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.).
Lectures cover principal topics in evolutionary biology including genetics, genome organization, population and quantitative genetics, the history of evolutionary theory, systematics, speciation and species concepts, co-evolution, and biogeography.
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.
Twenty-first century literary studies has seen a steadily growing interest in formalist literary theory. This trend has manifested in new movements, such as New Formalism, Historical Poetics, and Quantitative Formalism. This interest in formalism has been accompanied by a widely expressed desire for a better understanding of literary form, and to find ways to connect its study with cultural and political history. The archive of Russian Formalism, a protean movement which was active in the 1910s and 1920s, is a rich source for those interested in rethinking the concept of form today. Beginning in the 1960s and ‘70s, Russian Formalism was interpreted as the precursor to French Structuralism and Post-Structuralism. In this class we seek to recontextualize Russian Formalism—not in terms of the ideas of the Cold War period—but rather in light of the cultural and political milieu of revolutionary and Civil War era Russia. By connecting theories of form with the cultural and political contexts from which they emerged, our goal is to develop an understanding of form as a concept defined not only in aesthetic or linguistic terms, but also as a construct with sociopolitical import.
New York City has positioned itself as a global leader in the fight against climate change, often serving as a model for other jurisdictions to follow. This course explores the development and implementation of environmental legislation and policy in New York City during the past two decades. It includes discussions about historical context, environmental policymaking considerations, political processes, outcomes, and the role of stakeholders such as advocates, business, industry, labor, government actors, and community. Students will gain broad knowledge of key legislation and policies related to sustainability, resiliency, energy, emissions, waste and the circular economy, transportation, water and air quality, and green space. Furthermore, students will consider how environmental justice and equity play a role in the development of legislation and policy, and assess best practices for providing equitable treatment and engaging all communities. While the focus of the class will be on New York City, students will also learn about environmental policies implemented in other jurisdictions.
Introduction to Environmental Law and Policy in New York City is available to students in the Graduate Program for Sustainability Management. It is designed to provide future sustainability practitioners and others with a fundamental understanding of how legislation and policy is made, what influences this development, and how legislation and policy seek to address climate change in New York City in urban environments like New York City. Students will be able to use this knowledge to help government and public and private organizations achieve more sustainable solutions.
This is a semester-long elective class that will be taught on campus. Specific competencies or prerequisites are not required. This course will be interactive and discussion-intensive, engaging students to utilize and reflect critical and analytical thinking about how environmental legislation and policy is developed and how they can create innovative environmental legislation and policy in the future. Students will participate in class discussions, think critically about policy development and assigned readings, write a reaction essay on environmental justice and equity, and present their analysis to classroom colleagues. For the final project, students will write a research report and present their report to the class, focusing on a particular environmental policy topic, identifying areas where policymaking can be improved upon and/or expande
The fashion industry is an ideal case study on how governments, citizens and international institutions attempt to limit the environmental and social impacts of complex consumer industries with global supply chains. Historically, apparel and textiles have been at the center of some of the most consequential government actions under liberal Western democracy, including the abolition of slavery and the passage of the first workplace safety and labor laws in the United States. In recent years, fashion has returned to the center of dynamic policy debates within the sustainability and social impact space.
The $2.5 trillion global fashion industry’s social and environmental impacts often evade regulation. Major brands leverage long and opaque supply chains for raw materials and cheap manufacturing costs with very little accountability. Private regulation and voluntary commitments have policed fashion for the better part of four decades, an approach that arguably has ended in failures to protect human and environmental rights. The industry’s lack of accountability has cost lives, including the notorious Rana Plaza building collapse in 2013 where 1,132 garment makers died, and now contributes to a sizable percentage of annual climate change. Profits have been pushed to the top of the supply chain while garment makers consistently toil for poverty wages, and the pollution and environmental degradation of fashion is a burden almost exclusively carried by low-and-middle income nations and communities of color that manufacture clothing and produce raw materials.
But the tide is turning. Governments are being asked to step in and regulate the fashion industry. Can effective fashion policies police international supply chains and achieve their intended aims? Might they unleash unintended consequences and in what ways? This course is an introduction to the fast-evolving space of modern environmental and labor policy as it intersects with fashion, and which seeks to incentivize more responsible business behavior in the realm of social, environmental and governance impacts. The class will use recently passed and proposed fashion social and sustainability policies as our case studies, including the New York State Fashion Sustainability and Social Accountability Act; mandatory human rights due diligence in Europe; California’s Garment Worker Protection Act and Congress’s FABRIC Act; the FTC Green Guides and the UK CMA’s Green Claims Code; and Europe&rsquo
This course takes a dual-pronged approach to the importance of sustainability reporting: examining both the corporate perspective on preparing sustainability disclosures and the investor perspective on how these disclosures are used to inform capital allocation, risk assessment, and stewardship decisions. At a time when the sustainability reporting landscape—both voluntary and mandatory—is rapidly evolving, focusing on the investor perspective provides clarity. This approach helps students anchor their learning in what matters most for capital markets, enabling them to organize and lead sustainability reporting processes within their own organizations. The goal of this two-sided lens is to equip students with the skills to deliver decision-useful, transparent, and consistent sustainability information that aligns with the demands of today’s regulatory and investment environments.
In the first half of the course, students will explore the evolving landscape of sustainability frameworks and regulations. Key regulatory regimes—such as California’s SB 253 and SB 261, the EU’s CSRD, and the CSDDD and GRI, Sustainability Reports, ISSB —will serve as anchors for case discussions. These discussions will play a crucial role in helping students understand how to administer sustainability reporting as a strategic organizational function, and in emphasizing the organizational capacity and management practices needed to comply with these frameworks. By the end of the course, students will be able to design, manage, and implement the internal processes required to respond to mandatory and evolving ESG disclosure expectations.
The second half of the course will adopt the lens of the investor, exploring how ESG disclosures are integrated into decision-making across three asset classes: public equity, private equity/alternatives, and fixed income. Students will engage in structured modules for each asset class, assuming the role of institutional investors tasked with interpreting disclosures, engaging with companies, and making recommendations. Each module will feature live engagements with real-world investors, offering students direct insight into market practices and expectations.
Since the first Earth Day in 1970, artists have increasingly addressed ecological issues in their work. This trend has magnified greatly in the past two decades. Around the globe, artists are creating artwork that addresses the impact of loss of biodiversity, rising sea levels, extreme weather events, plastic pollution, and the fragility of our shared ecosystems. Their art raises awareness of the need to act collectively, suggesting frameworks for replacing anthropocentric and colonial approaches to nature, and amplifying the urgent need for environmental justice. In this pivotal moment of climate change, artists inspire by cultivating new narratives and giving form to the invisible or unimaginable, demonstrating how art can help awaken resolve and shape our next steps. They invite viewer participation and action, and suggest ways to make a difference. In the process, they expand our potential for empathy and agency.
The cultural sector has an important role to play in shifting attitudes that would lead to developing more sustainable and equitable global futures. Artists focus on both local and global environmental issues, expanding the field of climate change communication and at times offering out-of-the-box solutions. The artists covered in the course are cognizant of the need for systemic social change in order to achieve policy change. Blurring the boundaries between art and activism, many are working collaboratively across disciplines and with various communities to address both the physical and ethical dimensions of sustainability. Others work independently to provide new visions for the future. The course is designed for people who are interested in the contribution that art can play in creating fresh paradigms.
This one-credit seminar is designed for PhD students from any department in any school at Columbia University. We will read contemporary literature and examine case studies on designing, conducting, and communicating research projects that contribute to solutions to climate change and related problems of the Anthropocene. PhD students will have the opportunity to share their research and reflect on how it might contribute to solutions.
How do dancers, poets, and novelists use the resources of their genres to imagine new forms of embodiment and belonging? This graduate seminar brings together recent work in the fields of modernism, dance, and diaspora studies to explore the relationship between theories of movement, space, and dwelling in the literature and drama of global modernity. We will study representations of modern dance in literary works, as well as performances by modern dancers and choreographers, to consider the reciprocity and continuity of forms long associated with expressivity and social change. At the same time, we will chart how such texts become invested in strategic withholding and inexpression, or what performance scholar Tina Post has called “deadpan” aesthetics. Can there be a kind of revelation in concealment—or, conversely, a concealment in the guise of outward projection? At the level of form, how might we understand phenomena that seem to cross disciplinary lines, such as choreographic narration, kinaesthetic empathy, self-talk as social dress rehearsal, or theatrically-populated interior monologue? And how might these insights be brought to bear on the embodied and psychic experience of diaspora, that conundrum of enforced movement that can so often feel like stuckness-in-place?
Prerequisites: the instructor's written permission. This is a course for Ph.D. students, and for majors in Mathematics. Measure theory; elements of probability; elements of Fourier analysis; Brownian motion.
This course offers a comprehensive introduction to mass spectrometry (MS), a state-of-the-art technique widely used in modern chemical and biological research. Students will learn the theoretical principles, practical applications, and data interpretation across various MS techniques. Key topics include ionization methods, mass analyzers, and applications in organic and bio-organic compound analysis.
By the end of the course, students will develop both the theoretical understanding and practical skills needed to design and interpret MS experiments effectively.
This course will seek to raise and think through the following questions: What does it mean to talk today about a black radical tradition? What has it meant in the past to speak in these (or cognate) terms? And if we take the debate in part at least to inhabit a normative discursive space, an argumentative space in which to make claims on the moral-political present, what ought it to mean to talk about a black radical tradition?
The seminar will explore the Israeli-Palestinian (and Israeli-Arab) conflict from the beginning of the 20th century until today. The first part of the seminar will focus on the historical background informing the conflict and leading to the Palestinian refugee problem and the establishment of a Jewish, but not Palestinian, state in 1948. The second part of the seminar focuses on Palestinian-Arab citizens in Israel, Israel’s occupation of the West Bank and Gaza, the settlement project, and possible political solutions, as well as the USA's role and its impact on the conflict, the occupation, and the current Gaza war.
This seminar examines the history of archaeological thought from its antiquarian beginnings in the 19th century, through archaeology’s professionalization and redefinition as an anthropological science during the mid-20th century, to the emergence of archaeology as a critically self-reflexive discipline during the late-20th century, defined by complicated intellectual ties across the sciences, social sciences, and humanities. Our driving questions are epistemological. How have archaeologists understood the project of interpretation? How have they articulated their relationship to data? What has come to count as evidence and what has not? How have archaeologists organized material remains in the present to make claims about the past? What questions have been posed about past cultures, and how were these “cultures” constructed as objects of study in the first place? Is archaeology best understood as a generalizing science, a historically oriented humanity, or both—and how and why has the discipline’s answer to this question evolved over time? How do the situated positions of archaeologists within contemporary society impact the claims they make about the past?
This course will cover selected topics in virtual reality (VR) and augmented reality (AR). There are two main components, with everyone participating in both: papers and projects.
Topics include holomorphic functions; analytic continuation; Riemann surfaces; theta functions and modular forms.
Introduction to queuing analysis and simulation techniques. Evaluation of time-sharing and multiprocessor systems. Topics include priority queuing, buffer storage, and disk access, interference and bus contention problems, and modeling of program behaviors.
This Ph.D. seminar explores the inextricable connection between blackness and geographic inquiry by exploring the intersections of Black Studies and Geography. Considering Katherine McKittrick’s claim that Black geographies are ‘
the terrain
of political struggle itself’ or
where
the imperative of a perspective of struggle takes place,” we will situate the spatial relations of blackness by placing Black people at the core of spatial production and examine the mechanisms by which this takes place. In this course we ask: what are the limitations
and
possibilities of traditional geographies and how does Black study attend to these boundaries? How does Black geographic thought produce wider material and conceptual space for geographic knowledge? How does Black Studies account for and understand Black spatial condition, experience, and imaginaries?
Practical and theoretical issues relating to the teaching of psychology and the psychology of teaching.
Prerequisites: the instructors permission prior to registration. Please contact the instructors for more information. This graduate student field survey provides an overview of the scholarly study of American politics. The course has been designed for students who intend to specialize in American politics, as well as for those students whose primary interests are comparative politics, international relations, or political theory, but who desire an intensive introduction to the ;American; style of political science.
Prerequisites: the director of graduate studies' permission. Corequisites: ECON G6410. Consumer and producer behavior; general competitive equilibrium, welfare and efficiency, behavior under uncertainty, intertemporal allocation and capital theory, imperfect competition, elements of game theory, problems of information, economies with price rigidities.
New technologies for capturing carbon dioxide and disposing of it away from the atmosphere. Detailed discussion of the extent of the human modifications to the natural carbon cycle, the motivation and scope of future carbon management strategies and the role of carbon sequestration. Introduction of several carbon sequestration technologies that allow for the capture and permanent disposal of carbon dioxide. Engineering issues in their implementation, economic impacts, and the environmental issues raised by the various methods.
Prerequisites: the director of graduate studies' permission. Concept of full employment. Models of underemployment and theory applicability, determinants of consumption and of investment, multiplier and accelerator analysis, an introduction to monetary macroeconomics, the supply side and inflation. Integration of macroeconomics with microeconomic and monetary analysis.
Panel data or longitudinal data consist of multiple measures over time on a sample of individuals. These types of data occur extensively in both observational and experimental studies in social, behavioral, and health sciences. This course will provide an introduction to the principles and methods for the analysis of panel data. Whereas some supporting statistical theory will be given, emphasis will be on data analysis and interpretation of models for longitudinal data. Problems will be motivated by applications primarily in social sciences.
Prerequisites: ECON G6211, ECON G6212, ECON G6411, ECON G6412. The course will focus on the economic theory of matching both from a theoretical and empirical point of views. It is intended to give the attendees an overview of the fundamental theory of the optimal assignment problem, as well as its application to various fields such as labor, family and transportation economics. A particular emphasis is put on the empirical aspects and identification issues, and the main matching algorithms will also be discussed. The last part of the course tries to make a link with matching games with nontransferable (or partially transferable) utility and attempts to provide a unified treatment.
In this seminar we will take as our topic the long poem and the worlds, exterior and interior, that it both perceives and creates. Following some initial conceptual work to pin down the genre (if that’s the right word for it) as it developed before modernism, the heart of the course comes in the close study of three main examples in their entirety:
The Seasons
by James Thomson,
The Task
by William Cowper, and
The Prelude
by William Wordsworth. These major English poems, which date to the eighteenth and early nineteenth centuries, are all about growth, and they are in truth really, really long. They just keep growing and growing. They push, you might say, against their finitude. We will confront their too-much-ness and figure out how to think and feel about it, but also how to work with it, how to ride it. From week to week we will ask how the expansiveness of these authors relates on the one hand to their smaller-scale poetic techniques and on the other to their grand social, environmental, philosophical, and spiritual ambitions. The sheer energy these works demand of their readers can (this is the gamble of the long poem) make experiencing them deeply meaningful. In their own time they became tremendously influential models, radically reshaping what poetry could do and be, and they still have much to teach critical readers and creative writers today. Interspersed among the main examples on the schedule will be a few other (shorter!) poems from the same period. Along the way, although our focus will stay on primary texts, we will sample several different works of exemplary criticism. And we will end our semester with a glance ahead to the twentieth-century long poem. Active contributions (in and out of class) to discussion, a short paper, and (of course) a long paper make up the required coursework.
This seminar will address the major works of Aemilia Lanyer (1569-1645), Margaret Cavendish (1623-73), and Lucy Hutchinson (1620-81). There are many differences between the three writers: one was a royalist, one a republican and one something in between; one was largely indifferent to religion and the other two were devoted Protestants; two were active in print, one only in manuscript; two were skilled linguists, and one only read English (or so she claimed). Yet they also had a surprising amount in common: all three were actively involved in the central political conflicts of their time and suffered losses, imprisonment, harassment, and/or exile because of their political views; two (Cavendish and Hutchinson) wrote accounts and defenses of (their positions in) the English civil wars (and contributed to political thought and historiography more broadly); two (also Cavendish and Hutchinson) were actively engaged with and contributed to debates in natural philosophy; and all three were astonishingly original, and creative writers of literary, philosophical and polemical texts. Students will discuss many aspects of these three writers’ work, including the books they read as well as those they wrote; the genres to which they were committed (and in which they innovated); the household, local, national and international contexts in which they worked and in which their work was received; and their interlocutors and critics. While the three authors will be the explicit focus of the class, we will also discuss the idea of “the woman writer” - one which deserves our skepticism.
Prerequisites: ECON G6211 and ECON G6212 or the instructor's permission. This course provides an introduction to a number of exciting research questions in industrial organization and organizational economics. While most of the content is theoretical, great emphasis is placed on the testable implications of the models we study: related empirical work is surveyed. The course aims to bring students to the research frontier by identifying open research questions and highlighting particularly active research areas.
Commutative rings; modules; localization; primary decoposition; integral extensions; Noetherian and Artinian rings; Nullstellensatz; Dedekind domains; dimension theory; regular local rings.
Prerequisites: G6211, G6212, G6215, G6216, G6411, G6412 or the instructor's permission. This course covers prominent topics in micro-development economics. Lectures and readings will cover theoretical frameworks; emphasize empirical research; and highlight gaps in the literature.
This course provides an opportunity for students in the Music Department’s Composition DMA program to engage in off-campus practicum or internships in music composition for academic credit that will count towards the requirements for the degree.
Selected topics in theoretical computer science (advanced level). Content and prerequisites vary between sections and semesters. May be repeated for credit. Check "topics courses" webpage on the department website for more information on each section.
Selected topics in theoretical computer science (advanced level). Content and prerequisites vary between sections and semesters. May be repeated for credit. Check "topics courses" webpage on the department website for more information on each section.
Prerequisites: degree in biological sciences. Lectures by visiting scientists, faculty, and students; specific biological research projects; with emphasis on evolution, ecology, and conservation biology.
This proseminar, which meets alternate weeks for the full academic year, is required for third-year PhD students in the Department of English and Comparative Literature. The seminar will help you prepare for orals, develop your dissertation ideas, expand your research skills, produce articles for publication, and generally extend your professional skills. While we will read some practical “how to” literature and models, the focus will be on writing, workshopping material, and discussing process (time-management, organization, etc). Both out-of-class assignments and in-class writing exercises should serve to extend your ideas—or shake them loose—and bring you closer to a dissertation that represents your vision, makes others want to read your work, and reminds you why you care. By the end of the year, you will have a polished dissertation prospectus and should have submitted at least one article for publication (or have one close-to-ready for submission). Above all, the seminar offers a supportive community, an opportunity to try out ideas (cooked or still raw), and encouragement from your fellow scholar-writer-thinkers as you progress toward your orals and dissertation.
Introduction to analytic theory of PDEs of fundamental and applied science; wave (hyperbolic), Laplace and Poisson equations (elliptic), heat (parabolic) and Schroedinger (dispersive) equations; fundamental solutions, Greens functions, weak/distribution solutions, maximum principle, energy estimates, variational methods, method of characteristics; elementary functional analysis and applications to PDEs; introduction to nonlinear PDEs, shocks; selected applications.
In the later 20th century, Alfred Hitchcock’s reputation underwent a significant critical revaluation. No longer viewed as merely the “Master of Suspense,” he—and his work—became central objects of poststructuralist thought, embraced not only by film theorists but by world-renowned philosophers and critical theorists. This is a course on both Hitchcock’s films and 20th- and 21st-century critical theory. In conjunction with the films, we will read key texts by Alain Badiou, Gilles Deleuze, Freud, Fredric Jameson, Jacques Lacan, Laura Mulvey, Jacques Rancière, Tzvetan Todorov, Slavoj Žižek (and others). We will develop skills in close cinematic analysis and the parsing of theoretical texts, while exploring keywords in literary, media, and performance theory (narrative, apparatus, ideology, dispositif, subject, performativity, affect, gaze, fetish, frame, screen, theatricality, etc.).
The work of Sylvia Wynter presents readers with a multi-disciplinary corpus, spanning plays, critical essays, interviews, a novel, poetry, and dance. In addition to her overarching critique of the idea of “Man”, Wynter’s work invites us to rethink disciplinarity, genre, and how critical practice is defined. If we take seriously the creative component of Wynter’s work, the generative capacity and urgency of poesis, how then might we envision the contours and stakes of a “literary method” in the context of her work? By what means might we read her work, the kind of knowledge it produces by means of the literary, and the alternatives it offers us for thinking through the question of literary method? What, in short, does reading literature do? Does it reproduce complicity with or challenge the kinds of structures Wynter critiques?
Beginning with her essay “Rethinking ‘Aesthetics’” this seminar takes seriously the question of normative forces at work under the rubric of aesthetics to better understand elements at work (poetics, performatives, epistemologies, concepts) and the philosophic, anthropo-centric, ecologic, and racialized topographies that appear. The seminar is divided into three parts: the aesthetic, the performative, and the poetic.
Above all, this course aims to generate
readings
of Wynter’s work and its complex attentions to multiple threads and tensions that constitute and animate modern knowledge.
Topics include homology and homotopy theory; covering spaces; homology with local coefficients; cohomology; Chech cohomology.
This course is a PhD-level introduction to political economy. The first part of the course is mostly theoretical and covers the most widely used models in topics such as social choice, direct and indirect democracy, accountability, lobbying, and redistributive politics. The second part of the course is a mix of abstract theory, applied theory and empirical work, and it covers some of the most research-active areas in political economy, such as media, corruption, and institutions.
All art is political, but some art is made as a form of protest or to incite an audience to protest. Most often it is both. This course – though far from exhaustive in its coverage – will present a sample of genres (music, plastic arts, theater, dance, installation, photography) in a variety of locations and times to understand how art and artists have engaged in protest. Much of modern art is conceptual, using installations and performance, to communicate. Therefore, we will start the class by turning to T. J. Clark, the preeminent art historian, for his answer to the question, when did modern art begin? This question will lead us to explore the debate on the purpose of art. We will then move to how artists responded to moments of crisis in the early 20th century - world wars, economic depression, and the rise of fascism – because the art that emerged informs much of what we see today. Based on these foundational questions, the class will turn to case studies from around the globe.
Principles behind the implementation of millimeter-wave (30GHz-300GHz) wireless circuits and systems in silicon-based technologies. Silicon-based active and passive devices for millimeter-wave operation, millimeter-wave low-noise amplifiers, power amplifiers, oscillators and VCOs, oscillator phase noise theory, mixers and frequency dividers for PLLs. A design project is an integral part of the course.
Students spend two to four days per week studying the clinical aspects of radiation therapy physics. Projects on the application of medical physics in cancer therapy within a hospital environment are assigned; each entails one or two weeks of work and requires a laboratory report. Two areas are emphasized: 1. computer-assisted treatment planning (design of typical treatment plans for various treatment sites including prostate, breast, head and neck, lung, brain, esophagus, and cervix) and 2. clinical dosimetry and calibrations (radiation measurements for both photon and electron beams, as well as daily, monthly, and part of annual QA).
Overview of current work in Music Theory, an analysis, perception, and philosophy. Major areas of research and methodological challenges.
Advanced technology applications in radiation therapy physics, including intensity modulated, image guided, stereotactic, and hypofractionated radiation therapy. Emphasis on advanced technological, engineering, clinical, and quality assurance issues associated with high technology radiation therapy and the special role of the medical physicist in the safe clinical application of these tools.
Practical applications of diagnostic radiology for various measurements and equipment assessments. Instruction and supervised practice in radiation safety procedures, image quality assessments, regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate in clinical QC of the following imaging equipment: radiologic units (mobile and fixed), fluoroscopy units (mobile and fixed), angiography units, mammography units, CT scanners, MRI units and ultrasound units. The objective is familiarization in routine operation of test instrumentation and QC measurements utilized in diagnostic medical physics. Students are required to submit QC forms with data on three different types of radiology imaging equipment.
Modern power management integrated circuits (PMIC) design introduced comperhensively. Advanced topics in power management introduced, including linear regulators, digital linear regulators, switch-mode power converters, control schemes for DC-DC converters, compensation methods of DC-DC converters, power losses in DC-DC converters, switched capacitor converters, power converter modeling and simulation, design examples.
Topics include basic notions of groups with algebraic and geometric examples; symmetry; Lie algebras and groups; representations of finite and compact Lie groups; finite groups and counting principles; maximal tori of a compact Lie group.
This course will consider museums as reflectors of social priorities which store important objects and display them in ways that present significant cultural messages. Students visit several New York museums to learn how a museum functions.
Practical applications of nuclear medicine theory and application for processing and analysis of clinical images and radiation safety and quality assurance programs. Topics may include tomography, instrumentation, and functional imaging. Reports.
Radiation protection practices and procedures for clinical and biomedical research environments. Includes design, radiation safety surveys of diagnostic and therapeutic machine source facilities, the design and radiation protection protocols for facilities using unsealed sources of radioactivity – nuclear medicine suites and sealed sources – brachytherapy suites. Also includes radiation protection procedures for biomedical research facilities and the administration of programs for compliance to professional health physics standards and federal and state regulatory requirements for the possession and use of radioactive materials and machine sources of ionizing and non ionizing radiations in clinical situations. Individual topics are decided by the student and the collaborating Clinical Radiation Safety Officer.
Manifold theory; differential forms, tensors and curvature; homology and cohomology; Lie groups and Lie algebras; fiber bundles; homotopy theory and defects in quantum field theory; geometry and string theory.
The TMGT Capstone serves as the culmination of the M.S. in Technology Management program journey. In this course, students will apply the learnings from the entire program to solve a real-world challenge that an organization is facing with a technology solution.
The TMGT Capstone serves as the culmination of the M.S. in Technology Management program journey. In this course, students will apply the learnings from the entire program to solve a real-world challenge that an organization is facing with a technology solution.
The TMGT Capstone serves as the culmination of the M.S. in Technology Management program journey. In this course, students will apply the learnings from the entire program to solve a real-world challenge that an organization is facing with a technology solution.
Prerequisites: multi-variable differential calculus, linear algebra and basic real analysis. Introduction to the mathematical techniques needed for the study of economics and econometric methods. Topics include the vector spaces, Hilbert spaces, Banach spaces, linear transformations; optimization theory, and linear differential and difference equations.