# Mathematics

## Mathematics

**Departmental Contact:**

Professor Michael Woodbury

212-854-8962

mw2807@columbia.edu

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

To request a syllabus, please contact the course instructor and cc cp2817@columbia.edu. You can find contact information for an instructor on the university directory.

**MATH S0065D Basic Mathematics. ***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.

Summer 2019: MATH S0065D | |||||

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

MATH 0065 | 001/11630 | |
0 | 0 |

**MATH S1003D College Algebra and Analytic Geometry. ***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.

Summer 2019: MATH S1003D | |||||

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

MATH 1003 | 001/71578 | |
3 | 0 |

**MATH S1003Q College Algebra and Analytic Geometry. ***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.

Summer 2019: MATH S1003Q | |||||

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

MATH 1003 | 002/28237 | |
3 | 0 |

**MATH S1101D Calculus, I. ***3 points*.

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

Functions, limits, derivatives, introduction to integrals.

Summer 2019: MATH S1101D | |||||

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

MATH 1101 | 001/62667 | |
3 | 0 |

**MATH S1101Q Calculus, I. ***3 points*.

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

Functions, limits, derivatives, introduction to integrals.

Summer 2019: MATH S1101Q | |||||

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

MATH 1101 | 002/19325 | |
3 | 0 |

**MATH S1101X Calculus, I. ***3 points*.

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

Functions, limits, derivatives, introduction to integrals.

Summer 2019: MATH S1101X | |||||

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

MATH 1101 | 003/10414 | |
3 | 0 |

**MATH S1102D Calculus, II. ***3 points*.

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

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

Summer 2019: MATH S1102D | |||||

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

MATH 1102 | 001/67930 | |
3 | 0 |

**MATH S1102Q Calculus, II. ***3 points*.

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

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

Summer 2019: MATH S1102Q | |||||

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

MATH 1102 | 002/24589 | |
3 | 0 |

**MATH S1201D Calculus, III. ***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.

Summer 2019: MATH S1201D | |||||

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

MATH 1201 | 001/15677 | |
3 | 0 |

**MATH S1201Q Calculus, III. ***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.

Summer 2019: MATH S1201Q | |||||

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

MATH 1201 | 002/75626 | |
3 | 0 |

**MATH S1202D Calculus, IV. ***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

Summer 2019: MATH S1202D | |||||

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

MATH 1202 | 001/66714 | |
3 | 0 |

**MATH S1202Q Calculus, IV. ***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

Summer 2019: MATH S1202Q | |||||

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

MATH 1202 | 002/23373 | |
3 | 0 |

**MATH S2010D Linear Algebra. ***3 points*.

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

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

Summer 2019: MATH S2010D | |||||

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

MATH 2010 | 001/27021 | |
3 | 0 |

**MATH S2010Q Linear Algebra. ***3 points*.

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

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

Summer 2019: MATH S2010Q | |||||

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

MATH 2010 | 002/61451 | |
3 | 0 |

**MATH S2010X Linear Algebra. ***3 points*.

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

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

Summer 2019: MATH S2010X | |||||

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

MATH 2010 | 003/18109 | |
3 | 0 |

**MATH S2500D Analysis & Optimization. ***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.

Summer 2019: MATH S2500D | |||||

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

MATH 2500 | 001/70362 | |
3 | 0 |

**MATH S3027D Ordinary Differential Equations. ***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.

Summer 2019: MATH S3027D | |||||

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

MATH 3027 | 001/69146 | |
3 | 0 |

**MATH S3027Q Ordinary Differential Equations. ***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.

Summer 2019: MATH S3027Q | |||||

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

MATH 3027 | 002/25805 | |
3 | 0 |

**MATH S4061D Introduction to Modern Analysis, I. ***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.

Summer 2019: MATH S4061D | |||||

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

MATH 4061 | 001/16893 | |
3 | 0 |

**MATH S4061X Introduction to Modern Analysis, I. ***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.

Summer 2019: MATH S4061X | |||||

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

MATH 4061 | 002/76842 | |
3 | 0 |

**MATH S4062Q Introduction to Modern Analysis, II. ***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

Summer 2019: MATH S4062Q | |||||

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

MATH 4062 | 001/60235 | |
3 | 0 |