## 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 2019 offerings.

##### 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 | 001/11630 | M Tu W Th 4:30p - 6:05p 307 MATHEMATICS BUILDING | Milton Pesantez, Lindsay Piechnik | 0 | 3 |

###### 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.

###### 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 | 002/28237 | M Tu W Th 10:00a - 12:25p 407 MATHEMATICS BUILDING | Tomasz Owsiak | 3 | 6 |

###### 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 | 001/62667 | M Tu W Th 4:30p - 6:05p 417 MATHEMATICS BUILDING | Dobrin Marchev, Semen Rezchikov | 3 | 27 |

###### 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 | 002/19325 | M Tu W Th 10:45a - 12:20p 417 MATHEMATICS BUILDING | Carl Lian | 3 | 20 |

###### 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 | 003/10414 | M W 4:30p - 6:05p 520 MATHEMATICS BUILDING | Alexander Casti | 3 | 15 |

###### 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 | 001/67930 | M Tu W Th 1:00p - 2:35p 407 MATHEMATICS BUILDING | Renata Picciotto | 3 | 14 |

###### 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 | 002/24589 | M Tu W Th 4:30p - 6:05p 417 MATHEMATICS BUILDING | Mark Rychnovsky | 3 | 21 |

###### 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 | 001/15677 | M Tu W Th 6:15p - 7:50p 520 MATHEMATICS BUILDING | Yang An | 3 | 19 |

###### 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 | 002/75626 | M Tu W Th 6:15p - 7:50p 520 MATHEMATICS BUILDING | Hugo Falconet | 3 | 19 |

###### 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 | 001/66714 | M Tu W Th 1:00p - 2:35p 417 MATHEMATICS BUILDING | Keaton Naff | 3 | 9 |

###### 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 | 002/23373 | M Tu W Th 4:30p - 6:05p 307 MATHEMATICS BUILDING | Cheng Yu Tong | 3 | 10 |

###### 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 | 001/27021 | M Tu W Th 4:30p - 6:05p 407 MATHEMATICS BUILDING | Tat Sang Fung | 3 | 13 |

###### 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 | 002/61451 | M Tu W Th 6:15p - 7:50p 503 HAMILTON HALL | Tat Sang Fung | 3 | 24 |

###### 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 | 003/18109 | M W 6:15p - 7:50p 407 MATHEMATICS BUILDING | Clara Dolfen | 3 | 10 |

###### 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 | 001/70362 | M Tu W Th 2:45p - 4:20p 520 MATHEMATICS BUILDING | Stanislav Atanasov | 3 | 11 |

###### Mathematics in Contemporary Art

###### MATH S3015Q 3 points.

An exploration of how artists in the last 50 years have appropriated the visual language of mathematics and reinterpreted mathematical concepts. Artists will include Donald Judd, Richard Serra, and Robert Smithson. Visits to New York museums and galleries will be an essential component of the course. No mathematical background is assumed.

###### 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 | 001/69146 | M Tu W Th 10:45a - 12:20p 417 MATHEMATICS BUILDING | Henri Roesch | 3 | 7 |

###### 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 | 002/25805 | M Tu W Th 4:30p - 6:05p 407 MATHEMATICS BUILDING | Huaxin Liu | 3 | 26 |

###### 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 | 001/16893 | M Tu W Th 10:45a - 12:10p 520 MATHEMATICS BUILDING | Mitchell Faulk | 3 | 16 |

###### 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 | 002/76842 | Tu Th 6:15p - 7:50p 407 MATHEMATICS BUILDING | Fabio Nironi | 3 | 14 |

###### 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 | 001/60235 | M Tu W Th 10:45a - 12:10p 520 MATHEMATICS BUILDING | Karsten Gimre | 3 | 14 |