The course is designed for entering doctoral students and provides a rigorous introduction to the fundamental theory of optimization. It examines optimization theory in continuous, deterministic settings, including optimization in Euclidean as well as in more general, infinite-dimensional vector spaces. The course emphasizes unifying themes (such as optimality conditions, Lagrange multipliers, convexity, duality) that are common to all of these areas of mathematical optimization. Applications across a range of problem areas serve to illustrate and motivate the theory that is developed. Additionally, review sessions explaining how to solve complex optimization problems using CVX and Python are offered.
The aim of this course is to provide students a systematic training in key topics in modern supervised statistical learning and data mining. For the most part, the focus will remain on a theoretically sound understanding of the methods (learning algorithms) and their applications in complex data analysis, rather than proving technical theorems. Applications of the statistical learning and data mining tools in biomedical and health sciences will be highlighted.
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.
This is an advanced course for first-year Ph.D. students in Biostatistics. The aim is to provide a solid foundation of the theory behind linear models and generalized linear models. More emphasis will be placed on concepts and theory with mathematical rigor. Topics covered including linear regression models, logistic regression models, generalized linear regression models and methods for the analysis contingency tables.
This course is designed to increase student knowledge of Psychiatric Nurse Practitioner Case Narrative writing, and DNP competencies. Students will use case narratives as a framework to synthesize knowledge, assessment, and clinical thinking skills. Students will explore Social Justice competency, Competency D3C3 in depth. Students will develop a treatment intervention that identify and challenge biases that contribute to health disparities.
This fourteen-week elective, open to Research Arts Screen & TV Writing students, will provide vital directing advisement to Portfolio films. It covers pre-production and director’s prep.
Students get together to discuss the paper which will be presented at the IEOR-DRO seminar. One group of students (~2 students) presents. A faculty member is present to guide and facilitate the discussion. Students are evaluated on their effort in leading one of the discussions and participating in the other discussions
This course examines Generative AI technologies through both a technical and social lens. In
the first part of the course, students will develop hands-on experience in the technical workings
of LLMs, including prompt engineering, retrieval augmented generation, fine-tuning, and safety.
In the second part of the course, students will examine the social and ethical implications of
these technologies and examine the impact of these technologies on topics like content
creation, labor markets, and security.
Designed for students interested in advancing AI technology responsibly, this course
encourages critical thinking about AI's broader effects. Participants will gain practical skills and a
deeper understanding of how AI tools can be developed and utilized ethically and effectively in
various sectors.
This seminar-style course will lead students through the process of writing a Master's Essay in the form of an NIH-style grant application (required for the MS/POR degree track). The essay is undertaken during the fall semester of the second year of study. At the end of the fall term, each student submits a written research proposal following NIH guidelines for either an R01 or K (career development) award. The emphasis in this course is on the quality of the proposed research. The following February, students make an oral presentation to the POR Advisory Board, summarizing the research proposal. Final grades are awarded after the presentations in February.
This is a Law School course. For more detailed course information, please go to the Law School Curriculum Guide at: http://www.law.columbia.edu/courses/search
Weekly seminar of presentations and discussion of current topics in cognition.
Prerequisites: the instructor's permission. At least one foundational course in moral philosophy is recommended as background for this course. In this seminar we will take up several questions about moral understanding and insight. Questions we will consider include: Can trusting moral testimony ever be rational or right? Are the reasons to be cautions about relying on moral testimony moral reasons or epistemic reasons (or both)? What assumptions about moral knowledge do critics and defenders of moral testimony make? How does moral knowledge differ, if it does, from moral understanding? Is there such a thing as moral expertise? Is there any reason to think that moral expertise is more problematic than other kinds of expertise? Can emotions inform us about value? Under what conditions, if any, can emotions contribute to our understanding of value? Under what conditions are emotions impediments to moral knowledge or understanding? Can fictions help us gain moral insight? Can pictures ever be legitimate tools of moral persuasion?
In this course, students will apply the concepts and methods introduced in Statistical Practices and Research for Interdisciplinary Science (SPRIS) I to a real research setting. Each student will be paired with a Biostatistics faculty member. The student will participate in one of the mentor’s collaborative projects to learn how to be an effective member of an interdisciplinary team. The relationship will mimic that between a medical resident and an attending physician.
The SPRIS II experience will vary depending on the assigned faculty member, but all students will gain exposure to preparing collaborative grant applications, designing research studies, analyzing real data, interpreting and presenting results, and writing manuscripts. Mentors will help to develop the student’s data intuition skills, ability to ask good research questions, and leadership qualities. Where necessary, students may replicate projects already completed by the faculty mentor to gain experience.
For appropriately qualified students wishing to enrich their programs by undertaking literature reviews, special studies, or small group instruction in topics not covered in formal courses.
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.
You may be asked to serve as research subjects in studies under direction of the faculty while enrolled in this course. Participation in voluntary.
Presentation of doctoral student research and guest speakers.
This course will serve to provide an opportunity for Students who are Directing Concentrates to develop their thesis projects within a structured environment. The course may be taught in every week or alternating week formats. Students will be encouraged to submit ideas, treatments, scripts, rough cuts and fine cuts of their thesis films. The class is collaborative and serves as a base from which Directors can try out concepts and ideas, and receive input from fellow students as well as their thesis advisor.
Clinical and laboratory projects or field investigation related to nutrition, particularly in the area of growth and development.
This is a Law School course. For more detailed course information, please go to the Law School Curriculum Guide at: http://www.law.columbia.edu/courses/search
This workshop is the second course in a three-semester sequence that serves as the professional development core of the MPA in Environmental Science and Policy. Building on the foundation established during the summer semester, students continue to refine their management and analytical skills through applied work on simulated public sector sustainability projects.
Students work in teams to design and implement a one-year operational plan for an environmental sustainability program. Each project addresses real-world management and implementation challenges, including budgeting, staffing, political analysis, performance planning, and scheduling. Students are expected to draw on the scientific, economic, and policy tools they have acquired to date, applying them in an integrated and practical context.
The course emphasizes project management, teamwork, and professional communication. Students assume defined leadership roles, develop briefings, and produce a final report that outlines a feasible policy direction and operational strategy. Through simulated client interactions and instructor-led seminars, students gain firsthand experience with the complexities of managing environmental programs in the public and nonprofit sectors.