Courses

This course serves as an introduction to the study of international political and economic relations. We look at the connections between politics and economics as well as markets and governments and relate them to key substantive issue areas such as finance, trade, investment, marketing, income inequality and poverty, and globalization. In examining the issue areas, we shall look both at how scholars think about them and how private and public decision makers analyze and impact them. The teaching is informed by the sharing with students knowledge deriving from multiple disciplines, cultures, and languages to help them gain useful real-world insights.

Prerequisites: ITAL V1102 or W1102, or the equivalent. If you did not take Elementary Italian at Columbia in the semester preceding the current one, you must take the placement test, offered by the Italian Department at the beginning of each semester. Same course as ITAL V1201-V1202.

Prerequisites: MATH S1102, or the equivalent. Columbia College students who aim at an economics major AND have at least the grade of B in Calculus I may take Calculus III directly after Calculus I. However, all students majoring in engineering, science, or mathematics should follow Calculus I with Calculus II. Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers.

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.