Courses

Calculus I
Material includes the study of limits, derivatives, and applications of derivatives, as well as an introduction to integrals. Success in this course requires intense commitment to study and collaboration both in and out of class, along with active participation during class, and the ability to follow both written and verbal directions.   
The overarching objective of the course is for students to develop conceptual fluency and computational competence working with limits, derivatives, and their applications.   Students will enhance their quantitative reasoning, particularly through interpreting/analyzing charts and graphs in the study of limits and derivatives.  Problem solving skills will be augmented through applied word problems, particularly relating to optimization, related rates, and graphing.  Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. While collaborative projects will advance their ability to do so orally and visually.

Calculus I
Material includes the study of limits, derivatives, and applications of derivatives, as well as an introduction to integrals. Success in this course requires intense commitment to study and collaboration both in and out of class, along with active participation during class, and the ability to follow both written and verbal directions.   
The overarching objective of the course is for students to develop conceptual fluency and computational competence working with limits, derivatives, and their applications.   Students will enhance their quantitative reasoning, particularly through interpreting/analyzing charts and graphs in the study of limits and derivatives.  Problem solving skills will be augmented through applied word problems, particularly relating to optimization, related rates, and graphing.  Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. While collaborative projects will advance their ability to do so orally and visually.

Prerequisite for Calc III is Calc I.  
For exam placement, see dept site: https://math.barnard.edu/placement-calculus-classes

• To develop a conceptual understanding of the fundamental principles of multivariable differential calculus and explore their practical relevance to other branches of natural and social sciences.
• Students will enhance their critical thinking by using 3D graphical tools and engaging with three dimensional representations of curves, surfaces and solids.
• Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. 
• Problem solving skills will be augmented through applications in physics and real world problems involving the dynamics of movement, and optimization problems involving multiple inputs (parameters)

• The sequence of topics covered is as follows.

  • ​​​​1.  Vectors. Equations of lines and planes. Cylinders and quadric surfaces. 

  • 2. Vector functions. Space curves. Arc length and curvature. Applications.

  • 3. Functions of several variables. Partial derivatives. Gradient. Optimization. Lagrange multipliers.

  •  

Prerequisite for Calc III is Calc I.  
For exam placement, see dept site: https://math.barnard.edu/placement-calculus-classes

• To develop a conceptual understanding of the fundamental principles of multivariable differential calculus and explore their practical relevance to other branches of natural and social sciences.
• Students will enhance their critical thinking by using 3D graphical tools and engaging with three dimensional representations of curves, surfaces and solids.
• Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. 
• Problem solving skills will be augmented through applications in physics and real world problems involving the dynamics of movement, and optimization problems involving multiple inputs (parameters)

• The sequence of topics covered is as follows.

  • ​​​​1.  Vectors. Equations of lines and planes. Cylinders and quadric surfaces. 

  • 2. Vector functions. Space curves. Arc length and curvature. Applications.

  • 3. Functions of several variables. Partial derivatives. Gradient. Optimization. Lagrange multipliers.

  •  

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.

Prerequisites: MATH UN1101 (Calculus I) or equivalent courses. This course introduces students to mathematical modeling through hands-on, project-based learning. Topics include fundamental concepts from linear algebra, multivariable calculus, differential equations, probability and statistics, and introductory machine learning.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Groups, homomorphisms, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, finitely generated abelian groups.

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.