Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.
This course teaches students how to move from data analysis to model building and prediction. It introduces computational and systems-level approaches for understanding genomes, molecular and cellular networks, evolution, disease genetics, and virtual cells, helping students learn how quantitative models can be used to generate mechanistic insight and testable biological hypotheses.
Intensive study of a philosophical issue or topic, or of a philosopher, group of philosophers, or philosophical school or movement. Open only to Barnard senior philosophy majors.
These two-part mid-career global leadership development courses (1.5 credit course in the summer and spring) provide intensive, collaborative, and highly interactive hands-on instruction, constructive evaluation, and ample opportunities to transform theory into practice. It utilizes cutting-edge, research-based methodologies and customized case studies to build the next generation of leaders that turn differences into opportunities, ideas into solutions, and knowledge into action. Students will acquire a variety of leadership skills in global contexts, including cross-cultural negotiation strategies, consensus building, collaborative facilitation, persuasion, inclusionary leadership, design-thinking-based problem-solving techniques, and public speaking in knowledge-intensive industries. They will gain a competitive edge in their professional careers by participating in a variety of simulation games, role-playing exercises, and mock public policy panels to apply the skills they have learned and receive valuable feedback.
Prerequisites: MATH GU4051 Topology and / or MATH GU4061 Introduction To Modern Analysis I (or equivalents). Recommended (can be taken concurrently): MATH UN2010 linear algebra, or equivalent. The study of algebraic and geometric properties of knots in R^3, including but not limited to knot projections and Reidemeisters theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants.
A substantial paper, developing from an Autumn workshop and continuing into the Spring under the direction of an individual adviser. Open only to Barnard senior philosophy majors.
Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051 The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces.
This seminar examines ways in which Italy is understood and represented by Italians and non-Italians. It will analyze the formation of multiple discourses on Italy, how Italian culture and society are imagined, represented and/or distorted. Based on an anthropological perspective, this course will examine ways in which we can understand Italy through the intersections of pluralism, ethnicity, gender, and religion. The course will study how Italy strives for political and economic unity, while there is a concurrent push toward inequality, exclusion, and marginalization. Moreover, the course will analyze the revitalization of nationalism on one hand of regionalism on the other, and will focus on the concepts of territory, identity, and tradition. Short videos that can be watched on computer and alternative readings for those fluent in Italian will be assigned. There are no pre-requisites for this course.
Enrollment limited to 12 students. Mechatronics is the application of electronics and microcomputers to control mechanical systems. Systems explored include on/off systems, solenoids, stepper motors, DC motors, thermal systems, magnetic levitation. Use of analog and digital electronics and various sensors for control. Programming microcomputers in Assembly and C. Lab required.
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.
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 course examines Ukrainian cinema from Yosyp Tymchenko’s invention of the cinematograph in the 1890s to the present as both a transforming mirror and a maker of modern Ukrainian identity. It explores how film shapes collective self-representation, memory, and political imagination, and how Ukrainian filmmakers have negotiated questions of language, history, ethnicity, religion, and political belonging in a society shaped by prolonged colonial domination. The course examines cinema as both an instrument of imperial power and a medium of self-expression and resistance, focusing on the ways Ukrainian filmmakers have reproduced, negotiated, challenged, and sought to overcome inherited colonial legacies. An interdisciplinary course, it draws on history, literary studies, linguistics, theater and art history, and theories of national cinema, colonialism, and postcolonialism to examine the complex interactions among film, language, literature, politics, and historical memory. A comparative dimension situates Ukrainian cinema alongside other national cinemas shaped by imperial and colonial domination.
There are no prerequisites and the course assumes no prior knowledge of Ukrainian language, history, and culture.
Building the functional map of the fruit fly brain. Molecular transduction and spatio-temporal encoding in the early visual system. Predictive coding in the Drosophila retina. Canonical circuits in motion detection. Canonical navigation circuits in the central complex. Molecular transduction and combinatorial encoding in the early olfactory system. Predictive coding in the antennal lobe. The functional role of the mushroom body and the lateral horn. Canonical circuits for associative learning and innate memory. Projects in Python.
Leaders often invoke the lessons of history, but rarely talk about anything more than a few familiar episodes. Even if we can all agree that we should avoid another economic depression, and try not to get dragged into another war in Vietnam, do these analogies actually help us make decisions about the future? In this course, students will explore both the problems and the opportunities presented by using historical analysis to grapple with present and future challenges. They will develop a deeper understanding of the most often cited historical episodes, but also learn how to avoid using analogies in the place of more original thinking. That means developing all the critical tools and concepts of historical analysis, such as an attentiveness to continuity and change, contingency and inevitability, human agency and structural constraints. Students will also learn how NOT to think like a historian, such as using history like a weapon, and assuming present trends will continue indefinitely into the future. Knowing history, we will not be condemned to repeat it. Instead, we can make new and more original mistakes.
Prerequisites: one year each of biology and physics, or the instructor's permission. This is a combined lecture/seminar course designed for graduate students and advanced undergraduates. The course will cover a series of cases where biological systems take advantage of physical phenomena in counter intuitive and surprising ways to accomplish their functions. In each of these cases, we will discuss different physical mechanisms at work. We will limit our discussions to simple, qualitative arguments. We will also discuss experimental methods enabling the study of these biological systems. Overall, the course will expose students to a wide range of physical concepts involved in biological processes.
Please refer to Institute for African American and African Diaspora Studies Department for section-by-section course descriptions.
RNA has recently taken center stage with the discovery that RNA molecules sculpt the landscape and information contained within our genomes. Furthermore, some ancient RNA molecules combine the roles of both genotype and phenotype into a single molecule. These multi-tasking RNAs offering a possible solution to the paradox of which came first: DNA or proteins. This seminar explores the link between modern RNA, metabolism, and insights into a prebiotic RNA world that existed some 3.8 billion years ago. Topics include the origin of life, replication, and the origin of the genetic code; conventional, new, and bizarre forms of RNA processing; structure, function and evolution of key RNA molecules, including the ribosome, and RNA therapeutics including vaccines. The format will be weekly seminar discussions with presentations. Readings will be taken from the primary literature, emphasizing seminal and recent literature. Requirements will be student presentations, class participation, and a final paper.
Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010 Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sards theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stokes theorem.
An introduction to how the Earth and planets work. The focus is on physical processes that control plate tectonics and the evolution of planetary interiors and surfaces; analytical descriptions of these processes; weekly physical model demonstrations.
Basic concepts of seismology. Earthquake characteristics, magnitude, response spectrum, dynamic response of structures to ground motion. Base isolation and earthquake-resistant design. Wind loads and aeroelastic instabilities. Extreme winds. Wind effects on structures and gust factors.
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.
An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications.
Prerequisites: Organic chemistry and biology courses, neuroscience or neurobiology recommended, but not required. The study of the brain is one of the most exciting frontiers in science and medicine today. Although neuroscience is by nature a multi-disciplinary effort, chemistry has played many critical roles in the development of modern neuroscience, neuropharmacology, and brain imaging. Chemistry, and the chemical probes it generates, such as molecular modulators, therapeutics, imaging agents, sensors, or actuators, will continue to impact neuroscience on both preclinical and clinical levels. In this course, two major themes will be discussed. In the first one, titled Imaging brain function with chemical tools, we will discuss molecular designs and functional parameters of widely used fluorescent sensors in neuroscience (calcium, voltage, and neurotransmitter sensors), their impact on neuroscience, pros and cons of genetically encoded sensors versus chemical probes, and translatability of these approaches to the human brain. In the second major theme, titled Perturbation of the brain function with chemical tools, we will examine psychoactive substances, the basics of medicinal chemistry, brain receptor activation mechanisms and coupled signaling pathways, and their effects on circuit and brain function. We will also discuss recent approaches, failures and successes in the treatment of neurodegenerative and psychiatric disorders. Recent advances in precise brain function perturbation by light (optogenetics and photopharmacology) will also be introduced. In the context of both themes we will discuss the current and future possibilities for the design of novel materials, drawing on the wide molecular structural space (small molecules, proteins, polymers, nanomaterials), aimed at monitoring, modulating, and repairing human brain function. This course is intended for students (undergraduate and graduate) from the science, engineering and medical departments.
Introduction to stochastic processes and models, with emphasis on applications to engineering and management; random walks, gambler’s ruin problem, Markov chains in both discrete and continuous time, Poisson processes, renewal processes, stopping times, Wald’s equation, binomial lattice model for pricing risky assets, simple option pricing; simulation of simple stochastic processes, Brownian motion, and geometric Brownian motion. A specialized version of IEOR E4106 for MSE students.
A course on synthesis and processing of engineering materials. Established and novel methods to produce all types of materials (including metals, semiconductors, ceramics, polymers, and composites). Fundamental and applied topics relevant to optimizing the microstructure of the materials with desired properties. Synthesis and processing of bulk, thin-film, and nano materials for various mechanical and electronic applications.
This course builds on an introductory course in statistics and dives deeper into linear regression models, including generalized linear models, mixed/hierarchical models, model diagnostics, and model selection. It focuses on the practical applications of these methods rather than the mathematical complexities. A prior course or equivalent knowledge of fundamental concepts in statistics as well as familiarity with R programming are required pre-requisites for this course.
Prerequisites: at least two terms of Greek at the 3000-level or higher. Greek literature of the 4th century B.C. and of the Hellenistic and Imperial Ages.
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.
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 Augustus to 600 C.E.
This course develops students’ proficiency in formal and professional communication in Korean for business contexts. It deepens their understanding of Korean corporate culture, business practices, and broader socio-economic trends, while fostering the ability to analyze and respond critically to business-related issues using appropriate linguistic and cultural strategies.
Prerequisites: KORN UN3006 or the equivalent.
Prerequisites: LING UN3101 Language, like all components of culture, is structured and conventional, yet can nevertheless change over time. This course examines how language changes, firstly as a self-contained system that changes organically and autonomously, and secondly as contextualized habits that change in time, in space, and in communities. Workload: readings & discussion, weekly problems, and final examination.
Against the backdrop of the heated critical debate on the boundaries and limitations of the autobiographical genre, this course addresses the modern and contemporary tradition of autobiographical writings, focusing in particular (but not exclusively) on exploring and positing the potential difference between male and female autobiographers. More specifically, we will question the adequacy of the traditional model of autobiographical selfhood based on the assumption of unified, universal, exemplary and transcendent self to arrive at an understanding of women's autobiography. Topics to be addressed include: the crisis of the subject, je est un autre, the man with a movie camera, strategies of concealment and disclosures. Authors to be studied include: D'Annunzio, Pirandello, Svevo, Fellini, Moretti, Ortese, Ginzburg, Manzini, Cialente, Ramondino. In Italian
Ray optics, matrix formulation, wave effects, interference, Gaussian beams, Fourier optics, diffraction, image formation, electromagnetic theory of light, polarization and crystal optics, coherence, guided wave and fiber optics, optical elements, photons, selected topics in nonlinear optics.
This course will focus on one advanced topic in feminist philosophy. Potential topics include embodiment, gender, sexuality, oppression, intersectionality, and care ethics.
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.
Philology, broadly defined as the practice of making sense of texts, is a fundamental human activity that has been repeatedly institutionalized in widely separated places and times. In the wake of the formation of the modern academic disciplines in the nineteenth century and their global spread, it became difficult to understand the power and glory of older western philology, and its striking parallels with other pre- and early modern forms of scholarship around the globe. This class seeks to create a new comparative framework for understanding how earlier generations made sense of the texts that they valued, and how their practices provide still-vital models for us at a time of upheaval in the format and media of texts and in our scholarly approaches to them. Students will encounter key fields of philology—textual criticism, lexicography, grammar, and, above all, commentary—not in the abstract but as instantiated in relation to four foundational works—the Confucian Analects, the Ramaya?a of Valmiki, the Aeneid, and the Tale of Genji—and the scholarly traditions that grew up around them. We are never alone when we grapple with the basic question of how to read texts whose meaning is unclear to us. Over the course of the semester, this class will foster a global understanding of the deep roots and strange parallels linking contemporary reading and interpretation to the practices of the past.
Develops and applies non-equilibrium thermodynamics for modeling of transport phenomena in fluids and their mixtures. Continuum balances of mass, energy and momentum for pure fluids; non-equilibrium thermodynamic development of Newtons law of viscosity and Fouriers law; applications (conduction dominated energy transport, forced and free convection energy transport in fluids); balance laws for fluid mixtures; non-equilibrium thermodynamic development of Ficks law; applications (diffusion-reaction problems, analogy between energy and mass transport processes, transport in electrolyte solutions, sedimentation).
Advanced Business Chinese II is the continuation of Advanced Business Chinese I, both of which are designed to help Columbia students who have achieved the advanced level of proficiency in Chinese use the language to communicate effectively in professional contexts. Topics to be discussed include, but are not limited to, the concept of Face, Guanxi/Interpersonal obligations, Chinese modesty and humility, and Chinese style of negotiation and decision making.
Stress and deformation formulation in two-and three-dimensional solids; viscoelastic and plastic material in one and two dimensions energy methods.
Advanced senior-level/MS/PhD course covering interaction of laser light with matter in both classical and quantum domains. First half introduces microscopic origin of optical nonlinearities through formal derivation of nonlinear susceptibilities, emphasis on second- and third-order optical processes. Topics include Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference frequency generation, four-wave mixing, and self-phase modulation, including various applications of processes such as frequency conversion, and optical parametric amplifiers and oscillators. Second half describes two-level atomic systems and quantization of electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light discussed and techniques to generate such states outlined.
Elastic stresses at a crack; energy and stress intensity criteria for crack growth; effect of plastic zone at the crack; fracture testing applications. Fatigue characterization by stress-life and strain-life; damage index; crack propagation; fail safe and safe life analysis.
Design and implementation of operating systems. Topics include process management, process synchronization and interprocess communication, memory management, virtual memory, interrupt handling, processor scheduling, device management, I/O, and file systems. Case study of the UNIX operating system. A programming project is required.
Introduction to computer networks and the technical foundations of the Internet, including applications, protocols, local area networks, algorithms for routing and congestion control, security, elementary performance evaluation. Several written and programming assignments required.
Boltzmann’s entropy hypothesis and its restatement to calculate the Helmholtz and Gibbs free energies and the grand potential. Applications to interfaces, liquid crystal displays, polymeric materials, crystalline solids, heat capacity and electrical conductivity of crystalline materials, fuel cell solid electrolytes, rubbers, surfactants, molecular self assembly, ferroelectricity. Computational methods for molecular systems. Monte Carlo (MC) and molecular dynamics (MD) simulation methods. MC method applied to liquid-gas and ferromagnetic phase transitions. Deterministic MD simulations of isolated gases and liquids. Stochastic MD simulation methods.
An introduction to computer architecture and distributed systems with an emphasis on warehouse scale computing systems. Topics will include fundamental tradeoffs in computer systems, hardware and software techniques for exploiting instruction-level parallelism, data-level parallelism and task level parallelism, scheduling, caching, prefetching, network and memory architecture, latency and throughput optimizations, specialization, and an introduction to programming data center computers.
Prerequisites: the instructors permission. Introduction to the ecology and epidemiology of infectious diseases of humans and wildlife.
Introduction to the principles, methods and tools necessary to manage design and construction processes. Elements of planning, estimating, scheduling, bidding and contractual relationships. Valuation of project cash flows. Critical path method. Survey of construction procedures. Cost control and effectiveness. Field supervision.
This course examines the role and function of the modern zoo in the context of the modern conservation movement. Students will learn about the evolution of the zoological park from an entertainment venue to a reservoir of rare or otherwise endangered species of animals, and as a catalyst for conservation of these species.
A new approach to the classical problems of the sociology of knowledge - the social determination of knowledge and the social roles of those who create, possess, and distribute knowledge. This new approach rejects the current boundaries of inquiry and reunifies them as a network of practices straddling the boundaries of science and the professions.