This course will offer an examination of the birth and development of the Franciscan Order between 1200-1350. The topics will include Francis of Assisi, the foundation of the three orders of Franciscans, education, poverty, preaching, theology internal strife, antifraternalism, and relations with secular governments and papacy.
Prerequisite(s): IEOR E4106 or E3106. Required for undergraduate students majoring in OR:FE. Introduction to investment and financial instruments via portfolio theory and derivative securities, using basic operations research/engineering methodology. Portfolio theory, arbitrage; Markowitz model, market equilibrium, and the capital asset pricing model. General models for asset price fluctuations in discrete and continuous time. Elementary introduction to Brownian motion and geometric Brownian motion. Option theory; Black-Scholes equation and call option formula. Computational methods such as Monte Carlo simulation.
Prior knowledge of Python is recommended. Provides a broad understanding of the basic techniques for building intelligent computer systems. Topics include state-space problem representations, problem reduction and and-or graphs, game playing and heuristic search, predicate calculus, and resolution theorem proving, AI systems and languages for knowledge representation, machine learning and concept formation and other topics such as natural language processing may be included as time permits.
Digital communications for both point-to-point and switched applications is further developed. Optimum receiver structures and transmitter signal shaping for both binary and M-ary signal transmission. An introduction to block codes and convolutional codes, with application to space communications.
This course will cover research methods and research design in political science. We will focus on concrete and practical issues of conducting research: picking a topic, generating hypotheses, case selection, measurement issues, designing and conducting experiments, interviews, field work, archival research, coding data and working with data sets, combining quantitative and qualitative methods, etc. The course is designed for several audiences, including: (1) PhD students in Political Science, (2) MAO students undertaking a major research project, and (3) advanced undergrads contemplating an honors thesis, or another major research project.
This graduate course is only for M.S. Program in Financial Engineering students. Multivariate random number generation, bootstrapping, Monte Carlo simulation, efficiency improvement techniques. Simulation output analysis, Markov-chain Monte Carlo. Applications to financial engineering. Introduction to financial engineering simulation software and exposure to modeling with real financial data. Note: Students who have taken IEOR E4404 Simulation may not register for this course for credit.
Computational approaches to the analysis, understanding, and generation of natural language text at scale. Emphasis on machine learning techniques for NLP, including deep learning and large language models. Applications may include information extraction, sentiment analysis, question answering, summarization, machine translation, and conversational AI. Discussion of datasets, benchmarking and evaluation, interpretability, and ethical considerations.
Due to significant overlap in content, only one of COMS 4705 or Barnard COMS 3705BC may be taken for credit.
This graduate course is only for MS program in FE students. Modeling, analysis, and computation of derivative securities. Applications of stochastic calculus and stochastic differential equations. Numerical techniques: finite-difference, binomial method, and Monte Carlo.
This graduate course is only for M.S. Program in Financial Engineering students. Empirical analysis of asset prices: heavy tails, test of the predictability of stock returns. Financial time series: ARMA, stochastic volatility, and GARCH models. Regression models: linear regression and test of CAPM, non-linear regression and fitting of term structures.
Principles of Ethical Artificial Intelligence across technical and societal dimensions. Combines technical AI and machine learning implementations and ethical analysis. Students will learn to build, audit, and mitigate ethical risks in AI systems using tools like fairness libraries, explainability frameworks, and privacy-preserving techniques. Emphasizes coding, algorithmic critique, and real-world cases.
Topics include: foundations of AI ethics, fairness, interpretability, explainability, accountability, privacy, robustness, alignment, safety, and societal benefit.
Assessments include coding projects, bias auditing assignments, and ethical analysis papers.
Prerequisites: (Econ UN3211) and (ECON UN3213) and (STAT UN1201) This course uses economic theory and empirical evidence to study the links between financial markets and the real economy. We will consider questions such as: What is the welfare role of finance? How do financial markets affect consumers and firms? How do shocks to the financial system transmit to the real economy? How do financial markets impact inequality?
While helping students advance their levels of oral and written expression, this course focuses on literature of the modern and medieval periods, with particular emphasis on the development of the modern novella and traditional and new forms of poetry. In addition to literature, students are introduced to a wide variety of genres from political and cultural essays and blogs to newspaper translations of the early 20th century. They will be further exposed to ta?rof in reference to a wide variety of socio-cultural contexts and be expected to use ta?rof in class conversations. Students will be exposed to popular artists and their works and satirical websites for insight into contemporary Iranian culture and politics. No P/D/F or R credit is allowed for this class.
Prerequisites: POLS W4710 or the equivalent.
This course will
intensively
examine some of the data analysis methods which deal with problems occurring in the use of multiple regression analysis. It will stress computer applications and cover, as needed, data coding and data processing. Emphasis will also be placed on research design and
writing research reports
.
The course assumes that students are familiar with basic statistics, inference, and multiple regression analysis and have analyzed data using computer software (e.g., any standard statistical programs on micro-computers or larger machines -- Stata, “R”, SPSS, SAS, etc.). Students will be instructed on the use of the microcomputers and the R and Stata statistical software program(s) available as freeware (R) or in the CUIT computer labs (Stata; several campus locations) or through SIPA. The lectures and required discussion section will emphasize the use of “R.” Students may use whatever computer programs they prefer for all data analysis for the course. There may be an
additional fee
for classroom instructional materials.
This is the required discussion section for
POLS GU4712.
“Imag(in)ing the Ottoman Empire: A visual history, 18th-20th centuries” is an undergraduate/graduate seminar focusing on visual representations of the Ottoman Empire during the last two centuries of its existence, from the early eighteenth to the early twentieth century. The objective is to study the development of visual representations both
by
and
about
the Empire, from Ottoman miniatures to early European paintings, and from the surge of Western illustrated magazines to the local uses of photography. The seminar’s chronological thread will be complemented by a thematic structure designed to explore different aspects and influences concerning the production and diffusion of images: curiosity, documentation, exoticism, propaganda, orientalism, modernity, self-fashioning, eroticism, policing, to name just a few.
During the past 15 years the behavior of market options prices have shown systematic deviations from the classic Black-Scholes model. Examines the empirical behavior of implied volatilities, in particular the volatility smile that now characterizes most markets, the mathematics and intuition behind new models that can account for the smile, and their consequences for hedging and valuation.
In the first half of this course we will read the major works of Freud that make up his “metapsychology.” Metapsychology is psychoanalysis’ “speculative superstructure,” the most philosophical part of psychoanalytic theory, providing a broad theoretical “standpoint” on the mind that is both informed by and guides both empirical research and clinical practice. Freud articulated four metapsychologies (dynamic, economic, topographical, and structural). The aim will be to read Freud somewhat as we read, for example, Aristotle’s or Kant’s or Nietzsche’s moral psychology. What are the basic theoretical posits? What are these claims based on? From what perspective (first-personal or third-personal) are these claims made? How does Freud’s picture advance our own practical self-understanding? Etc.
In the second half of the course we will read some major responses to Freud in the context of philosophical moral psychology. So we will read some critical theorists, some engagements with psychoanalytic theory regarding gender and race, and some contemporary analytic philosophers.
Selected topics of interest in the area of quantitative finance. Offerings vary each year; some topics include energy derivatives, experimental finance, foreign exchange and related derivative instruments, inflation derivatives, hedge fund management, modeling equity derivatives in Java, mortgage-backed securities, numerical solutions of partial differential equations, quantitative portfolio management, risk management, trade and technology in financial markets.
This course is the second course in the graduate-level sequence on quantitative political methodology offered in the Department of Political Science. Students will learn (1) a framework and methodologies for making causal inferences from experimental and observational data, and (2) statistical theories essential for causal inference. Topics include randomized experiments, estimation under ignorability, instrumental variables, regression discontinuity, difference-indifferences, and causal inference with panel data. We also cover statistical theories, such as theories of ordinary least squares and maximum likelihood estimation, by connecting them to causal inference methods. This course builds on the materials covered in POLS 4700 and 4720 or theirequivalent (i.e., probability, statistics, linear regression, and logistic regression).
This is the required discussion section for
POLS GU4722.
May be repeated for credit; content varies.
Prerequisites: Must have completed MDES 2702, equivalent two years of Persian or the instructor's permission.
This course provides experience reading and analyzing Persian language texts, as well as translating them into English. We will also spend some time learning how to read different kinds of paleography, and about various manuscript and print conventions and practices. Supplementary scholarly readings in English will situate the Persian texts. There will be a translation workshop at the end of the semester with related texts of the students choosing, in preparation for a final translation project. No P/D/F or R credit is allowed for this class.
This course is the fourth course in the graduate-level sequence on quantitative political methodology offered in the Department of Political Science. Students will learn a variety of advanced topics in quantitative methods for descriptive and causal inference, such as simulated-data experimentation, statistical graphics, experimental design, Bayesian inference, multilevel modeling, ideal-point and measurement-error models, and time/spatial/network models. This course builds on the materials covered in POLS 4700, 4720, 4722, and 4724, or their equivalent courses (i.e., probability, statistics, linear regression, logistic regression, causal inference with observational and experimental data, and knowledge of the statistical computing environment R).
This is the required discussion section for
POLS GU4726.
(Lecture). Beginning with an overview of late medieval literary culture in England, this course will cover the entire Canterbury Tales in the original Middle English. We will explore the narrative and organizational logics that underpin the project overall, while also treating each individual tale as a coherent literary offering, positioned deliberately and recognizably on the map of late medieval cultural convention. We will consider the conditions—both historical and aesthetic—that informed Chaucer’s motley composition, and will compare his work with other large-scale fictive works of the period. Our ultimate project will be the assessment of the Tales at once as a self-consciously “medieval” production, keen to explore and exploit the boundaries of literary convention, and as a ground-breaking literary event, which set the stage for renaissance literature.
An introduction to the recent development in quantum optimization and quantum machine learning using gate-based Noisy Intermediate Scale Quantum (NISQ) computers. IBM’s quantum programming framework Qiskit is utilized. Qbits, quantum gates and quantum measurements, quantum algorithms (Grover’s search, Simon’s algorithm, quantum Fourier transform, quantum phase estimation) quantum optimization (quantum annealing, QAOA, variational quantum eigensolver), quantum machine learning (quantum support vector machine, quantum neural networks).
Prerequisites: POLS GU4700 or equivalent level of calculus. Introduction to noncooperative game theory and its application to strategic situations in politics. Topics include solution concepts, asymmetric information, and incomplete information. Students should have taken POLS GU4700 or have equivalent background in calculus. Permission of instructor required.
This is the required discussion section for POLS GU4730.
Advanced course in computer vision. Topics include convolutional networks and back-propagation, object and action recognition, self-supervised and few-shot learning, image synthesis and generative models, object tracking, vision and language, vision and audio, 3D representations, interpretability, and bias, ethics, and media deception.
MS IEOR students only. Application of various computational methods/techniques in quantitative/computational finance. Transform techniques: fast Fourier transform for data de-noising and pricing, finite difference methods for partial differential equations (PDE), partial integro-differential equations (PIDE), Monte-Carlo simulation techniques in finance, and calibration techniques, filtering and parameter estimation techniques. Computational platform will be C++/Java/Python/Matlab/R.
This course provides students with an overview of environmental research, covering the conceptualization of research projects, the grantmaking process, and article writing. Throughout the semester, students will attend lectures from Columbia researchers and professionals from other organizations. These lectures will cover their current projects and how they communicate their findings in various settings, communities, cultures, and industries. The lecturers will also discuss different aspects of the research process and the practicalities of project development. Students will learn the basics of grant writing and research methodology, write an academic research paper, and participate in a colloquium, with the aim of providing them with tangible transferable skills.
Data, models, visuals; various facets of AI, applications in finance; areas: fund, manager, security selection, asset allocation, risk management within asset management; fraud detection and prevention; climate finance and risk; data-driven real estate finance; cutting-edge techniques: machine learning, deep learning in computational, quantitative finance; concepts: explainability, interpretability, adversarial machine learning, resilience of AI systems; industry utilization
What is “globalization”? How does it change the way we think about or show art today? What role does film and media play in it? How has critical theory itself assumed new forms in this configuration moving outside post-war Europe and America? How have these processes helped change with the very idea of ‘contemporary art’? What then might a transnational critical theory in art and in thinking look like today or in the 21st century? In this course we will examine this cluster of questions from a number of different angles, starting with new questions about borders, displacements, translations and minorities, and the ways they have cut across and figured in different regions, in Europe or America, as elsewhere. In the course of our investigations, we will look in particular at two areas in which these questions are being raised today -- in Asia and in Africa and its diasporas. The course is thus inter-disciplinary in nature and is open to students in different fields and areas where these issues are now being discussed.
This course examines the history of science, technology and medicine in the modern Middle East. We will consider a number of themes from energy infrastructures and communication and transportation systems to modern medical, agricultural and environmental developments.
Prerequisites: ECON UN3211 and ECON UN3213 The world is being transformed by dramatic increases in flows of people, goods and services across nations. Globalization has the potential for enormous gains but is also associated to serious risks. The gains are related to international commerce where the industrial countries dominate, while the risks involve the global environment, poverty and the satisfaction of basic needs that affect in great measure the developing nations. Both are linked to a historical division of the world into the North and the South-the industrial and the developing nations. Key to future evolution are (1) the creation of new markets that trade privately produced public goods, such as knowledge and greenhouse gas emissions, as in the Kyoto Protocol; (2) the updating of the Breton Woods Institutions, including the creation of a Knowledge Bank and an International Bank for Environmental Settlements.
Computational techniques for analyzing genomic data including DNA, RNA, protein and gene expression data. Basic concepts in molecular biology relevant to these analyses. Emphasis on techniques from artificial intelligence and machine learning. String-matching algorithms, dynamic programming, hidden Markov models, expectation-maximization, neural networks, clustering algorithms, support vector machines. Students with life sciences backgrounds who satisfy the prerequisites are encouraged to enroll.
Basic statistical principles and algorithmic paradigms of supervised machine learning.
Prerequisites:
Multivariable calculus (e.g. MATH1201 or MATH1205 or APMA2000), linear algebra (e.g. COMS3251 or MATH2010 or MATH2015), probability (e.g. STAT1201 or STAT4001 or IEOR3658 or MATH2015), discrete math (COMS3203), and general mathematical maturity. Programming and algorithm analysis (e.g. COMS 3134).
COMS 3770 optionally satisfies all math prerequisites for this course.
Course overview: The goal of this course is to engage upper-level undergraduates and beginning graduate students in an immersive intellectual experience at the intersection of rigorous scientific inquiry and the history of innovation in molecular biology. The central theme will be curiosity and critical thinking as the twin drivers of both technological innovation and scientific discovery. The course will be divided into a series of modules focused on analysis and presentation of original research papers related to one important breakthrough in molecular biology that occurred during the past century. A prominent theme of the course will be the persistently unpredictable trajectory linking technical research and methodological developments to breakthrough science. Approximately six-to-eight original research papers will be covered in each module, spanning topics from the development of the methods that made the breakthrough possible through practical application of the resulting knowledge.
Three or four of the following breakthroughs will likely be covered in 2023:
Discovery and clinical application of insulin by Banting & Best.
Development of the Trikafta triple drug treatment for cystic fibrosis.
Development of CRISPR for human genetic engineering.
Genetics and pharmacological treatment of human hyperlipidemia.
Development of the Gleevec tyrosine kinase inhibitor to cure Ph+ leukemias.
Development of “next-generation” nucleic acid sequencing methods.
This seminar
explores a tradition of historical writing (historiography) that constructs “Africa and France,” or “France and Africa,” or “FrançAfrique” as an historical object and as an object of knowledge. That body of writing accounts in various and sometimes contadictory ways for the peculiar, intense, and historically conflictual relationship that exists between France and the sub-Saharan nation-states that are its former African colonies.
Tracing the discovery of the role of DNA tumor viruses in cancerous transformation. Oncogenes and tumor suppressors are analyzed with respect to their function in normal cell cycle, growth control, and human cancers. SCE and TC students may register for this course, but they must first obtain the written permission of the instructor, by filling out a paper Registration Adjustment Form (Add/Drop form). The form can be downloaded at the URL below, but must be signed by the instructor and returned to the office of the registrar. http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
How language structure and usage varies according to societal factors such as social history and socioeconomic factors, illustrated with study modules on language contact, language standardization and literacy, quantitative sociolinguistic theory, language allegiance, language, and power.
Care is central to the interpersonal claim that is made by the other. It is a response that recognizes and satisfies a need. Care can be motivated by pain and sorrow, but also by desire and the desire for recognition. But while care is a fundamental aspect of healing, it can also be a demand that extracts obligations and liabilities. Care is an ambiguous concept that always already contains or is determined by its oppositions; we will begin by analyzing the concept of care itself, drawing on resources from the history and philosophy of medicine as well as literary sources. Ideals of care that many of us have for our loved ones are difficult to render at scale, and are often in tension with the for-profit motivations behind the development of medications, the administration of healthcare services, and the distribution of goods. We will consider the sorts of compromises that are made every day through readings in literature, history, political science and philosophy and also through first-person experience in the form of a practicum that that will run parallel to the course.
Introduction to human spaceflight from a systems engineering perspective. Historical and current space programs and spacecraft. Motivation, cost, and rationale for human space exploration. Overview of space environment needed to sustain human life and health, including physiological and psychological concerns in space habitat. Astronaut selection and training processes, spacewalking, robotics, mission operations, and future program directions. Systems integration for successful operation of a spacecraft. Highlights from current events and space research, Space Shuttle, Hubble Space Telescope, and International Space Station (ISS). Includes a design project to assist International Space Station astronauts.
This course offers an understanding of the interdisciplinary field of environmental, health and population history and will discuss historical and policy debates with a cross cutting, comparative relevance: such as the making and subjugation of colonized peoples and natural and disease landscapes under British colonial rule; modernizing states and their interest in development and knowledge and technology building, the movement and migration of populations, and changing place of public health and healing in south Asia. The key aim of the course will be to introduce students to reading and analyzing a range of historical scholarship, and interdisciplinary research on environment, health, medicine and populations in South Asia and to introduce them to an exploration of primary sources for research; and also to probe the challenges posed by archives and sources in these fields. Some of the overarching questions that shape this course are as follows: How have environmental pasts and medical histories been interpreted, debated and what is their contemporary resonance? What have been the encounters (political, intellectual, legal, social and cultural) between the environment, its changing landscapes and state? How have citizens, indigenous communities, and vernacular healers mediated and shaped these encounters and inserted their claims for sustainability, subsistence or survival? How have these changing landscapes shaped norms about bodies, care and beliefs? The course focuses on South Asia but also urges students to think and make linkages beyond regional geographies in examining interconnected ideas and practices in histories of the environment, medicine and health. Topics will therefore include (and students are invited to add to these perspectives and suggest additional discussion themes): colonial and globalized circuits of medical knowledge, with comparative case studies from Africa and East Asia; and the travel and translation of environmental ideas and of medical practices through growing global networks.
Characterization of stochastic processes as models of signals and noise; stationarity, ergodicity, correlation functions, and power spectra. Gaussian processes as models of noise in linear and nonlinear systems; linear and nonlinear transformations of random processes; orthogonal series representations. Applications to circuits and devices, to communication, control, filtering, and prediction.
Introduction to the mathematical tools and algorithmic implementation for representation and processing of digital pictures, videos, and visual sensory data. Image representation, filtering, transform, quality enhancement, restoration, feature extraction, object segmentation, motion analysis, classification, and coding for data compression. A series of programming assignments reinforces material from the lectures.
Embedded system design and implementation combining hardware and software. I/O, interfacing, and peripherals. Weekly laboratory sessions and term project on design of a microprocessor-based embedded system including at least one custom peripheral. Knowledge of C programming and digital logic required.
How to write the city? What is an archive for writing the city? What liminal and marginal perspectives are available for thinking about writing the city? What is the place of the city in the global south in our historical imagination? Our attempt in this seminar is to look at the global south city from the historical and analytical perspectives of those dispossessed and marginal. Instead of ‘grand’ summations about “the Islamic City” or “Global City,” we will work meticulously to observe annotations on power that constructs cities, archives and their afterlives. The emphasis is on the city in South Asia as a particular referent though we will learn to see Cairo, New York, and Istanbul.
The goal of synthetic organogenesis is to use stem cells to reconstitute aspects of embryo development and organ formation in vitro. Examines the molecular basis of human embryogenesis. Introduces synthetic organogenesis as an interdisciplinary field. Students learn to recognize generic molecular mechanisms behind signaling and cell lineage specification. Covers recent advances in applying engineering and contemporary biology to creating organoids and organs on chips using human stem cells.
North Korea is widely regarded as a country without a history; as enigmatic as it is isolated. Dispensing with this cliché, this course invites students to engage with North Korean history using a variety of primary and secondary sources. We begin in the medieval period to trace the distinct features of the northern region that made it uniquely receptive to outside ideas. Understanding the north as a frontier zone of experimentation and adaption allows us to examine the attractive power of modernity in the north during the early twentieth century via the influence of Christianity, capitalism and communism. Utilizing texts and materials made in North Korea and internationally, including feature and documentary films, women’s magazines, graphic novels, literary fiction and testimony, the course investigates the conditions within which knowledge about North Korea has been produced, circulated and repressed. Key topics to be explored include the history of Christianity and capitalism in Pyongyang and the northern provinces, communist cadres in the 1930s, the allure of the North in the 1940s, the Korean War and the purges that followed, North Korea’s relations with neighbors and the world, and the high cost its citizens pay for the country’s brutal sanction economy.
Many materials properties and chemical processes are governed by atomic-scale phenomena such as phase transformations, atomic/ionic transport, and chemical reactions. Thanks to progress in computer technology and methodological development, now there exist atomistic simulation approaches for the realistic modeling and quantitative prediction of such properties. Atomistic simulations are therefore becoming increasingly important as a complement for experimental characterization, to provide parameters for meso- and macroscale models, and for the in-silico discovery of entirely new materials. This course aims at providing a comprehensive overview of cutting-edge atomistic modeling techniques that are frequently used both in academic and industrial research and engineering. Participants will develop the ability to interpret results from atomistic simulations and to judge whether a problem can be reliably addressed with simulations. The students will also obtain basic working knowledge in standard simulation software.
China's search for a new order in the long twentieth century with a focus on political, social and cultural change.
Prerequisites: Recommended preparation: a solid background in basic chemistry. Introduction to geochemical cycles involving the atmosphere, land, and biosphere; chemistry of precipitation, weathering reactions, rivers, lakes, estuaries, and groundwaters; students are introduced to the use of major and minor ions as tracers of chemical reactions and biological processes that regulate the chemical composition of continental waters.
:
Philanthropy & Just Societies
will enable Columbia undergraduate students to learn about the history of philanthropy, to understand best practices and ethical underpinnings, to debate its potential in making more just societies, and to consider what it means to give and receive aid at different scales. Students will have the opportunity to participate directly in philanthropic work.
Prerequisite(s): Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design.