## Mathematics

The Mathematics Department offers introductory and advanced level courses during the summer term.

Please note, it is not necessary to complete pre-requisites at Columbia University. Students are expected to meet pre-requisite requirements prior to registration.

The courses on this page reflect Summer 2018 offerings. Scheduling and instructor information will be posted in Spring 2018.

Note: Courses are subject to change at the discretion of the University.

##### Courses

Expand All###### Basic Mathematics

###### MATH S0065D 0 points.

0 academic points, billed as 2 points. Does not carry credit toward the bachelor's degree. May be taken for Pass/Fail credit only.

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*. Negative numbers, fractions, decimal notation, percentages, powers and roots, scientific notation, introduction to algebra, linear and quadratic equations, Pythagorean theorem, coordinates and graphs.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 0065 | 001/12207 | 0 | 0 |

###### College Algebra and Analytic Geometry

###### MATH S1003D 3 points.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1003 | 001/67292 | 3 | 0 |

###### College Algebra and Analytic Geometry

###### MATH S1003Q 3 points.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1003 | 002/23950 | 3 | 0 |

###### Calculus, I

###### MATH S1101D 3 points.

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

Functions, limits, derivatives, introduction to integrals.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1101 | 001/15039 | 3 | 0 |

###### Calculus, I

###### MATH S1101Q 3 points.

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

Functions, limits, derivatives, introduction to integrals.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1101 | 002/74987 | 3 | 0 |

###### Calculus, I

###### MATH S1101X 3 points.

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

Functions, limits, derivatives, introduction to integrals.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1101 | 003/66076 | 3 | 0 |

###### Calculus, II

###### MATH S1102D 3 points.

Prerequisites: *MATH S1101* Calculus I, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1102 | 001/22734 | 3 | 0 |

###### Calculus, II

###### MATH S1102Q 3 points.

Prerequisites: *MATH S1101* Calculus I, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1102 | 002/13823 | 3 | 0 |

###### Calculus, III

###### MATH S1201D 3 points.

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.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1201 | 001/73771 | 3 | 0 |

###### Calculus, III

###### MATH S1201Q 3 points.

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.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1201 | 002/64860 | 3 | 0 |

###### Calculus, IV

###### MATH S1202D 3 points.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1202 | 001/21518 | 3 | 0 |

###### Calculus, IV

###### MATH S1202Q 3 points.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1202 | 002/12607 | 3 | 0 |

###### Linear Algebra

###### MATH S2010D 3 points.

Prerequisites: *MATH S1201* Calculus III, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2010 | 001/72555 | 3 | 0 |

###### Linear Algebra

###### MATH S2010Q 3 points.

Prerequisites: *MATH S1201* Calculus III, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2010 | 002/29214 | 3 | 0 |

###### Linear Algebra

###### MATH S2010X 3 points.

Prerequisites: *MATH S1201* Calculus III, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2010 | 003/63644 | 3 | 0 |

###### Analysis & Optimization

###### MATH S2500D 3 points.

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.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2500 | 001/20302 | 3 | 0 |

###### Ordinary Differential Equations

###### MATH S3027D 3 points.

Prerequisites: *MATH S1201*, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3027 | 001/11391 | 3 | 0 |

###### Ordinary Differential Equations

###### MATH S3027Q 3 points.

Prerequisites: *MATH S1201*, or the equivalent.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3027 | 002/71339 | 3 | 0 |

###### Introduction to Modern Analysis, I

###### MATH S4061D 3 points.

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.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4061 | 001/27998 | 3 | 0 |

###### Introduction to Modern Analysis, I

###### MATH S4061X 3 points.

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.

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4061 | 002/62428 | 3 | 0 |

###### Introduction to Modern Analysis, II

###### MATH S4062Q 3 points.

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

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4062 | 001/19086 | 3 | 0 |