Courses

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.

Linear algebra with a focus on probability and statistics. The course covers the standard linear algebra topics: systems of linear equations, matrices, determinants, vector spaces, bases, dimension, eigenvalues and eigenvectors, the Spectral Theorem and singular value decompositions. It also teaches applications of linear algebra to probability, statistics and dynamical systems giving a background sufficient for higher level courses in probability and statistics. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, probability distributions and the limit theorems, as well as Markov chains, curve fitting, regression, and pattern analysis. The course contains applications to life sciences, chemistry, and environmental life sciences. No a prior i background in the life sciences is assumed.

This course is best suited for students who wish to focus on applications and practical approaches to problem solving. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics. Math majors, joint majors, and math concentrators must take MATH UN2010 Linear Algebra, which focuses on linear algebra concepts and foundations that are needed for upper-level math courses. MATH UN2015 (Linear Algebra and Probability) does NOT replace MATH UN2010 (Linear Algebra) as prerequisite requirements of math courses. Students may not receive full credit for both courses MATH UN2010 and MATH UN2015.

Linear algebra with a focus on probability and statistics. The course covers the standard linear algebra topics: systems of linear equations, matrices, determinants, vector spaces, bases, dimension, eigenvalues and eigenvectors, the Spectral Theorem and singular value decompositions. It also teaches applications of linear algebra to probability, statistics and dynamical systems giving a background sufficient for higher level courses in probability and statistics. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, probability distributions and the limit theorems, as well as Markov chains, curve fitting, regression, and pattern analysis. The course contains applications to life sciences, chemistry, and environmental life sciences. No a prior i background in the life sciences is assumed.

This course is best suited for students who wish to focus on applications and practical approaches to problem solving. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics. Math majors, joint majors, and math concentrators must take MATH UN2010 Linear Algebra, which focuses on linear algebra concepts and foundations that are needed for upper-level math courses. MATH UN2015 (Linear Algebra and Probability) does NOT replace MATH UN2010 (Linear Algebra) as prerequisite requirements of math courses. Students may not receive full credit for both courses MATH UN2010 and MATH UN2015.

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 V1102-MATH V1201 or the equivalent and MATH V2010. Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control.

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.