Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, Ascoli-Arzela theorem, Stone-Weierstrass theorem.
This course introduces you to the rich and diverse tradition of Chinese art by focusing on materials and techniques. We will discuss a wide array of artistic media situated in distinct cultural contexts, examining bronzes, jade, ceramics, paintings, sculptures, and textiles in the imperial, aristocratic, literary, religious, and commercial milieus in which they were produced. In addition to developing your skills in visual-material analysis, this course will also acquaint you with the diverse cultures that developed in China’s center and periphery during its five thousand (plus) years of history. Emphasis will be placed on understanding how native artistic traditions in China interacted with those in regions such as the Mongolian steppe, Tibetan plateau, and Central Asia.
The second term of this course may not be taken without the first. Power series, analytic functions, Implicit function theorem, Fubini theorem, change of variables formula, Lebesgue measure and integration, function spaces.
This seminar will examine the concept of cultural heritage as a body of goods, tangible and intangible, that come to us from the past - sometimes from antiquity, sometimes from more recent historical periods - and for which we are responsible for the present and future generations. The environment is an important part of cultural heritage too, with nature and its peculiar beauties. Similarly, practices, traditions, crafts and customs are a crucial component of cultural heritage. Over time, cultural heritage has become an increasingly broad and complex category: experts, scientists and professionals involved continue to multiply, and the disciplines continue to specialize. Even the very concept of cultural heritage is quite dynamic and frequently modified and reinterpreted. Based on an anthropological perspective and within the framework of a cultural heritage considered among the most valuable in the arts, both visual and literary, Italy’s artistic, archaeological, library and archival treasures will be a regular source of analysis and discussion. This course will examine ways in which we can understand cultural heritage through the intersections of several components: identity, nationalism, colonialism, ethnicity, gender, and religion, just to mention a few. Students will take into account several elements: how regional and international agencies and policies operate and interact with each other, the many threats to cultural heritage (wars and conflicts, natural disasters, climate change, illicit trafficking, and some forms of tourism), and the role of sustainability. The course will encourage students to acquire analytical reasoning and critical thinking, through a combination of textual and visual interpretation and class discussion. There are no pre-requisites for this course.
In English
Study ecology, evolution, and conservation biology in one of the world’s most biologically spectacular settings, the wildlife-rich savannas of Kenya. Although we will meet have a few meetings during the fall semester, the majority of the coursework will be completed during a 16 day field trip to Kenya during winter break. Students will spend their time immersed in an intensive field experience gaining sophisticated training in fieldwork and biological research. Note that there is a lab fee to cover all in-country expenses, and students are also responsible for the cost of airfare to and from Kenya.
Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061 A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.
This course integrates the principles of database systems, AI agents, and health informatics. Students will gain expertise in the following areas:
Multimodal Data Engineering:
Ingesting, cleaning, and normalizing heterogeneous data (time-series sensor data, unstructured clinical notes, structured FHIR records)
Agentic Architectures:
Designing LLM-based agents capable of tool use (function calling), planning, and memory management (LangChain, LlamaIndex).
Retrieval-Augmented Generation (RAG):
Implementing vector databases and semantic search strategies optimized for personal health contexts.
Privacy and Ethics:
Understanding HIPAA compliance, differential privacy, and the ethical implications of AI "hallucinations" in health advice.
HCI for Health:
Designing applications and interfaces that foster trust, explainability, and engagement in self-tracking and patient-provider communication.
Domain Knowledge:
Understanding the basics of chronic disease management, personal health monitoring, and clinical decision support.
Prerequisites: (CHEM UN1403 and CHEM UN1404) or (CHEM UN1604) or (CHEM UN2045 and CHEM UN2046) , or the equivalent. Principles governing the structure and reactivity of inorganic compounds surveyed from experimental and theoretical viewpoints. Topics include inorganic solids, aqueous and nonaqueous solutions, the chemistry of selected main group elements, transition metal chemistry, metal clusters, metal carbonyls, and organometallic chemistry, bonding and resonance, symmetry and molecular orbitals, and spectroscopy.
Prerequisites: Two semesters of a rigorous, molecularly-oriented, introductory biology course, such as UN2005 (
Inc.,
Biochemistry of DNA & Proteins, basic Genetics, Metabolism & Cell Physiology
) and UN2006 (
Cell biology, inc. intra-cellular transport, phagocytosis, protein regulation, as well as Inter-cellular communication, inc., cell-cell contact, receptors/ligands & transporters
). This course will cover the integration of innate and adaptive immune systems, as well as how immune response contributes to health and disease (
e.g., Infectious disease, allergies, autoimmunity, immune deficiencies, the microbiome and cancer immunotherapy
). Students will also become familiar with important immunological methods, which will provide an opportunity to explore some of the current literature. Sophomores will require permission from their advisor to enroll, and graduate student will require the instructor’s permission to enroll. SPS, Barnard, and TC students may register for this course with the instructor’s approval on a Registration Adjustment Form (Add/Drop form), which can be downloaded (
http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
) and then returned to the office of the registrar.
The course looks at works produced in the more than 20 countries that make up Latin America. Our investigations will take us from the Southern Cone nations of South America, up through Central American and the Caribbean, to Mexico to the north. We will cover styles from the colonial influences present in post-independence art of the early 19th century, to installation art found at the beginning of the 21st century. Along the way we will consider such topics as, the relationship of colonial style and academic training to forging an independent artistic identity; the emergence and establishment of a modern canon; experimentations in surrealism, neo-concretism, conceptual art, and performance. We will end the course with a consideration of Latinx artists working in the U.S.
While focusing on the Decameron, this course follows the arc of Boccaccios career from the Ninfale Fiesolano, through the Decameron, and concluding with the Corbaccio, using the treatment of women as the connective thread. The Decameron is read in the light of its cultural density and contextualized in terms of its antecedents, both classical and vernacular, and of its intertexts, especially Dantes Commedia, with particular attention to Boccaccios masterful exploitation of narrative as a means for undercutting all absolute certainty. Lectures in English; text in Italian, although comparative literature students who can follow with the help of translations are welcome.
While focusing on the Decameron, this course follows the arc of Boccaccios career from the Ninfale Fiesolano, through the Decameron, and concluding with the Corbaccio, using the treatment of women as the connective thread. The Decameron is read in the light of its cultural density and contextualized in terms of its antecedents, both classical and vernacular, and of its intertexts, especially Dantes Commedia, with particular attention to Boccaccios masterful exploitation of narrative as a means for undercutting all absolute certainty. Lectures in English; text in Italian, although comparative literature students who can follow with the help of translations are welcome.
“Quand on refuse, on dit non”, said Ivorian novelist Ahmadou Kourouma towards the end of his life. Taking this stance as a starting point, this seminar will explore, through the lens of the novel, major political upheavals in the Francophone world during the 1950s, 60s and 70s. We will shed light on the history of decolonization, May 68, the feminist movement, and struggles against racism and injustice by delving into the imaginary worlds of six leading francophone novelists: Marguerite Duras, Ahmadou Kourouma, Assia Djebar, Hélène Cixous, George Perec and Édouard Glissant.
Prerequisite: open to public. Presentations by medical informatics faculty and invited international speakers in medical informatics, computer science, nursing informatics, library science, and related fields.
Elementary introduction to fundamental concepts and techniques in classical analysis; applications of such techniques in different topics in applied mathematics. Brief review of essential concepts and techniques in elementary analysis; elementary properties of metric and normed spaces; completeness, compactness, and their consequences; continuous functions and their properties; Contracting Mapping Theorem and its applications; elementary properties of Hilbert and Banach spaces; bounded linear operators in Hilbert spaces; Fourier series and their applications.
Elementary introduction to fundamental concepts and techniques in classical analysis; applications of such techniques in different topics in applied mathematics. Brief review of essential concepts and techniques in elementary analysis; elementary properties of metric and normed spaces; completeness, compactness, and their consequences; continuous functions and their properties; Contracting Mapping Theorem and its applications; elementary properties of Hilbert and Banach spaces; bounded linear operators in Hilbert spaces; Fourier series and their applications.
Basic theory of quantum mechanics, well and barrier problems, the harmonic oscillator, angular momentum identical particles, quantum statistics, perturbation theory and applications to the quantum physics of atoms, molecules, and solids.
Foundational for the Master of Science in Earth and Environmental Engineering degree. Provides broader understanding of engineering tools critical/ essential to success in large-scale, engineering projects. Divided into two parts: Module on global/regional flows, and systems approach, and Module on Engineering Principles in Earth & Environmental Engineering. Guest lectures on several topics will be provided.
Probability and simulation. Statistics building on knowledge in probability and simulation. Point and interval estimation, hypothesis testing, and regression. A specialized version of IEOR E4150 for MSE and MSBA students who are exempt from the first half of IEOR E4101. Must obtain waiver for E4101.
In revisiting two major authors of the Italian modern novel, the course investigates the relation between fiction and the conditions of modernity (personal risk, anxiety and lack of control on reality, secularization, to name a few). Special attention will be paid to the response of the novelistic discourse to modernity, and to Italy's peculiarly peripheral position in the modern world. Primary texts will be read in Italian, while theoretical references will be in English.
A first course on crystallography. Crystal symmetry, Bravais lattices, point groups, space groups. Diffraction and diffracted intensities. Exposition of typical crystal structures in engineering materials, including metals, ceramics, and semiconductors. Crystalline anisotropy.
This course will begin by clearly defining what sustainability management is and determining if a sustainable economy is actually feasible. Students will learn to connect environmental protection to organizational management by exploring the technical, financial, managerial, and political challenges of effectively managing a sustainable environment and economy. This course is taught in a case-based format and will seek to help students learn the basics of management, environmental policy and sustainability economics. Sustainability management matters because we only have one planet, and we must learn how to manage our organizations in a way that ensures that the health of our planet can be maintained and bettered. This course is designed to introduce students to the field of sustainability management. It is not an academic course that reviews the literature of the field and discusses how scholars thing about the management of organizations that are environmentally sound. It is a practical course organized around the core concepts of sustainability.
Basic probability theory, including independence and conditioning, discrete and continuous random variable, law of large numbers, central limit theorem, and stochastic simulation, basic statistics, including point and interval estimation, hypothesis testing, and regression; examples from business applications such as inventory management, medical treatments, and finance. A specialized version of IEOR E4150 for MSE and MSBA students.
Students of sustainable development are faced with an array of global challenges that warrant scholarly inquiry. Social science questions are particularly well suited for qualitative research. This course will provide an overview of social science research methods, with a focus on building a toolkit for undergraduate students. We begin with an overview of the science of knowing. How do we generate scientific hypotheses in the social sciences, and then how can we find out whether those hypotheses are accurate? An exploration of a range of qualitative research methods will occupy the majority of our class time, including interviewing, case studies, questionnaires, surveys, coding, and participant observation. Toward the end of the course we consider how mixed methods allow for the integration of quantitative tools in the social sciences. Throughout, students will both study and practice these research methods, experimenting to better understand the strengths and challenges associated with each approach. The course will end with poster presentations in which students share their own research and justify the methods they have employed.
This undergraduate-level introductory course provides an overview of the science of nutrition and nutrition's relationship to health promotion and disease prevention. The primary focus is on the essential macronutrients and micronutrients, including their chemical structures, food sources, digestion and absorption, metabolism, storage, and excretion. Students develop the skills to evaluate dietary patterns and to estimate caloric requirements and nutrient needs using tools such as Dietary Guidelines for Americans, My Plate, Nutrition Facts Labels, and Dietary Reference Intakes.
Prerequisites: at least two terms of Greek at the 3000-level or higher. Readings in Greek literature from Homer to the 4th century B.C.
Prerequisites: KORN W4006 or the equivalent. Selections from advanced modern Korean writings in social sciences, literature, culture, history, journalistic texts, and intensive conversation exercises.
Prerequisites: at least two terms of Latin at the 3000-level or higher. Latin literature from the beginning to early Augustan times.
This undergraduate-level introductory course is the first of a two-course-series on human anatomy and physiology. Using a body systems approach, we will study the anatomical structure and physiological function of the human body. Foundational concepts from chemistry, cell biology, and histology are reviewed and built upon through the progression of topics. Each of the body systems will be studied for their structure, function, and mechanisms of regulation. The core concepts of levels of organization, interdependence of systems, and homeostasis will be emphasized throughout the course. This beginner level course will lay the foundation for further advanced study of physiology and pathophysiology within a nursing curriculum.
In their research, scholars of religion employ a variety of methods to analyze texts ranging from historical documents to objects of visual culture. This course acquaints students with both the methods and the materials utilized in the field of religious studies. Through guided exercises, they acquire research skills for utilizing sources and become familiarized with dominant modes of scholarly discourse. The class is organized around a series of research scavenger hunts that are due at the start of each week's class and assigned during the discussion section (to be scheduled on the first day of class). Additional class meeting on Thursdays.
Crystal structure and energy band theory of solids. Carrier concentration and transport in semiconductors. P-n junction and junction transistors. Semiconductor surface and MOS transistors. Optical effects and optoelectronic devices. Fabrication of devices and the effect of process variation and distribution statistics on device and circuit performance. Course shares lectures with ELEN E3106, but the work requirements differ. Undergraduate students are not eligible to register.
Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov chains, renewal reward processes. Applications: queueing, reliability, inventory, and finance.
This undergraduate-level introductory course is the second of a two-course series on human anatomy and physiology. Using a body systems approach, we will study the anatomical structure and physiological function of the human body. Foundational concepts from chemistry, cell biology, and histology are reviewed and built upon through the progression of topics. Each of the body systems will be studied for their structure, function, and mechanisms of regulation. The core concepts of levels of organization, interdependence of systems, and homeostasis will be emphasized throughout the course. This beginner level course will lay the foundation for further advanced study of physiology and pathophysiology within a nursing curriculum.
Supply chain management, model design of a supply chain network, inventories, stock systems, commonly used inventory models, supply contracts, value of information and information sharing, risk pooling, design for postponement, managing product variety, information technology and supply chain management; international and environmental issues. Note: replaced IEOR E4000 beginning in fall 2018.
Fundamental concepts of probability and statistics applied to biology and medicine. Probability distributions, hypothesis testing and inference, summarizing data and testing for trends. Signal detection theory and the receiver operator characteristic. Lectures accompanied by data analysis assignments using MATLAB as well as discussion of case studies in biomedicine.
Continuum frame-work for modeling non-equilibrium phenomena in fluids with clear connections to the molecular/microscopic mechanisms for conductive transport. Continuum balances of mass and momentum; continuum-level development of conductive momentum flux (stress tensor) for simple fluids; applications of continuum framework for simple fluids (lubrication flows, creeping flows). Microscopic developments of the stress for simple and/or complex fluids; kinetic theory and/or liquid state models for transport coefficients in simple fluids; Langevin/Fokker- Plank/Smoluchowski framework for the stress in complex fluids; stress in active matter; applications for complex fluids.
This online undergraduate-level introductory course focuses on the core concepts and principles of microbiology. We will explore how microorganisms co-exist and interact with humans creating both beneficial and pathological results. We will survey the diversity of microorganisms, their classification, and the essential processes needed for survival; which will dictate the environments in which they can thrive. This exploration of microorganism diversity will include topics such as microbial nutrition and metabolism, genetics, and antimicrobial mechanisms employed by and against microorganisms. Special attention will be given to understanding the human immune system, mechanisms of infection by pathogenic microorganisms, and the role non-harmful microbiota serve in supporting immune function. The weekly lab component of this course will support and complement each learning module and familiarize students with basic microbiologic lab techniques.
This course will compare and contrast the theories of the political, the state,freedom, democracy, sovereignty and law, in the works of the following key 20th and 21st century continental theorists: Arendt, Castoriadis, Foucault, Habermas, Kelsen, Lefort, Schmitt, and Weber. It will be taught in seminar format.
Introduction to basic probability; hazard function; reliability function; stochastic models of natural and technological hazards; extreme value distributions; Monte Carlo simulation techniques; fundamentals of integrated risk assessment and risk management; topics in risk-based insurance; case studies involving civil infrastructure systems, environmental systems, mechanical and aerospace systems, construction management. Not open to undergraduate students.
Introduction to basic probability; hazard function; reliability function; stochastic models of natural and technological hazards; extreme value distributions; Monte Carlo simulation techniques; fundamentals of integrated risk assessment and risk management; topics in risk-based insurance; case studies involving civil infrastructure systems, environmental systems, mechanical and aerospace systems, construction management. Not open to undergraduate students.
The fundamentals of database design and application development using databases: entity-relationship modeling, logical design of relational databases, relational data definition and manipulation languages, SQL, XML, query processing, physical database tuning, transaction processing, security. Programming projects are required.
Aims to develop and harness the modeling, analytical, and managerial skills of engineering students and apply them to improve the operations of both service and manufacturing firms. Structured as a hands-on laboratory in which students "learn by doing" on real-world consulting projects (October to May). The student teams focus on identifying, modeling, and testing (and sometimes implementing) operational improvements and innovations with high potential to enhance the profitability and/or achieve sustainable competitive advantage for their sponsor companies. The course is targeted toward students planning careers in technical consulting (including operations consulting) and management consulting, or pursuing positions as business analysts in operations, logistics, supply chain and revenue management functions, positions in general management, and future entrepreneurs.
This introductory course covers human development across the lifespan. The course will provide an overview of development and the complexity of human growth through physical, cognitive, emotional, and social capacities. A review of historical and modern-day developmental theories as well as more complex interpersonal constructs, such as cultural variations, will be discussed. Special emphasis is placed upon examining the dynamic interplay between biology and environment with relevant application to nursing practice. The role of social and cultural stressors such as racism and socioeconomics in shaping human development will be examined. This undergraduate-level course will lay the foundation for further advanced study of human development within a nursing curriculum.
Advanced Business Chinese is designed to help students who have studied at least three years of Chinese (or the equivalent) to achieve greater proficiency in the oral and written use of the language and gain knowledge in depth about China’s business environment and proven strategies. Student will critically examine the successes and failures of firms within the Chinese business arena.
In this introductory undergraduate course students will learn how vital the study of Biostatistics is to ensure that clinical and public health practices are supported by reliable evidence. Students will gain an appreciation for the hazards of applying human intuition to probability and statistical questions. This course is designed to explore the collection, analysis, and presentation/visualization of biologic and health data using statistical methods. Students will learn and apply fundamental concepts and techniques of descriptive statistics. Students will also learn basic fundamental concepts of inferential statistics.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119) Design and implementation of large-scale distributed and cloud systems. Teaches abstractions, design and implementation techniques that enable the building of fast, scalable, fault-tolerant distributed systems. Topics include distributed communication models (e.g. sockets, remote procedure calls, distributed shared memory), distributed synchronization (clock synchronization, logical clocks, distributed mutex), distributed file systems, replication, consistency models, fault tolerance, distributed transactions, agreement and commitment, Paxos-based consensus, MapReduce infrastructures, scalable distributed databases. Combines concepts and algorithms with descriptions of real-world implementations at Google, Facebook, Yahoo, Microsoft, LinkedIn, etc.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119) Design and implementation of large-scale distributed and cloud systems. Teaches abstractions, design and implementation techniques that enable the building of fast, scalable, fault-tolerant distributed systems. Topics include distributed communication models (e.g. sockets, remote procedure calls, distributed shared memory), distributed synchronization (clock synchronization, logical clocks, distributed mutex), distributed file systems, replication, consistency models, fault tolerance, distributed transactions, agreement and commitment, Paxos-based consensus, MapReduce infrastructures, scalable distributed databases. Combines concepts and algorithms with descriptions of real-world implementations at Google, Facebook, Yahoo, Microsoft, LinkedIn, etc.