radiation form periodic and non-periodic motions. Radiation from antennas and antenna arrays. Lienard-Wiechert fields, the relativistic form of the Larmor radiation forumla, synchrotron radiation, bremsstrahlung, undulator and wiggler radiation. Electric dipole and magnetic dipole radiation. Scattering of electromagnetic radiation, the differential scattering cross-section, low-energy and high-energy approximations, scattering from a random or periodic array of scatterers. Radiation reaction force, Feynman-Wheeler theoryy. The macroscopic Maxwell equations (spatial averaging to get P, M, D, H). Convolutions, linear materials (permittivity, permeability, and conductivity), causality, analytics continuation, Kramers-Kronig relations. Propagation of monochromatic plane waves in isotropic and non-isotropic linear materials, ordinary ad extraordinary waves. Cherenkov radiation, transition radiation.
Required of all incoming sociology doctoral students. Prepares students who have already completed an undergraduate major or its equivalent in some social science to evaluate and undertake both systematic descriptions and sound explanations of social structures and processes.
This course introduces students to central questions and debates in the fields of African American Studies, and it explores the various interdisciplinary efforts to address them. The seminar is designed to provide an interdisciplinary foundation and familiarize students with a number of methodological approaches. Toward this end we will have a number of class visitors/guest lecturers drawn from members of IRAAS's Core and Affiliated Faculty.
An M.S. degree requirement. Students attend at least three Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics and submit reports on each.
An M.S. degree requirement. Students attend at least three Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics and submit reports on each.
This course explores the challenges of understanding the global world in which we live, a world that demands new conceptual approaches and ways of thinking. The objectives are:
To examine multidisciplinary approaches to key global issues through readings, class discussions, and conversations with select CGT faculty members as guest speakers. This will take place through multi-week modules that center on a critical issue, asking students to familiarize themselves with key questions and context, engage with an expert on the topic, and apply their insights to a specific case or question.
To develop a focused and feasible research project and hone the practices of scholarly data collection, analysis, and communication through workshops and assignments. This work begins in the fall and continues to completion in the spring semester of the seminar. The perspectives and skills developed in M.A. Seminar will support students in the development and completion of their thirty-five page M.A. essays, which they will present to each other and to CGT faculty at the Spring Symposium.
The purpose of this R-credit seminar is to support intermediate PhD students as they embark on advanced research projects. It begins and ends with workshops for doctoral students at the earliest stages of their dissertations: its meetings in weeks 2, 3, and 4 are devoted to the dissertation prospectus, and its final ones in weeks 11, 12, and 13 are for sharing dissertation chapter drafts or research plans. In the other weeks, the seminar expands to include interested post-MPhil doctoral students at any stage, and focuses on the process of publishing in academic journals, culminating in the completion of a submittable article draft. Most important of all, the seminar provides an opportunity for community-building at a time when graduate students are not generally in coursework together, offered in a spirit of mutually affirming collaboration.
Eulerian and Lagrangian descriptions of motion. Stress and strain rate tensors, vorticity, integral and differential equations of mass, momentum, and energy conservation. Potential flow.
This class will look at selected eras of theater with an emphasis on performance.
Debye screening. Motion of charged particles in space- and time-varying electromagnetic fields. Two-fluid description of plasmas. Linear electrostatic and electromagnetic waves in unmagnetized and magnetized plasmas. The magnetohydrodynamic (MHD) model, including MHD equilibrium, stability, and MHD waves in simple geometries.
Prerequisites: the instructors permission prior to registration. A survey of selected issues and debates in political theory. Areas of the field discussed include normative political philosophy, history of political thought, and the design of political and social institutions.
“Theories and Methods” courses in any field are commonly unwieldy beasts. They cannot but be a compromise-formation between contemporary questions and texts, ideas, and definitions (alongside a whole lot of problems) that we have inherited as “canonical” in a field. In the best case, such a course is a passageway into deeper engagement with a field, its histories, its complexities, and its possibilities from which we might wrest and build viable futures. Disciplinary fields are structures where power and knowledge are produced and reproduced. The study of religion is no exception. The questions of “how is ‘religion’ constructed as a category here?” and “what work does the designation of something or someone as ‘religious’ do?” will, therefore, accompany us throughout our work over the course of this semester. We will also examine how different methodological commitments shape what objects of study and which questions come to the fore for the study of religion. This course will explore how the study of religion is not reducible to the study of traditions and communities that are readily recognized as “religious.” However, the vexed histories of the construction of “religion” as a category of knowledge production does also not negate that there are large, varied, and flourishing communities of practice beyond the university for whom whether or not “religion” exists is not at all a question. Holding these layers of complexity in play, this course seeks to introduce students exemplarily to key texts and concepts that have shaped the study of religion as we encounter it today as an academic discipline.
First semester of the doctoral program sequence in applied statistics.
To design and manage successful economic policy, professionals need a sophisticated command of modern microeconomics. This course strengthens and extends understanding of microeconomic theory, and gives practice applying it. We study the relationship between market structure and market performance, exploring conditions under which policy intervention can improve market performance, and when it can be counter-productive. Both distributional and efficiency aspects of intervention are stressed. An introduction to formal strategic analysis is included, along with its application in the modern theory of auctions.
This seminar is PART 2 for second and third year students who are writing their MPhil thesis. It will assume the form of a yearlong seminar during which students design, research, and write up their MPhil projects. These projects can be based on any kind of sociological method, quantitative or qualitative. The thesis will assume the form of an article that can be submitted to a social science journal. The seminar will help you to find an interesting question, a way to answer it, and a mode of communicating this to fellow sociologists in a way that they might find worth paying attention to. The summer break between the two semesters will allow students who don’t come to the first semester with ready-to-analyze data to gather such data (through ethnographic work, archival research, scraping the internet, combining existing survey data, etc.).
Prerequisites: STAT GR6102 Modern Bayesian methods offer an amazing toolbox for solving science and engineering problems. We will go through the book Bayesian Data Analysis and do applied statistical modeling using Stan, using R (or Python or Julia if you prefer) to preprocess the data and postprocess the analysis. We will also discuss the relevant theory and get to open questions in model building, computing, evaluation, and expansion. The course is intended for students who want to do applied statistics and also those who are interested in working on statistics research problems.
Like many fields of learning, biostatistics has its own vocabulary often seen in medical and public health literature. Phrases like statistical significance", "p-value less than 0.05", "95% confident", and "margin of error" can have enormous impact in a world that relies on statistics to make decisions: Should Drug A be recommended over Drug B? Should a national policy on X be implemented? Does Vitamin C truly prevent colds? However, do we really know what these terms and phrases mean? Understanding the theory and methodology behind study design, estimation and hypothesis testing is crucial to ensuring that findings and practices in public health and biomedicine are supported by reliable evidence.
Introduction to Historical Musicology: the history of the discipline, major areas of research, source materials, and methodological problems.
This course provides students with a structured framework for analyzing major macroeconomic policy challenges in advanced and emerging economies. It covers long-run growth dynamics, income distribution, general equilibrium adjustment to shocks, and the design and limits of monetary and fiscal policy. Emphasis is placed on modern macroeconomic thinking rooted in expectations, dynamic behavior, and solid micro-foundations. Students will study models such as Solow growth, Real Business Cycle, and New Keynesian frameworks to understand issues like secular stagnation, inflation, sovereign debt, and financial sector crises. The course integrates theory with current policy debates, drawing on recent global events and empirical evidence. It is designed to build intuitive understanding and disciplined policy analysis, with technical content supported by pre-recorded videos and recitations. Students will complete short analytical assignments, a midterm, and a final exam, gaining tools to think critically and constructively about macroeconomic policy in both national and international contexts.
Prerequisites: STAT GR6102 or instructor permission. The Deparatments doctoral student consulting practicum. Students undertake pro bono consulting activities for Columbia community researchers under the tutelage of a faculty mentor.
This is a Public Health Course. Public Health classes are offered on the Health Services Campus at 168th Street. For more detailed course information, please go to Mailman School of Public Health Courses website at http://www.mailman.hs.columbia.edu/academics/courses
A two-semester intensive screenwriting workshop with one instructor. The Screenwriting 3 and Screenwriting 4 class sequence allows for the careful and more sustained development of a feature-length script. In the fall semester, students further develop an idea for a screenplay and write the first act (approximately 30 pages). In the spring semester, students finish writing the script and, time permitting, begin a first revision.
MIA Politics I Core.
This course introduces MIA students to foundational theories and analytical frameworks used to understand international affairs and the global political economy. Drawing on literature from international relations, comparative politics, political sociology, and economics, the course examines the evolution of international relations scholarship and key debates shaping the field. Through weekly discussions, case-based readings, and structured debates, students will critically engage with competing perspectives on power, institutions, regimes, markets, and global order. Special attention is given to American scholarly traditions and real-world applications, including contemporary issues such as war, climate change, and global inequality.
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A seminar on the theory and practice of translation from the perspective of comparative diaspora studies, drawing on the key scholarship on diaspora that has emerged over the past two decades focusing on the central issue of language in relation to migration, uprooting, and imagined community. Rather than foregrounding a single case study, the syllabus is organized around the proposition that any consideration of diaspora requires a consideration of comparative and overlapping diasporas, and as a consequence a confrontation with multilingualism, creolization and the problem of translation. The final weeks of the course will be devoted to a practicum, in which we will conduct an intensive workshop around the translation projects of the student participants.
Prerequisites: Required course for first year Ph.D. students and second year M.A. students on academic track. Covers foundational topics and developments in many branches of ecology, including population, community, and ecosystems ecology.