Summer Sessions | Courses | Mathematics

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. 

 

Courses
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Calculus, I
MATH S1101X 3 points.

Functions, limits, derivatives, introduction to integrals.

Course
Number
Section/Call
Number
Times/Location Instructor Points Enrollment
MATH 1101 003/66076 M W 4:30p - 6:05p
520 MATHEMATICS BUILDING
Alexander Casti 3 Open
Introduction to Modern Analysis, I
MATH S4061X 3 points.

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 Tu Th 6:15p - 7:50p
520 MATHEMATICS BUILDING
Fabio Nironi 3 Open
Linear Algebra
MATH S2010X 3 points.

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 M W 6:15p - 7:50p
520 MATHEMATICS BUILDING
Qixiao Ma 3 Open
Analysis & Optimization
MATH S2500D 3 points.

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 M Tu W Th 2:45p - 4:20p
520 MATHEMATICS BUILDING
Dobrin Marchev 3 Open
Basic Mathematics
MATH S0065D 0 points.

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 M Tu W Th 4:30p - 6:05p
307 MATHEMATICS BUILDING
Lindsay Piechnik 0 Open
Calculus, I
MATH S1101D 3 points.

Functions, limits, derivatives, introduction to integrals.

Course
Number
Section/Call
Number
Times/Location Instructor Points Enrollment
MATH 1101 001/15039 M Tu W Th 4:30p - 6:05p
417 MATHEMATICS BUILDING
Feiqi Jiang 3 Open
Calculus, II
MATH S1102D 3 points.

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 M Tu W Th 1:00p - 2:35p
520 MATHEMATICS BUILDING
Ivan Danilenko 3 Open
Calculus, III
MATH S1201D 3 points.

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 M Tu W Th 6:15p - 7:50p
417 MATHEMATICS BUILDING
Penka Marinova 3 Open
Calculus, IV
MATH S1202D 3 points.

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 M Tu W Th 1:00p - 2:35p
417 MATHEMATICS BUILDING
Mitchell Faulk 3 Open
College Algebra and Analytic Geometry
MATH S1003D 3 points.

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 M Tu W Th 10:00a - 12:25p
407 MATHEMATICS BUILDING
Tomasz Owsiak 3 Open
Introduction to Modern Analysis, I
MATH S4061D 3 points.

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 M Tu W Th 10:45a - 12:20p
417 MATHEMATICS BUILDING
Drew Youngren 3 Open
Linear Algebra
MATH S2010D 3 points.

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 M Tu W Th 4:30p - 6:05p
312 MATHEMATICS BUILDING
Yang An 3 Open
Ordinary Differential Equations
MATH S3027D 3 points.

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 M Tu W Th 10:45a - 12:20p
520 MATHEMATICS BUILDING
Karsten Gimre 3 Open
Calculus, I
MATH S1101Q 3 points.

Functions, limits, derivatives, introduction to integrals.

Course
Number
Section/Call
Number
Times/Location Instructor Points Enrollment
MATH 1101 002/74987 M Tu W Th 10:45a - 12:20p
608 SCHERMERHORN HALL
Shuai Wang 3 Open
Calculus, II
MATH S1102Q 3 points.

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 M Tu W Th 4:30p - 6:05p
407 MATHEMATICS BUILDING
Elena Giorgi 3 Open
Calculus, III
MATH S1201Q 3 points.

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 M Tu W Th 6:15p - 7:50p
417 MATHEMATICS BUILDING
Shizhang Li 3 Open
Calculus, IV
MATH S1202Q 3 points.

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 M Tu W Th 4:30p - 6:05p
417 MATHEMATICS BUILDING
Pak Hin Lee 3 Open
College Algebra and Analytic Geometry
MATH S1003Q 3 points.

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 M Tu W Th 10:00a - 12:25p
407 MATHEMATICS BUILDING
Penka Marinova 3 Open
Introduction to Modern Analysis, II
MATH S4062Q 3 points.

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 M Tu W Th 10:45a - 12:20p
417 MATHEMATICS BUILDING
Dobrin Marchev 3 Open
Linear Algebra
MATH S2010Q 3 points.

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 M Tu W Th 6:15p - 7:50p
407 MATHEMATICS BUILDING
Darren Gooden 3 Open
Ordinary Differential Equations
MATH S3027Q 3 points.

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 M Tu W Th 4:30p - 6:05p
312 MATHEMATICS BUILDING
Zhechi Cheng 3 Open