Electro-optics: principles; electro-optics of liquid crystals and photo-refractive materials. Nonlinear optics: second-order nonlinear optics; third-order nonlinear optics; pulse propagation and solitons. Acousto-optics: interaction of light and sound; acousto-optic devices. Photonic switching and computing: photonic switches; all-optical switches; bistable optical devices. Introduction to fiber-optic communications: components of the fiber-optic link; modulation, multiplexing and coupling; system performance; receiver sensitivity; coherent optical communications.
This is the first course of the second year PhD econometrics sequence with emphasis on both economic applications and computationally intense methods for analysis of large and/or complex models. Students can attend the whole sequence or only one of them. While the details of the econometric techniques will be discussed extensively, the core and focus of the course is on the applications of these techniques to the study of actual data. Students will be practiced in econometric methods through computer-based exercises.
Prerequisites: Students should have a good understanding of graduate econometrics and should have taken ECON G6411 and G6412.
Analysis of stress and strain. Formulation of the problem of elastic equilibrium. Torsion and flexure of prismatic bars. Problems in stress concentration, rotating disks, shrink fits, and curved beams; pressure vessels, contact and impact of elastic bodies, thermal stresses, propagation of elastic waves.
Prerequisites: L6231 This is a Law School course. For more detailed course information, please go to the Law School Curriculum Guide at: http://www.law.columbia.edu/courses/search
Prerequisites: L6231 This is a Law School course. For more detailed course information, please go to the Law School Curriculum Guide at: http://www.law.columbia.edu/courses/search
Communicating in Organizations is a survey course that explores aspects of day-to-day managerial communication relating to presentations and other high-profile moments and more familiar elements of interpersonal communication. The course uses many teaching techniques: short lectures, individual and group exercises, video-recorded presentations, role plays, case discussions, video clips, and writing assignments. It is highly experiential, with exercises or presentations scheduled in most sessions. Initially, we’ll focus on the communication skills and strategies that help you present your ideas to others. I’ll ask you to do two benchmark assignments―a letter and a brief presentation―to assess the abilities you bring to the course. In several of our class sessions, you’ll be the one “in front of the room,” delivering either a prepared talk or brief, impromptu comments. Such assignments will allow you to develop your skills as a presenter. I’ll also discuss the link between listening and speaking, showing you how developing your listening skills will improve your effectiveness as a speaker. And we’ll explore several elements of visual communication, including how to design effective visual aids and written documents. To communicate effectively in such roles as coach, interviewer, negotiator, or facilitator, you need to be skilled at listening, questioning, observing behavior, and giving feedback. We’ll practice each of these skills in-class exercises and assignments. The Social Style instrument will provide detailed feedback about how others view your communication style. You’ll discover how style differences may lead to miscommunication, missed opportunities, or mishandled conflict.
An introduction to fundamental concepts of quantum optics and quantum electrodynamics with an emphasis on applications in nanophotonic devices. The quantization of the electromagnetic field; coherent and squeezed states of light; interaction between light and electrons in the language of quantum electrodynamics (QED); optical resonators and cavity QED; low-threshold lasers; and entangled states of light.
Mechanics of small-scale materials and structures require nonlinear kinematics and/or nonlinear stress vs. strain constitutive relations to predict mechanical behavior. Topics include variational calculus, deformation and vibration of beam, strings, plates, and membranes; fracture, delamination, bulging, buckling of thin films, among others. Thermodynamics of solids will be reviewed to provide the basis for a detailed discussion of nonlinear elastic behavior as well as the study of the equilibrium and stability of surfaces.
Prerequisites: A4404: or the instructor's permission Discussion of major issues in transportation at several levels, from national to local, and covering the economic, political, and social implications of decision-making in transportation. Current topics and case studies are investigated.\n \n
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Prerequisites: (ECON GR6211 and ECON GR6212 and ECON GR6215 and ECON GR6216 and ECON GR6412 and ECON GR6411 and This course will provide an overview of current research on the economics of education. The course will pay special attention to: i) the use of credible research designs, and ii) the use of theory in evaluating the mechanisms that underlie the identied eects
The Professional Issues in Nurse-Midwifery course is designed to concentrate on the transition from student to beginning nurse-midwife practitioner. It examines the history of the profession and the role of its leadership organizations including the ACNM. Students will submit articles for publication to the Journal of Midwifery and Women’s Health. The course curriculum also examines current critical issues that impact on the profession, both national and international, and addresses organizational and legislative means of effecting change.
This graduate course is designed to explore the ways in which research can be approached through artistic practices. Through interdisciplinary approaches, students will explore and develop the use of artistic methodologies in their research practices, culminating in a final multidisciplinary art project that demonstrates the integration of these practices into their research.
See Law School Curriculum Guide for details.
Introduction to optical interconnects and interconnection networks for digital systems. Fundamental optical interconnects technologies, optical interconnection network design, characterization, and performance evaluation. Enabling photonic technologies including free-space structures, hybrid and monolithic integration platforms for photonic on-chip, chip-to-chip, backplane, and node-to-node interconnects, as well as photonic networks on-chip.
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Prerequisites: Completion of 1st year graduate program in Economics, or the instructor's permission. The standard model of economic behavior describes a perfectly rational, self interested utility maximizer with unlimited cognitive resources. In many cases, this provides a good approximation to the types of behavior that economists are interested in. However, over the past 30 years, experimental and behavioral economists have documented ways in which the standard model is not just wrong, but is wrong in ways that are important for economic outcomes. Understanding these behaviors, and their implications, is one of the most exciting areas of current economic inquiry. This course will study three important topics within behavioral economics: Bounded rationality, temptation and self control and reference dependent preferences. It will draw on research from behavioral economics, experimental economics, decision theory, psychology and neuroscience in order to describe the models that have been developed to explain failures of the standard approach, the evidence in support of these models, and their economic implications.
Prerequisites: permission of the faculty member who will direct the teaching. Participation in ongoing teaching.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MIA & MPA Quantitative I Core.
This course introduces the fundamentals of statistical analysis, with applications in public policy, management, and the social sciences. Students will begin with basic techniques for describing and summarizing data and progress toward more advanced methods for inference and prediction. The course emphasizes practical tools for interpreting quantitative data and drawing evidence-based conclusions about the social world.
MPA Quantitative II Core.
This course introduces regression analysis as a key tool for policy analysis and program evaluation. Emphasizing causal inference, students will learn to assess the impacts of programs and policies using both experimental and non-experimental methods. The first half of the course reviews foundational concepts from Quant I and builds toward multiple regression techniques; the second half applies those tools to real-world policy settings. Designed for future practitioners, the course focuses on applying and communicating statistical concepts in accessible, non-technical language, and prepares students for advanced coursework in data analysis and program evaluation.
MPA Quantitative II Core.
This course introduces regression analysis as a key tool for policy analysis and program evaluation. Emphasizing causal inference, students will learn to assess the impacts of programs and policies using both experimental and non-experimental methods. The first half of the course reviews foundational concepts from Quant I and builds toward multiple regression techniques; the second half applies those tools to real-world policy settings. Designed for future practitioners, the course focuses on applying and communicating statistical concepts in accessible, non-technical language, and prepares students for advanced coursework in data analysis and program evaluation.
MPA Quantitative II Core.
This course introduces regression analysis as a key tool for policy analysis and program evaluation. Emphasizing causal inference, students will learn to assess the impacts of programs and policies using both experimental and non-experimental methods. The first half of the course reviews foundational concepts from Quant I and builds toward multiple regression techniques; the second half applies those tools to real-world policy settings. Designed for future practitioners, the course focuses on applying and communicating statistical concepts in accessible, non-technical language, and prepares students for advanced coursework in data analysis and program evaluation.
MPA Quantitative II Core.
This course introduces regression analysis as a key tool for policy analysis and program evaluation. Emphasizing causal inference, students will learn to assess the impacts of programs and policies using both experimental and non-experimental methods. The first half of the course reviews foundational concepts from Quant I and builds toward multiple regression techniques; the second half applies those tools to real-world policy settings. Designed for future practitioners, the course focuses on applying and communicating statistical concepts in accessible, non-technical language, and prepares students for advanced coursework in data analysis and program evaluation.
Health economics provides theories and tools for understanding, predicting, and changing human behavior. Understanding and changing the behavior of firms and individuals, designing health policies, and managing firms and organizations concerned with delivering health care and improving health, requires a solid foundation in health economics. In this course, students will learn the concepts in health economics most relevant and important to public health professionals and how these economic concepts can be applied to improving health care and the public health systems. Students will identify the basic concepts of health economics for the purposes of solving problems using these concepts, and apply these concepts in new contexts within public health.
Why does the government play such a central role in the health of its citizens? What factors unique to American politics have given us the healthcare system we currently have, and how much change can be accomplished within our philosophical and ethical confines? How do political changes yield policy shifts - or not? This course analyzes the role of major institutions - the central government, the federal system, the private sector, interest groups, and so on - in formulating and implementing health policy in the United States. We will discuss underlying normative issues and crossnational perspectives on healthcare to situate American healthcare policy along a broader global political spectrum, and attempt to forecast what changes are likely - or unlikely - to occur. Topics will include political history, policy formation and recommendations, market forces and economic influences, and more.
Single-cell genomics and genome-wide functional screens serve as core technologies for modern systems biology. Multi-modal single-cell analysis has transformed our ability to interrogate biological processes and gene regulation, even in complex tissues. Combining these powerful observational tools with CRISPR-based functional perturbations could lead to computational models that can predict cellular behavior. This course will explore the foundational principles underlying these experimental technologies, discuss their applications in basic and translational research, and introduce computational approaches for gleaning biological insight from high-dimensional genomic data.
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This course is intended to give the student a broad understanding of the components of the health care system and the basic management principles of hospital organization and management. The course will employ a variety of learning formats for students including lectures by the instructors, guest lecturers with special expertise, case studies and student presentations. Emphasis will be on the historical trends of health care statistics and operating data of health care institutions; the history of hospitals and health care systems; their organization and finances; regulatory controls; management strategies; accreditation and professional standards; government; private insurance; administrative leadership and professional interactions, emergency services, healthcare trends and marketing.
In this course, students will enhance and deepen their understanding of how the human voice and articulators partner together to create language. They will explore their own individual Idiolects and gain the skills to recalibrate their instruments in order to enhance the expressiveness and dynamic contrast of their speech. The phonemes of the International Alphabet (IPA) will be employed to specify the sounds of Detailed North American English (DNAE).
This hands-on course explores how data visualization, storytelling, and generative artificial intelligence can be combined to transform quantitative analysis into effective policy communication. Building on the concepts and methods introduced in Quantitative Techniques I or an equivalent graduate-level statistics course, students will learn to communicate analytical findings clearly, accurately, and persuasively to technical, managerial, and executive audiences.
The course introduces foundational principles of data visualization alongside the practical use of contemporary generative AI tools to support the full analytics-to-story workflow, from organizing and interpreting data to developing presentations, policy briefs, and executive summaries. Through applied exercises, in-class laboratories, and a collaborative project, students will learn how to communicate uncertainty, maintain analytical rigor, and translate quantitative evidence into actionable recommendations.
By the end of the course, students will be able to design effective visualizations, critically evaluate AI-generated outputs, tailor communications to different stakeholder audiences, and convert complex quantitative findings into compelling policy narratives that support decision-making.
In the 1890s, Frederick Mathias (F.M.) Alexander, a Shakespearian actor and spoken recitalist from Australia, began experiencing severe voice loss after he performed. The medical profession of his day prescribed vocal rest which worked well enough until Alexander’s next performance when he would leave the stage as hoarse as before. Frustrated that his vocal issues were not resolving, Alexander intuited that it must be something that he was doing to himself while he performed that was contributing to the loss of his voice. Doctors agreed with Alexander but they were at a loss to say what he was doing that was causing his problems.Thus began F. M.’s journey. The discoveries he made are what we now know as the Alexander Technique, and in the past 100 plus years, AT has become a valuable part of the curriculum in music conservatories and drama schools throughout the world. Many extraordinary actors have been lifelong students of the Alexander Technique for the many ways it helps their body, voice and breath in performance.
Our work together is experiential and sensory, and it involves a way of thinking which is highly creative and improvisational. It is an art, and it takes time to evolve in us. At the beginning things are bound to be confusing. You are learning a new language—a language of body and breath—and you cannot understand it through your old ways of feeling or visualizing. Confusion is absolutely normal, but it shifts as you develop a new awareness of yourself. Our work is a process of discovery and the only requirement for you as a student is to stay open and to try not to worry about getting something “right.” This is easier said than done, but I will be reminding you of it all the time. It helps if you can keep a “beginner’s mind” so that every lesson becomes a source of wonder.
For an actor, your body is your instrument and how you use your body determines how well you move on stage, produce your voice, and perform. The Alexander Technique is a mind-body discipline that helps students improve their psycho-physical coordination while helping them become aware of physical habits that may be inhibiting their breathing and the expressiveness, energy and strength of their voice and body. In our work together, you will begin to gain an awareness of improved physical coordination and ease leading to a freer and more expressive voice and body.
Vocal production relies on psychological and physical coordination—an alignmen
Covers biomaterials that are instructive or have been designed or engineered to be instructive; structure-function-property relationships in natural and synthetic biomaterials. Advances in understanding of material properties emphasized; including electroactivity, chemical, mechanical, geometry/architecture, and the modification of material surfaces and context of their effect on biological function. Evolving field of smart biomaterials discussed. Exercises/demonstrations using materials characterization equipment conducted.
This course examines the integration of arts and cultural experiences within healthcare systems to advance patient care, staff resilience, and community trust. Students will explore historical, social, and policy foundations of arts in health—from WPA-era murals to contemporary interventions addressing chronic disease, social isolation, and structural inequities—while engaging with evidence-informed programming and evaluation methods. The curriculum highlights organizational strategies for embedding the arts systemwide, fostering positive institutional culture, and enhancing operational and economic outcomes in complex healthcare organizations. Experiential exercises, case studies, and field observations illuminate arts-based interventions across hospitals, correctional facilities, and community settings, including partnerships with leading cultural institutions. The course emphasizes how arts programming functions as a social determinant–informed intervention, integrating innovative referral pathways and social screenings to address social isolation, loneliness, and psychosocial needs in communities.
NONFICTION LECTURE
This course is designed to help MA-level students improve their researching and writing skills, and become adept at distilling acquired knowledge into straightforward prose. The aim is to assist students in being more effective communicators regardless of whether they pursue careers in academia, journalism, government service, private enterprise or the non-governmental sector. The course will also promote better understanding of how to get work published by mass media outlets. The course places particular emphasis on practical work, including the preparation of commentaries and book reviews concerning current affairs in Eurasia. Lectures examine the basic elements of editing, interviewing and concise writing. Other lectures focus on how to maintain personal and digital security while living and researching/working in Eurasia, and discuss best practices on harnessing social media for career advancement. Guest speakers will provide additional perspectives on ways to make writing on academic topics more accessible to the general reading public, and how to leverage expertise in Eurasian-area affairs in ways that can jump-start careers.
The current market places increasing demands on healthcare managers so it is essential that individuals possess basic skills related to financial management and financial reporting. Current events make these demands more dynamic than ever. This course is intended for students who are interested in expanding their knowledge of healthcare financial issues and/or pursuing careers that involve financial management in the healthcare sector. The focus will be on non-profit healthcare delivery organizations.
How is the health care system organized? Who pays the bill? Why have efforts to enact national health insurance failed? What role does government now play in the US health care system, and how do different levels of government share these tasks? Contrary to many perceptions, the fervent debate of these questions is not a recent phenomenon; these are issues that have been argued vigorously throughout American political history. Exploring these debates is critical both to the development of public health policy and the management of delivery systems.
This course focuses on policy and management issues that affect all health care practitioners. We will examine, among other topics, the historical foundations of the American health care system, the rise of managed care, the make-up of the healthcare workforce, the key issues on the nation’s long-term care policy agenda, and ways in which government can encourage good quality care. This introductory course is intended for MHA students and serves to fulfill a core course requirement in Health Policy and Management.
How is the health care system organized? Who pays the bill? Why have efforts to enact national health insurance failed? What role does government now play in the US health care system, and how do different levels of government share these tasks? Contrary to many perceptions, the fervent debate of these questions is not a recent phenomenon; these are issues that have been argued vigorously throughout American political history. Exploring these debates is critical both to the development of public health policy and the management of delivery systems.
This course focuses on policy and management issues that affect all health care practitioners. We will examine, among other topics, the historical foundations of the American health care system, the rise of managed care, the make-up of the healthcare workforce, the key issues on the nation’s long-term care policy agenda, and ways in which government can encourage good quality care. This introductory course is intended for MHA students and serves to fulfill a core course requirement in Health Policy and Management.
POETRY LECTURE
In Russia, Ukraine, Moldova, Belarus, and other countries of the Eurasia region, corruption is systemic. Corruption, defined as the abuse of public trust and power for private gain, is institutionalized in government at the national, regional, and local levels. Formal government decision-making processes have been captured by informal networks of political and business elites who exert significant control over the allocation of public resources. They utilize this control to make illegal financial gains with the support of government authorities and protection of the law.
When President Putin began Russia’s expanded military invasion of Ukraine on February 24, 2022, the imprisoned Russian anticorruption activist and political opposition leader Alexey Navalny was on trial once again over fabricated charges of embezzlement. Though Mr. Navalny faced another 15 years in a penal colony, he seized the opportunity during his February 24 hearing to publicly state his opposition to Russia’s war on Ukraine. “This war between Russia and Ukraine was unleashed to cover up the theft from Russian citizens and divert their attention from problems that exist inside the country,” he said.
This seminar examines the role that Russia’s systemic corruption played as a cause of Russia’s war against Ukraine. Is the war an extension, and drastic escalation, of the Putin regime’s campaign against both his own citizens and the citizens of post-Maidan Ukraine? We will consider how the Kremlin’s strategic use of corruption is threatening the sovereignty of other nations in Eurasia.
This seminar analyzes the political economy, power relationships, historical and cultural factors that have engendered systemic corruption in Eurasian countries. We identify different types of corrupt systems that have emerged in the regions. We will also examine how systemic corruption causes conflict and war, and poses a threat to the global economy and democracy. Finally, we analyze various anti-corruption reforms to understand why some failed while others succeeded.
The seminar will benefit SIPA and Harriman Institute students who specialize in regional studies of countries of the Eurasia. It will also benefit SIPA and other graduate students who specialize in international security, economics, finance, energy, law, development, conflict resolution, and journalism. To achieve a deep understanding of Eurasia corruption, we will examine
Analytics and Managerial Decision-Making I is the first of two required quantitative methods courses taken in sequence by all MHA students. These courses are foundational to the MHA curriculum. The two courses are fully integrated with respect to materials, exercises and cases, and by a two-term, team-based application project.
Managers are continually confronted with the need to make significant decisions concerning the organizational and financial performance of a health organization, based on a combination of strategic intention, practical experience, and interpretation and application of complex data and information. Data analysis is one tool that supports such decision-making. This course is designed to provide management students with the tools to generate and present data-driven and model-based management recommendations that are meaningful and implementable.
The course focuses on learning basic tools for the collection, analysis, and presentation of data in support of managerial/executive decision-making. Topics will include introductory data and statistical exploration from basic descriptive statistics to population and market estimation, comparison testing and decision-making, sampling design and analysis, and predicting/forecasting using linear regression. Using Excel as an additional tool, the course develops analytical skills to prepare managers to make and to present informed decisions in the overall healthcare sector.
Principles of electromechanical energy conversion. Overview of electric motor types: DC, induction, and permanent magnet synchronous motors. Power electronic converters and modulation techniques. Torque-speed characteristics, dynamic response, efficiency analysis. Scalar and vector control methods. Motor modeling and simulation. Drive system components and integration. Applications in industrial automation, robotics, and electric vehicles.
Counterfactuals play a key role in philosophy, linguistics, psychology, decision theory, game theory, artificial
intelligence, and many other related fields. Our goal for this course is to cover foundational work on
counterfactuals (with some attention paid to indicative conditionals as well). Though our reading list has
a historical component, its primary purpose is to familiarize students with contemporary state of play. We
will focus on distinctions and applications that have become an essential part of the working philosopher’s
toolkit.
This seminar is an investigation into the network of relations between three things: (I) the nature of a domain of entities, including their properties and relations; (II) the capacity to have mental states about them; and (III) the capacity to know and to make reasonable judgements about them. As a subpart of this investigation, as a special case at one level up: we are sometimes concerned with the network of relations between: (I’) the nature of a domain of entities consisting of, or involving, intentional contents themselves, their properties and relations; (II’) the capacity of have mental states about them; and (III’) the capacity to know and make reasonable judgements about them.
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In
this seminar, we will see that they are not. Whether a physical theory is deterministic—whether
it fixes a unique future given the present—can depend on one’s stance on axioms of set theory
about which there is intractable disagreement. This is not a quirk of exotic toy models. It reaches
into the heat equation, quantum mechanics, statistical mechanics, and general relativity. The
seminar builds from the ground up. We begin with the philosophy of determinism: what it
means, why it matters, and how it has traditionally been formalized. We then develop enough set
theory and descriptive set theory to state the key results precisely. In the second half, we work
through the sensitivity results in detail, showing how the content of fundamental physical
theories shifts with the set-theoretic background. We conclude by asking what this means for
debates about mathematical pluralism, scientific realism, and the boundary between mathematics
and physics.
No prior knowledge of set theory or mathematical physics is assumed. The seminar is open to
graduate students in philosophy and, with permission, to advanced graduate students in
mathematics, physics, and related fields.