Mathematics

Departmental Contact:
Ms. Mary Young
410 Mathematics
212-854-2432
my@math.columbia.edu

OFFICIAL MAKEUP DATES FOR UNIVERSITY HOLIDAYS

May 31, replaces the Memorial Day holiday.

July 5, replaces the Independence Day holiday

NOTE

The University reserves the right to withdraw or modify the courses of instruction or to change the instructors as may become necessary.

Click on course title to see course description and schedule.

Summer 2013

Mathematics

  • MATH S0065D. Basic Mathematics. 2 pts.
    Runs from the week of May 28 to Jul 05

    Designed for students who have not attended school for some time or who do not have a firm grasp of high school mathematics. Recommended as a prerequisite for Math S1003. This course does not carry credit toward the bachelor's degree; Pass/Fail only. Negative numbers, fractions, decimal notation, percentages, powers and roots, scientific notation, introduction to algebra, linear and quadratic equations, Pythagorean theorem, coordinates and graphs.

  • MATH S1003D. College Algebra and Analytic Geometry. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: Mathematics score of 550 on the SAT exam, taken within the past year.

    Recommended preparation: Math S0065. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits.

  • MATH S1003Q. College Algebra and Analytic Geometry. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: Mathematics score of 550 on the SAT exam, taken within the past year.

    Recommended preparation: Math S0065. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits.

  • MATH S1101D (Section 1). Calculus, I. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: High school mathematics through trigonometry or MATH S1003, or the equivalent.

    Functions, limits, derivatives, introduction to integrals.

  • MATH S1101Q (Section 2). Calculus, I. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: High school mathematics through trigonometry or MATH S1003, or the equivalent.

    Functions, limits, derivatives, introduction to integrals.

  • MATH S1101X (Section 3). Calculus, I. 3 pts.
    Runs from the week of May 28 to Aug 16

    Prerequisites: High school mathematics through trigonometry or MATH S1003, or the equivalent.

    Functions, limits, derivatives, introduction to integrals.

  • MATH S1102D (Section 1). Calculus, II. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: MATH S1101, or the equivalent.

    Methods of integration, applications of the integral, Taylor's theorem, infinite series.

  • MATH S1102Q (Section 2). Calculus, II. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: MATH S1101, or the equivalent.

    Methods of integration, applications of the integral, Taylor's theorem, infinite series.

  • MATH S1201D (Section 1). Calculus, III. 3 pts.
    Runs from the week of May 28 to Jul 05

    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.

  • MATH S1201Q (Section 2). Calculus, III. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    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.

  • MATH S1202D (Section 1). Calculus, IV. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: MATH S1201, or the equivalent.

    Double and triple integrals. Change of variables. Line and surface integrals. Grad, div, and curl. Vector integral calculus: Green's theorem, divergence theorem, Stokes' theorem

  • MATH S1202Q (Section 2). Calculus, IV. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: MATH S1201, or the equivalent.

    Double and triple integrals. Change of variables. Line and surface integrals. Grad, div, and curl. Vector integral calculus: Green's theorem, divergence theorem, Stokes' theorem

  • MATH S2010D (Section 1). Linear Algebra. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: MATH S1201, or the equivalent.

    Matrices, vector spaces, linear transformation, Eigenvalues and Eigenvectors, canonical forms, applications.

  • MATH S2010Q (Section 2). Linear Algebra. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: MATH S1201, or the equivalent.

    Matrices, vector spaces, linear transformation, Eigenvalues and Eigenvectors, canonical forms, applications.

  • MATH S2010X (Section 3). Linear Algebra. 3 pts.
    Runs from the week of May 28 to Aug 16

    Prerequisites: MATH S1201, or the equivalent.

    Matrices, vector spaces, linear transformation, Eigenvalues and Eigenvectors, canonical forms, applications.

  • MATH S2500D. Analysis & Optimization. 3 pts.
    Runs from the week of May 28 to Jul 05

    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.

  • MATH S3027D (Section 1). Ordinary Differential Equations. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: MATH S1201, or the equivalent.

    Equations of order one, linear equations, series solutions at regular and singular points. Boundary value problems. Selected applications.

  • MATH S3027Q (Section 2). Ordinary Differential Equations. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: MATH S1201, or the equivalent.

    Equations of order one, linear equations, series solutions at regular and singular points. Boundary value problems. Selected applications.

  • MATH S4061D (Section 1). Introduction to Modern Analysis, I. 3 pts.
    Runs from the week of May 28 to Jul 05

    Prerequisites: MATH S1202, S2010, or the equivalent. NOTE: 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.

  • MATH S4061X (Section 2). Introduction to Modern Analysis, I. 3 pts.
    Runs from the week of May 28 to Aug 16

    Prerequisites: MATH S1202, S2010, or the equivalent. NOTE: 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.

  • MATH S4062Q. Introduction to Modern Analysis, II. 3 pts.
    Runs from the week of Jul 08 to Aug 16

    Prerequisites: MATH S4061, or the equivalent with the instructor's permission.

    Equicontinuity. Contraction maps with applications to existence theorems in analysis. Lebesgue measure and integral. Fourier series and Fourier transform