Before registering, the student must submit an outline of the proposed work for approval by the supervisor and the chair of the Department. Advanced study in a specialized field under the supervision of a member of the department staff. May be repeated for credit.
Prerequisites: the instructors permission. Individual research and tutorial in archaeology for advanced graduate students.
Guided reading and research on a topic or in a field chosen by the student in consultation with a member of the faculty. Required for Ph.D candidates, ideally during the semester when they prepare the dissertation proposal (prospectus) under the supervision of a potential sponsor.
Prerequisites: the instructors permission. Individual research in all divisions of anthropology and in allied fields for advanced graduate students
An internship arranged through the Museum Anthropology program of 10 hrs/week (for 3 credits) or 20 hrs/week (for 6). Involves meaningful work, requires keeping a journal and writing a paper at the completion of the semester. Not to be taken without permission of the program directors, usually after completing the Museum Anthropology core courses.
This course provides a general introduction to mathematical statistics and statistical decision theory for doctoral students in biostatistics. It covers elementary decision theory, Bayes rules, Neyman-Pearson theory, uniformly most power tests, similar tests, uniformly most powerful unbiased tests, confidence sets; basic asymptotic criteria, estimation methods and their asymptotic properties, M-estimators, U-statistics, statistical functionals; likelihood ratio tests, Wald tests, Rao's score tests, and their asymptotic properties, Pitman efficiency. This course will prepare students to their theory qualifying exam.
This course covers basic concepts and methods in applied probability and stochastic modeling. The intended audience is master's and doctoral students in programs such as EE, CS, IEOR, Statistics, Mathematics, and those in the DRO division in the Business School. In terms of prerequisites, basic familiarity with probability theory and stochastic processes will be assumed (an ideal preliminary course is IEOR 6711: Stochastic Modeling I, but a more basic substitute will do as well). The topics and material covered in this course complement those covered in IEOR 6712: Stochastic Modeling II, hence the two courses can be taken simultaneously. The exposition will be (mostly) rigorous, yet intentionally skirting some measure-theoretic details; for those interested in such details they can be found in measure theoretic textbooks and other courses (e.g., Probability Theory I/II given in the statistics/math department).
This course offers an advanced introduction Markov Decision Processes (MDPs)-a formalization of the problem of optimal sequential decision making under uncertainty-and Reinforcement Learning (RL)-a paradigm for learning from data to make near optimal sequential decisions. The first part of the course will cover foundational material on MDPs. We'll then look at the problem of estimating long run value from data, including popular RL algorithms like temporal difference learning and Q-learning. The final part of the course looks at the design and analysis of efficient exploration algorithms, i.e. those that intelligently probe the environment to collect data that improves decision quality. This a doctoral level course. Students should have experience with mathematical proofs, coding for numerical computation, and the basics of statistics, optimization, and stochastic processes.
FILM AF 9120 TV Revision
The goal of TV Revision is to bring in a completed pilot and then completely revise it in one semester. Students will initially present their full scripts for feedback in class discussion, then map a plan for rewriting with their instructor. Deadlines throughout the semester will focus on delivery of revised pages.
The work can range from an intensive page 1 rewrite to focus on selected areas in a script. Reading of all scripts in the workshop and participation in class discussion is required.
There is an application process to select students for the class.
The purpose of the course is to broadly cover topics in Operations Management and Operations Research, as well as areas of interest to the Decision, Risk, and Operations division at CBS. It will consist of 3-hour sessions, each on a different topic, with the intent to introduce you to the topic, pique your interest, expose you to the methodologies and research areas people are working on, and help you think about what types of courses to take in the future in order to prepare yourself for this course. We will ask students to submit a one-page summary of each session or a particular paper discussed in the session. PhD students are invited to take the course and/or select certain sessions to attend. Spring 2022 Faculty instructors (each teaching one session) will be Mark Broadie, Paul Glasserman, Fanyin Zheng, Jing Dong, Will Ma, Hongyao Ma.
May be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year.
Statistical physics studies the macroscopic phenomena that emerge when a large number of simple units (like atoms or molecules) come together. Deep understanding developed in such study, especially the study of so-called
“spin glasses”
by Parisi, Mezard and others, has been leveraged to great effect in diverse areas including image processing, machine learning, computer science, and theoretical biology. This research-oriented PhD class will begin with the fundamentals of spin glasses. We will then proceed to the cavity method and message passing algorithms, including exciting recent developments in obtaining (1-\epsilon)-approximation algorithms for a range of problems satisfying “full replica symmetry breaking”. Lastly, we will cover some recent work by Peski on matching markets which has a distinct statistical physics flavor, with agents replacing atoms/molecules. More broadly, we will ask if statistical physics can tell us something about market equilibria, and perhaps about how to design better markets.
The detailed syllabus is available at:
https://docs.google.com/document/d/1zuxJglbabDMOTTVoF3gfo1GgwaU9zaLAuT6s_plv_w4/edit?usp=sharing
This course serves as the cumulative experience for those in the Clinical Research Methods (CRM) Track in the Department of Biostatistics. By the end of the semester, students are expected to produce a submission ready manuscript to a journal appropriate to their field of study.
The Statistical Practices and Research for Interdisciplinary Sciences (SPRIS, P9185) is a required course for the PhD and DrPH students in the Department of Biostatistics. The goal is to prepare doctoral students to be effective statisticians to collaborate in an interdisciplinary team and to identify novel statistical research problems with important public health and medical applications. The course aims to provide guidelines and insights of the arts and sciences of consulting, collaboration, and translation of statistical methods to medical studies. Practically useful technical skills acquired from previous coursework will be enhanced and illustrated through applications to real world problems in class projects. Important statistical issues currently undergoing extensive debate will be introduced. Examples of conducting original statistical research to develop new methods addressing real world challenges will be discussed. Career-development related topics will be covered to prepare students to become effective independent and interdisciplinary researchers. Class projects will showcase examples of how to analyze real world data.
This is a Pass/Fail zero credit course, “BME Master's Thesis” for MS students who are in the process of doing a thesis (BMEN E9100). It would be registered for before/during the final semester, the semester when the student will be defending the thesis. It must be approved by the faculty mentor.
This course is restricted to PhD in Sustainable Development
Departmental colloquium in statistics.
SEMINARS IN BLS II – SPRING 2027 SEMESTER
(Formerly CMBS G9202 “Seminars in CMBS II”)
The overall goals of this full-year course are to: Learn about (1) biomedical life sciences, broadly defined; (2) research at Columbia/VP&S; (3) scientists as individuals; (4) how to give a research presentation to an educated – but non-expert – audience; (5) how to give and receive useful feedback.
This capstone workshop serves as the culminating experience for students in the MPA in Environmental Science and Policy. Working in teams, students conduct applied policy analysis on real-world environmental and sustainability challenges for public and nonprofit sector clients. Project topics are selected to reflect current global and domestic policy needs, with recent clients including The Nature Conservancy, the World Bank, the Wildlife Conservation Society, and philanthropic initiatives supporting sustainable workforce housing.
Under faculty supervision, students develop project control plans, conduct fieldwork and stakeholder interviews, analyze data, and prepare professional-quality final reports and briefings for clients. The workshop emphasizes practical experience with multidisciplinary policy design and implementation, stakeholder engagement, and collaborative project management. Students sharpen their research, writing, and communication skills while contributing to actionable policy solutions.
This course has two primary objectives: first, to provide a structured way to think about—and conduct research in—the field of sustainable development. Second, to introduce formal models of dynamic, coupled human and environmental systems.
This course aims to introduce you to the basic concepts of environmental economics.
All graduate students are required to attend the departmental colloquium as long as they are in residence. Advanced doctoral students may be excused after three years of residence. No degree credit is granted.
Critical Thinking and Analysis in Environmental Health Sciences is a culminating experience for EHS students in which they will synthesize the knowledge and experiences they have gained in their MPH core, department specialization and certificate coursework. The primary objective of this course is to enable students to critically examine and analyze a body of scientific knowledge and to effectively communicate such knowledge to lay and scientific audiences. An interactive, highly participatory experience, it typically focuses, in depth, on one or two topics within the field of Environmental Health Science that are of current national and international interest and represent a major human public health concern. The Capstone course will reinforce fundamental concepts acquired through prior departmental and certificate based coursework related to the underlying scientific basis of human health concerns arising from environmental exposure. The pedagogical approach of this course will utilize a combination of outside reading, didactic instruction, engaging class discussion and team-based learning. Students will be required to critically evaluate current knowledge and present, both orally and in writing, the broad outlines and specific aims of a research proposal to address critical gaps in understanding. At the completion of this course, students are expected to be able to critically evaluate and assess scientific evidence as well as successfully conceptualize, create and defend a research proposal. The ability to communicate research concepts and clear, cogent and well thought out research proposals, either orally and written, are essential for many students preparing entry into the workforce, whether in government service, profit or non-profit corporations, academia, scientific research, policy and planning, administration or regulatory affairs. Graduating EHS MPH students are expected to have considerable facility in public speaking skills, interpretation of scientific literature, critical thinking and analysis of published research findings. Each semester, in consultation with the class, a relevant and timely topic is selected to examine in depth. Creation of a NIEHS-style grant application concerning a previously unaddressed topic is an important component of this class.
Departmental colloquium in probability theory.
A colloquiim in applied probability and risk.
A colloquium on topics in mathematical finance
Graduate research directed toward solution of a problem in mineral processing or chemical metallurgy