Prerequisites:
MATH V2010
,
MATH W4041
,
MATH W4051
.
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 course presents and examines post-Soviet Ukrainian culture. Students will learn about the significant achievements, names, events, scandals and polemics in contemporary Ukrainian culture and will see how they have contributed to Ukraine’s post-Soviet identity. Centered on the most important successes in literature, the course will also explore the key developments in music and visual art in this period. The course will look at what images have come to represent Ukraine and how they were created. By also studying Ukrainian culture with regards to its relationship with Ukraine’s changing political life, students will obtain a good understanding of the dynamics of today’s Ukraine and the development of Ukrainians as a nation in the 21st century. The course will be complemented by audio and video presentations and, through the Harriman Institute’s on-going Contemporary Ukrainian Literature Series, will offer students the unique opportunity to meet several leading Ukrainian writers in-person. Entirely in English with a parallel reading list for those who read Ukrainian.
This is an interdisciplinary course introducing students to the historical, juridical, and literary constructions of human rights as concept, practice, and discourse. Coursework is geographically and thematically comparative with readings in history, law, political philosophy, anthropology, criticism, and literature. Students are expected to engage with the following questions: How did ideas about rights emerge and give rise to the juridical development of ‘human rights?’ What kinds of human subjects do rights discourses presuppose and/or produce? What does human rights law achieve, and how? And how, if at all, does literature reveal the human rights’ system’s social, ethical, and political possibilities and limits?
Prerequisites: ELEN E1201.
Recommended: ELEN E3000. 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. A lab fee of $75.00 is collected.
Prerequisites:
MATH V1202
or the equivalent, and
MATH V2010
. The second term of this course may not be taken without the first.
Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites:
MATH V1202
or the equivalent, and
MATH V2010
. The second term of this course may not be taken without the first.
Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
The course is designed to teach students the foundations of network analysis including how to manipulate, analyze and visualize network data themselves using statistical software. We will focus on using the statistical program R for most of the work. Topics will include measures of network size, density, and tie strength, measures of network diversity, sampling issues, making ego-nets from whole networks, distance, dyads, homophily, balance and transitivity, structural holes, brokerage, measures of centrality (degree, betweenness, closeness, eigenvector, beta/Bonacich), statistical inference using network data, community detection, affiliation/bipartite networks, clustering and small worlds; positions, roles and equivalence; visualization, simulation, and network evolution over time.
This course is designed to the interdisciplinary and emerging field of data science. It will cover techniques and algorithms for creating effective visualizations based on principles from graphic design, visual art, perceptual psychology, and cognitive science to enhance the understanding of complex data. Students will be required to complete several scripting, data analysis and visualization design assignments as well as a final project. Topics include: data and image models, social and interactive visualizations, principles and designs, perception and attention, mapping and cartography, network visualization. Computational methods are emphasized and students will be expected to program in R, Javascript, D3, HTML and CSS and will be expected to submit and peer review work through Github. Students will be expected to write up the results of the project in the form of a conference paper submission.
The Proseminar fulfills two separate goals within the Free-Standing Masters Program in Sociology. The first is to provide exposure, training, and support specific to the needs of Masters students preparing to move on to further graduate training or the job market. The second goal is to provide a forum for scholars and others working in qualitative reserach, public sociology, and the urban environment.
Prerequisites: Permission of the instructor. Enrollment limited to 15. Preregistration required.
The evolution of scientific thinking from the 12th to the 16th centuries, considering subjects such as cosmology, natural history, quantification, experimentation, the physics of motion, and Renaissance perspective. At every point we link proto-scientific developments to social and technological developments in the society beyond the schools.
An introduction to Bayesian statistical methods with applications to the social sciences. Considerable emphasis will be placed on regression modeling and model checking. The primary software used will be Stan, which students do not need to be familiar with in advance. Student in the course will access the Stan library via R, so some experience with R would be helpful but not required. Any QMSS student is presumed to have sufficient background. Any non-QMSS students interested in taking this course should have a comparable background to a QMSS student in basic probability. Topics to be covered are a review of calculus and probability, Bayesian principles, prediction and model checking, linear regression models, Bayesian data collection, Bayesian calculations, Stan, the BUGS language and JAGS, hierarchical linear models, nonlinear regression models, missing data, stochastic processes, and decision theory.
This two-semester sequence supports students through the process of finding a fieldwork site, beginning the field work required to plan for and develop a Masters thesis, and the completion of their Masters thesis.
This seminar gives you an opportunity to do original sociological research with the support of a faculty member, a teaching assistant, and your fellow classmates.
Prerequisites:
MATH V1202, MATH V3027, STAT W4150, SEIOW4150
, or their equivalents.
The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the BlackûScholes formula, and binomial models.
Prerequisites: QMSS G4070
This course builds upon foundational spatial analysis concepts and skills built in the introductory GIS course through the application of advanced spatial statistical modeling tools. Topics covered include 1) Graphical and quantitative description of spatial data, 2) Kriging, block kriging and cokriging, 3) Common variogram models, 4) Spatial autoregressive models, estimation and testing, 5) Spatial non-stationarity and associated modeling procedures and 6) Spatial sampling procedures. Use of open-source software (Primarily the R software package) with emphasis on analysis of real data from the environmental and social sciences will be the substantive focus of the class. Students will do a series of in-class labs and develop a final research project from these labs or an independent project.
Prerequisites: three MAFN core courses, at least three credits of MAFN-approved electives, and the instructor's permission. See the MAFN website for details.
This course provides an opportunity for MAFN students to engage in unpaid internships for academic credit on a pass / fail basis. Students need to secure an internship and get it approved by the instructor. For unpaid internships only.
This course covers features of the C++ programming language which are essential in quantitative/computational finance and its applications. We start by covering basic C++ programming features and then move to some more advance features. We utilize these features for financial engineering and quantitative finance applications primarily for pricing of financial derivatives and computational finance. Those applications include transform techniques, Monte Carlo simulation, calibration and parameter estimation techniques.
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.
Course covers modern statistical and physical methods of analysis and prediction of financial price data. Methods from statistics, physics and econometrics will be presented with the goal to create and analyze different quantitative investment models.
The course will cover practical issues such as: how to select an investment universe and instruments, derive long term risk/return forecasts, create tactical models, construct and implement an efficient portfolio,to take into account constraints and transaction costs, measure and manage portfolio risk, and analyze the performance of the total portfolio.
Prerequisites: familiarity with Brownian motion, Itôs formula, stochastic differential equations, and Black-Scholes option pricing.
Nonlinear Option Pricing is a major and popular theme of research today in quantitative finance, covering a wide variety of topics such as American option pricing, uncertain volatility, uncertain mortality, different rates for borrowing and lending, calibration of models to market smiles, credit valuation adjustment (CVA), transaction costs, illiquid markets, super-replication under delta and gamma constraints, etc. The objective of this course is twofold: (1) introduce some nonlinear aspects of quantitative finance, and (2) present and compare various numerical methods for solving high-dimensional nonlinear problems arising in option pricing.
Topics in the Black Experience:Reading Black Girls This seminar coincides with Black Girl Movement: A National Conference, which will be held at Columbia University on April 7-April 9, 2015. We will read an interdisciplinary selection of scholarly and creative texts that center the experience of Black girls in the United States. In addition to reading and class discussion, students will help to build a website that serves as a bibliographic resource for future study. Students will also serve as volunteers, hosts and ambassadors for Conference participants. Conference attendance is required. The course will culminate in a final group project that assesses the current state of research and writing on black girls and suggests directions for future scholarship and policy initiatives.
Gospel Music in Modern America This course will track the evolution of religion and music in African American history across the twentieth century to the present day. Beginning with the emergence of the Gospel-Blues during the 1920s, we will explore the ways in cultural aesthetics, religious imaginings and institutional formations have come together to shape the development of black musical forms, sacred and secular alike, across the evolving genres of blues, jazz, r&b, hip hop, neo-soul and more.
Topics in the Black Experience:Race & (Un)making of the America City This seminar examines the role that race and other socially defined differences have played, and continue to play in the economic development, spatial organization and symbolic construction of American cities. We will situate contemporary discussions and debates about urban “gentrification,” associated with deindustrialization and neo-liberal economic policies, within the longue durée of race-based spatial, occupational and symbolic exclusions and consider how these dividing practices have shaped the production of both popular culture and academic knowledge relating to U.S. cities, their problems, and populations. Finally, we will examine how African Americans and other racialized groups have resisted these exclusions, producing alternative and oppositional forms of cultural expression, socioeconomic organization and urban knowledge.
African-American Politics in the Era of Obama and Black Lives Matter This seminar will explore the meaning and significance of African-American politics at a time when the nation has a black president, nearly four dozen members of the Congressional Black Caucus and a burgeoning new black social justice movement. Students will examine the influence and limits of electoral politics and its synergy with grassroots activism in a country where African Americans make up only 13 percent of the population. We'll also analyze the role of black Republicans, black conservatism and respectability politics. Finally, students will develop proposals for sustainable African American political movements that transcend the current occupant of the White House.
How did a small Italian settlement by the Tiber River rise to become the capital of a vast Mediterranean Empire? How did this same city reinvent itself as the spiritual capital of Western Christendom? How were these dramatic changes registered, recorded, remembered, forgotten or erased in the urban fabric? This course ‘reads’ the multilayered city of Rome from its origins through the Middle Ages: Part I: From Village to Empire; Part II: A Christian Capital; Part III: Reform and Renewal in the Middle Ages. Each meeting focuses on select sites or monuments in the city, each paired with a primary text, to consider larger economic, social, cultural, religious, and political changes taking place in Rome and the impact that they had on the urban landscape. Throughout, we will delve into the methodological challenges faced by scholars in understanding these changes. Students will be encouraged to think creatively about the intersections of history and legend and the participation of monuments in their wider urban setting.
Prerequisites:
MATH W4051
or
MATH W4061
and
MATH V2010
.
Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sard's theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stoke's theorem.
Prerequisites: at least one year of coursework in single-variable calculus and not being freaked-out by multivariable calculus. Physics coursework through a calculus-based treatment of classical mechanics and electromagnetism. One year of general chemistry (either AP Chemistry or a college course). One year of college coursework in molecular/cellular biology and biochemistry equivalent to Biology
C2005
-
2006
at Columbia.
Rigorous introduction to the theory underlying biophysical methods, which are illustrated by practical applications to biomedical research. Emphasizes the approach used by physical chemists to understand and analyze the behavior of molecules, while also preparing students to apply these methods in their own research. Course modules cover: (i) statistical analysis of data; (ii) solution thermodynamics; (iii) hydrodynamic methods; (iv) light-scattering methods; and (v) spectroscopic methods, especially fluorescence. Recitations focus on curve-fitting analyses of experimental data.
A survey of the relationships between people and plants in a variety of cultural settings. Sustainability of resource use, human nutrition, intellectual property rights, and field methodologies are investigated.
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.
Prerequisites: ENME E3106 or the equivalent.
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.
Decision analytic framework for operating, managing, and planning water systems, considering changing climate, values and needs. Public and private sector models explored through US-international case studies on topics ranging from integrated watershed management to the analysis of specific projects for flood mitigation, water and wastewater treatment, or distribution system evaluation and improvement.
Prerequisites: MECE E3100 or equivalent.
Fluid dynamics and analyses for mechanical engineering and aerospace applications: boundary layers and lubrication, stability and turbulence, and compressible flow. Turbomachinery as well as additional selected topics.
This course is offered through the School of Professional Studies.
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.
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.
Prerequisites: Must be registered in the Management Science and Engineering (MSE) MS Program
The first two weeks will be a brief review of probability theory with emphasis on probability distributions that are of significant importance in the management and business end of operations research. Poisson distribution, Normal distribution, lognormal distribution, gamma distribution, beta distribution, Student's-T distribution; heavy-tailed versus light-tailed distributions. The next several weeks will be a mix of learning how to simulate from the above distributions, as well as learning the basics of Markov chains in both discrete and continuous time (which includes an introduction to the Poisson process). The binomial lattice model and random walks (including the gambler's ruin problem) will be used as examples with applications in option pricing, risk and portfolio management and inventory. Stopping times will be introduced as well. The last several weeks will cover an introduction to Brownian motion, and geometric Brownian motion, how it can be simulated at a finite number of time points, and how it can be used to model risky assets, and other important processes in risk and portfolio management and inventory theory.
Prerequisites: two years of college Polish or the instructor's permission.
Extensive readings from 19th- and 20th-century texts in the original. Both fiction and nonfiction, with emphasis depending on the interests and needs of individual students.
This seminar explores space race, architecture and cinematography of the Cold War in a bi-polarized world with special emphasis on cultural memories, curatorial practices, and object-based learning. Being extracted from literature and journalism, tested on the territory of mass media and popular culture, Cold War phenomenon operates with the illusional nature of canonic cultural codes, empowering visional metaphors with the military instrumental and vocabulary of forms. Operating with the concept of synthetic, anti-biological and quasi-transparent Nylon Curtain versus the solidity of the iron barrio might allow us to look at the Cold War phenomenon even more critically and to contextualize it within the broader fabric of contemporary arts and its transcultural agenda.
Prerequisites:
MATH V1101
and
V1102
or the equivalent.
A calculus-based introduction to probability theory. Topics covered include random variables, conditional probability, expectation, independence, Bayes' rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov's inequality.
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.
Prerequisites: Probability and Statistics at the level of SIEO W3600 or SIEO W4150 or instructor permission.
This graduate course is only for MS&E, IE and OR students. This is also required for students in the Undergraduate Advanced Track. This course introduces students to operations research and stochastic processes. Operations research is concerned with quantitative decision problems, generally involving the allocation and control of limited resources, often in the presence of significant uncertainty. Stochastic processes are collections of random variables, usually indexed by time. [In stochastic process models, time can be regarded as either discrete or continuous.] For example, we might use stochastic processes to model the evolution of a stock price over time, the damage claims received by an insurance company over time, the work-in-process inventory in a factory over time or the number of calls waiting in a telephone call center over time, all of which evolve with considerable uncertainty. Among the stochastic processes to be considered are discrete-time Markov chains, random walks, continuous-time Markov chains, Poisson processes, birth-and-death processes, renewal processes, renewal-reward processes, Brownian motion and geometric Brownian motion. Among the engineering applications to be considered are queuing, inventory and finance.
Prerequisites: Probability and Statistics at the level of SIEO W3600 or SIEO W4150 or instructor permission.
This graduate course is only for MS&E, IE and OR students. This is also required for students in the Undergraduate Advanced Track. This course introduces students to operations research and stochastic processes. Operations research is concerned with quantitative decision problems, generally involving the allocation and control of limited resources, often in the presence of significant uncertainty. Stochastic processes are collections of random variables, usually indexed by time. [In stochastic process models, time can be regarded as either discrete or continuous.] For example, we might use stochastic processes to model the evolution of a stock price over time, the damage claims received by an insurance company over time, the work-in-process inventory in a factory over time or the number of calls waiting in a telephone call center over time, all of which evolve with considerable uncertainty. Among the stochastic processes to be considered are discrete-time Markov chains, random walks, continuous-time Markov chains, Poisson processes, birth-and-death processes, renewal processes, renewal-reward processes, Brownian motion and geometric Brownian motion. Among the engineering applications to be considered are queuing, inventory and finance.