Prerequisites:
STAT W4105
or the equivalent.
Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
Prerequisites:
STAT W4105
and
STAT W4107
or the equivalent.
Available to SSP, SMP Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.
Prerequisites:
STAT G6501
or the equivalent.
Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
What motivates governments to protect citizens from economic hardships by implementing social welfare programs instead of relying on private market solutions? What explains the quantitative and qualitative variation in social protection schemes across countries with similar income levels? This course explores these issues by examining the politics, economics, and history behind the creation and maintenance of social welfare systems in advanced industrialized countries. It introduces students to key concepts and recent research in the field of social policy. Through the case method, small group exercises, and panel presentations, this course provides a forum for students to engage, debate, and write about contemporary trends such as aging, fiscal austerity, housing crisis, and technological and social innovation. This course also offers various tools—the fundamentals of knowledge transfer, contingency planning, relaxation strategies, and body language—to assist you in improving and diversifying your oral presentation skills.
This course is dedicated to Ukraine’s Revolution of Dignity, or Euromaidan—the attempt to develop independent governance with civic values. The course traces the historical and cultural foundations of Maidan, examines its tradition from multiple and competing perspectives, and considers the impact of Russian imperial and neo-imperial practices in Ukraine and beyond.
This is a Public Health Course. Public Health classes are offered on the Health Services Campus at 168th Street.For more detailed course information, please go to Mailman School of Public Health Courses website at http://www.mailman.hs.columbia.edu/academics/courses
This term the course will focus on the responses of Israeli poetry, since the 1940s, to the Holocaust, dwelling on issues of ideological attitudes and the complex poetic concerns emanating from the need to write on the unspeakable or "the negative sublime." Poems by U.Z.Greenberg, Nathan Alterman, Abba Kovner, Dan Pagis, and others will be analyzed.
This course will look at the development of a modern market economic system in Russia from perestroika through the collapse of the USSR, the creation of the Russian Federation, the privatization process and the Putin era. The focus will be on the creation of new commercial and business practices and the restructuring of the legal system. We will look closely at the key players in these processes and analyze successes and failures. Guest speakers who were themselves involved in this history will add on-the-ground insights into our examination of the changes.
In the last 18 months, it became ever clearer that the assumption that in and around Europe values, institutions and habits are converging toward some general denominator was a fallacy. The clearest problem case is Russia. In the official discourses, and in personal encounters, one gets the clear message that 'Western' values are not only not shared, but actually addressed often in an explicit and contemptuous way. Democracy, individuality and pluralism are despised, and replaced by more collective orientations, based on certain interpretations of history, and on sobornost'. This seminar aims at the question of when it should turn out that values' distinctions and institutional settings between East and West are significant, what options are available to co-exist or even cooperate in a joint framework?
The Ongoing Tale of Russia - EU energy relations: Will the “Energy Marriage” Between Russia and the EU Endure the Latest Political Storm? The EU’s recent move toward a unified energy policy has made Russia anxious. On April 13, 2015, Alexey Miller, the CEO of Gazprom, admitted that the business model Gazprom has been following in Europe for many years is falling apart. So, what is Russia going to do? Gazprom executives are claiming that the company has come up with a new business model toward its European partners. What is this new model? And what is Russia's new energy strategy? The course will explore these questions.
This Human Rights practicum course focuses on the Western Balkans of the Former Yugoslavia in a contemporary context. The course focuses on war crimes and their respective consequences that have occurred during the most recent Balkan Wars 1991-1999 in the Former Yugoslav states and will include a detailed review and examination of human rights policies and practices carried out by international, regional and national bodies, laws, organizations, frameworks of transitional justice and evaluative tools employed in an effort to stabilize a post-war, post-Communist, post-conflict scenario. The course will present and examine in detail policies and practices deployed by international and national state structures to address the legacies of war crimes and the emergence of new human rights issues that are currently present in the Former Yugoslav space. The course will require students to prepare a 10-page paper on a human rights issue in the region, analyze the issues, review implementation to date and recommend policy initiatives that will address the problem (75 percent of the grade). Students are expected read weekly assignments and regularly participate and attend the class, which will constitute 25 percent of their final grade. Failure to attend class without a justifiable explanation will be penalized by a reduction of one grade letter.
(Seminar). This seminar will examine European and American avant-garde aesthetics through the poetry, poetics, theory, and politics of "movements" like Surrealism, Objectivism, Oulipo, Minimalism, and Conceptualism. Texts include works from C. S. Peirce, Walter Benjamin, Theodor Adorno, Andre Breton, Louis Zukofsky, Ezra Pound, John Ashbery, Robert Smithson, Clark Coolidge, Fredric Jameson, Lyn Hejinian, Susan Howe, Craig Dworkin, Tan Lin, Caroline Bergvall, and others.
Prerequisites: permission of the departmental adviser to Graduate Studies.
Prerequisites: MATH V2030.
A graduate-level introduction to classical and modern feedback control that does not presume an undergraduate background in control. Scalar and matrix differential equation models and solutions in terms of state transition matrices. Transfer functions and transfer function matrices, block diagram manipulations, closed loop response. Proportional, rate, and integral controllers, and compensators. Design by root locus and frequency response. Controllability and observability. Luenberger observers, pole placement, and linear-quadratic cost controllers.
Prerequisites: the instructor's permission.
In this year-long sequence students gain familiarity with the materials used in electroacoustic music and the techniques and equipment that are employed to transform and organize these materials into compositions. Individual projects are assigned.
Prerequisites: the instructor's permission prior to registration.
A survey of selected issues and debates in political theory. Areas of the field discussed include normative political philosophy, history of political thought, and the design of political and social institutions.
(Seminar). This seminar examines the discourse of sexual panic in the period from 1880-1930. It focuses on the role of sexuality in the production of racial identities and the organization and control of urban space. Specifically, it looks at the slum and the ghetto as an intersex zone in which interracial intimacy, same sex relations, and promiscuous sociality thrive. The seminar will look at novels, reform and documentary photographs, sociological studies and early cinema in the making of Chinatown, the immigrant slum, and the black ghetto as zones of vice, anarchy, sexual excess and experimentation.
Prerequisites: SIPA U6501
The goal of this course is to enable students to evaluate the policy relevance of academic research. While academic research frequently considers treatments that approximate a potential public policy, such prima facie relevance alone does not inform policy. In particular, public policy is predicated on the credible estimation of causal treatment effects. For example, although researchers frequently document the strong correlation between years of schooling and better health, this tells us surprisingly little (and arguably nothing) about the health effects of public tuition assistance, compulsory school laws, or any other program that raises educational attainment. Policies guided by statistical correlations - even the regression-adjusted estimates that dominate the academic literature - will frequently have unintended and even perverse real-world effects. Policymakers must distinguish between causal estimates that should inform policy design and statistical correlations that should not. The catch is that distinguishing correlation from causation in empirical studies is surprisingly difficult. Econometric technique alone does not provide a reliable path to causal inference. Applications of instrumental variables (IV) techniques, while wildly popular, arguably obscure sources of identification more often than isolating exogenous variation. Similar concerns apply to popular panel data and fixed effects (FE) models, which can eliminate certain unobservable sources of bias. Furthermore, causal claims by a study's author should be regarded with skepticism - frequently this is merely the marketing of a non-transparent statistical correlation. Put differently, when has a researcher portrayed his empirical result as a mere correlation when in fact he/she had identified a credible causal impact? A basic theme of the course is that identification strategy - the manner in which a researcher uses observational [real-world] data to approximate a controlled/randomized trial (Angrist & Pischke, 2009) - is the bedrock of causal inference. Econometric technique cannot rescue a fundamentally flawed identification strategy. In other words, econometrics and identifications strategies are complements in the production of causal estimates, not substitutes. Examples of appropriate econometric technique applied to compelling identification strategies will be described to illustrate this approach (most often from health economics), along with their implications for public policy.