Courses

Prerequisites: MATH S1202, MATH S2010, or the equivalent. Students must have a current and solid background in the prerequisites for the course: multivariable calculus and linear algebra. Elements of set theory and general topology. Metric spaces. Euclidian space. Continuous and differentiable functions. Riemann integral. Uniform convergence.

The purpose of this foundational course is to introduce Columbia undergraduate students, in the context of their Global Core curriculum, to the seminal field of critical theory. The historical domain of this course is within the last century and its geographical spectrum is global. European critical thinkers are included in this course but not privileged. Thinkers from Asia, Africa, Europe, North, South, and Latin America, are examined here in chronological order and in equal democratic footing with each other. This course as a result is decidedly cross-cultural, one step forward towards de-alienating critical thinkers from around the globe and the issues they address without pigeonholing them as something “other” or “different.” The course is designed and offered in the true spirit of the “Global Core.” The purpose of the course is to reach for the common denominator of serious critical thinking about the fate of our humanity and the health of our social relations in an increasingly fragile world—where the false binaries of “the West” and “the Rest” no longer hold. The roster of critical thinkers we will examine is by no means exhaustive but representative. Any number of other critical thinkers can be added to this roster but none of those we will examine can be excluded from them. The course is divided into thirteen successive weeks and for each week a number of seminal, original, and groundbreaking texts are identified. Each week we will examine selected passages from these texts. The course is designed as a lecture course, and my lectures are based on the totality of these texts but students will be assigned specific shorter passages to read.

As music moves into the 21st century, we find ourselves surrounded by an ever-evolving landscape of technological capability. The world of music, and the music industry itself, is changing rapidly, and with that change comes the opening – and closing – of doorways of possibility. What does this shift mean for today’s practicing artist or composer? With big label recording studios signing and nurturing fewer and fewer artists, it seems certain that, today, musicians who want to record and distribute their music need to be able to do much of the recording and production work on their own. But where does one go to learn how to do this – to learn not only the “how to” part of music production, but the historical underpinnings and the development of the music production industry as well? How does one develop a comprehensive framework within which they can place their own artistic efforts? How does one learn to understand what they hear, re-create what they like and develop their own style? This class, “Recorded Sound,” aims to be the answer. It’s goal is to teach artists how to listen critically to music from across history and genres in order to identify the production techniques that they hear, and reproduce those elements using modern technology so they can be incorporated into the artist’s own musical works.

Prerequisites: this course uses elementary concepts from calculus, and students should therefore have some basic background in differentiation and integration. Assignments to discussion sections are made after the first lecture. Basic introduction to the study of mechanics, fluids, and thermodynamics. The accompanying laboratory is PHYS S1291D. NOTE: There are two recitation sessions that meet for one hour each week. The recitation times will be selected at the first class meeting.

Prerequisites: PHYS S1201. May be taken before or concurrently with this course. Laboratory for PHYS S1201D. Assignments to laboratory sections are made after the first lecture, offered Mon/Wed or Tues/Thurs 10.30AM-1.30PM.

This course introduces students to international relations through the lens of world order— how it emerged, how it operates, and why it is now under strain. Students examine how power, institutions, law, domestic politics, and leadership shape cooperation and conflict among states. Rather than treating international relations as abstract theory, the course emphasizes concrete puzzles: why wars occur despite their costs, why democracies rarely fight one another, and why rules sometimes constrain powerful states and sometimes fail, and international law is often weaker than many might expect. The course also explores competing visions of world order, including American, European, Chinese, Islamic, African, and Non-Aligned perspectives, especially in the context of deglobalization. In the final weeks, students apply these ideas to the U.S.–China rivalry and to existential challenges such as nuclear war and environmental stress. The course is designed for students from all majors and emphasizes analytical reading, clear argumentation, and informed discussion of contemporary global politics. 

This course introduces students to international relations through the lens of world order— how it emerged, how it operates, and why it is now under strain. Students examine how power, institutions, law, domestic politics, and leadership shape cooperation and conflict among states. Rather than treating international relations as abstract theory, the course emphasizes concrete puzzles: why wars occur despite their costs, why democracies rarely fight one another, and why rules sometimes constrain powerful states and sometimes fail, and international law is often weaker than many might expect. The course also explores competing visions of world order, including American, European, Chinese, Islamic, African, and Non-Aligned perspectives, especially in the context of deglobalization. In the final weeks, students apply these ideas to the U.S.–China rivalry and to existential challenges such as nuclear war and environmental stress. The course is designed for students from all majors and emphasizes analytical reading, clear argumentation, and informed discussion of contemporary global politics. 

Political theory examines the ideas and institutions that shape political life.  This course introduces key texts and arguments about the best way to organize political power, how it should be used, and for what purpose.

We will address these larger questions by studying how major thinkers, ancient and modern, analyzed political diversity, division, and conflict.  What are the sources of conflicting identities, interests, passions, and values in politics?  How can partisanship and contestation avoid degenerating into open war and unjust domination?  Which institutions, laws, and practices are best able to manage conflict consistent with other political goals, such as freedom, equality, justice?  

Course goals: Demonstrate broad knowledge of key texts, thinkers, concepts, and debates in the history of political thought; compare, contrast, and classify definitions of diversity and their political significance; interpret texts and reconstruct their core arguments and concepts; evaluate arguments, concepts, and theories in terms of consistency, plausibility, and desirability; develop persuasive interpretations and arguments through textual analysis; present and defend ideas and arguments clearly in writing and discussion.

In this course, students will gain familiarity with some of the major questions and theoretical frameworks in the American Politics subfield of political science and learn how to think theoretically and empirically about politics.