Summer Sessions | Courses | Mathematics

Course information is posted for 2021. Please check back at a later time for updated 2022 course offerings.

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.

Check the Directory of Classes for the most up-to-date course information.

Summer 2021 Session Information

  • SESSION A courses are May 3–June 18, 2021
  • SESSION B courses are June 28–August 16, 2021
Courses
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BASIC MATHEMATICS
MATH0065S001 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 Session Times/Location
MATH0065S001 001/10913 Summer A Subterm Mo 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Lindsay Piechnik
0 Closed for Online Registration On-Line Only
COLLEGE ALGEBRA-ANLYTC GEOMTRY
MATH1003S001 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 Session Times/Location
MATH1003S001 001/10945 Summer B Subterm Mo 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Zoe Margaret Himwich
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
CALCULUS I
MATH1101S001 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 Session Times/Location
MATH1101S001 001/10275 Summer A Subterm Mo 08:30 AM–10:05 AM
Tu 08:30 AM–10:05 AM
We 08:30 AM–10:05 AM
Th 08:30 AM–10:05 AM

Instructor Points Enrollment Method of Instruction
Andrew Blumberg
3 Closed for Online Registration On-Line Only
CALCULUS I
MATH1101S002 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 Session Times/Location
MATH1101S002 002/10925 Full Trm Crs Mo 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Alexander Casti
3 Closed for Online Registration On-Line Only
CALCULUS I
MATH1101S003 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 Session Times/Location
MATH1101S003 003/10946 Summer B Subterm Th 10:45 AM–12:20 PM
Mo 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Shalin Parekh
3 Registration Block
(w/ Self-Managed Wait List)
On-Line Only
CALCULUS I
MATH1101S004 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 Session Times/Location
MATH1101S004 004/14313 Summer B Subterm We 06:15 PM–07:50 PM
Mo 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM
Tu 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Tat Sang Fung
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
CALCULUS II
MATH1102S001 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 Session Times/Location
MATH1102S001 001/10276 Summer A Subterm Th 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
Mo 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Zachary Sylvan
3 Closed for Online Registration On-Line Only
CALCULUS II
MATH1102S002 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 Session Times/Location
MATH1102S002 002/10947 Summer B Subterm Mo 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Weitao Zhu
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
CALCULUS III
MATH1201S001 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 Session Times/Location
MATH1201S001 001/10277 Summer A Subterm Mo 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM
We 06:15 PM–07:50 PM
Tu 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Nathan Dowlin
3 Closed for Online Registration On-Line Only
CALCULUS III
MATH1201S002 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 Session Times/Location
MATH1201S002 002/10278 Summer A Subterm Mo 01:00 PM–02:35 PM
Tu 01:00 PM–02:35 PM
Th 01:00 PM–02:35 PM
We 01:00 PM–02:35 PM

Instructor Points Enrollment Method of Instruction
Andrew Ahn
3 Closed for Online Registration On-Line Only
CALCULUS III
MATH1201S003 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 Session Times/Location
MATH1201S003 003/10948 Summer B Subterm We 06:15 PM–07:50 PM
Mo 06:15 PM–07:50 PM
Tu 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Maithreya Sitaraman
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
CALCULUS III
MATH1201S004 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 Session Times/Location
MATH1201S004 004/12743 Summer B Subterm Mo 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Tomasz Owsiak
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
CALCULUS IV
MATH1202S001 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 Session Times/Location
MATH1202S001 001/10918 Summer A Subterm Mo 01:00 PM–02:35 PM
Tu 01:00 PM–02:35 PM
Th 01:00 PM–02:35 PM
We 01:00 PM–02:35 PM

Instructor Points Enrollment Method of Instruction
Juan Alvaro Munoz Echaniz
3 Closed for Online Registration On-Line Only
CALCULUS IV
MATH1202S002 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 Session Times/Location
MATH1202S002 002/10949 Summer B Subterm Mo 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Alexander Pieloch
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
LINEAR ALGEBRA
MATH2010S001 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 Session Times/Location
MATH2010S001 001/10279 Summer A Subterm Mo 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Gus Schrader
3 Closed for Online Registration On-Line Only
LINEAR ALGEBRA
MATH2010S002 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 Session Times/Location
MATH2010S002 002/10928 Full Trm Crs We 06:15 PM–07:50 PM
Mo 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Song Yu
3 Closed for Online Registration On-Line Only
LINEAR ALGEBRA
MATH2010S003 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 Session Times/Location
MATH2010S003 003/10952 Summer B Subterm We 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM
Mo 06:15 PM–07:50 PM
Tu 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Cheng Yu Tong
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
ORDINARY DIFFERENTIAL EQUATION
MATH2030V001 3 points.
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.
Course Number Section/Call Number Session Times/Location
MATH2030V001 001/10919 Summer A Subterm Mo 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Samuel DeHority
3 Closed for Online Registration On-Line Only
ORDINARY DIFFERENTIAL EQUATION
MATH2030V002 3 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.

Course Number Section/Call Number Session Times/Location
MATH2030V002 002/10954 Summer B Subterm Mo 04:30 PM–06:05 PM
Tu 04:30 PM–06:05 PM
We 04:30 PM–06:05 PM
Th 04:30 PM–06:05 PM

Instructor Points Enrollment Method of Instruction
Tsz Kiu Aaron Chow
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
ORDINARY DIFFERENTIAL EQUATION
MATH2030V003 3 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.

Course Number Section/Call Number Session Times/Location
MATH2030V003 003/12812 Summer A Subterm Mo 06:15 PM–07:50 PM
Tu 06:15 PM–07:50 PM
We 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Ka-Yi Ng
3 Closed for Online Registration On-Line Only
ANALYSIS AND OPTIMIZATION
MATH2500S001 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 Session Times/Location
MATH2500S001 001/10921 Summer A Subterm Tu 02:45 PM–04:20 PM
Th 02:45 PM–04:20 PM
Mo 02:45 PM–04:20 PM
We 02:45 PM–04:20 PM

Instructor Points Enrollment Method of Instruction
Nguyen Dung
3 Closed for Online Registration On-Line Only
NUMBER THEORY AND CRYPTOGRAPHY
MATH3020V001 3 points.
Prerequisites: one year of calculus. Prerequisite: One year of Calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications.
Course Number Section/Call Number Session Times/Location
MATH3020V001 001/10280 Summer A Subterm Th 01:00 PM–02:30 PM
Mo 01:00 PM–02:30 PM
We 01:00 PM–02:30 PM
Tu 01:00 PM–02:30 PM

Instructor Points Enrollment Method of Instruction
William Chen
3 Closed for Online Registration On-Line Only
SUPERVISED READINGS I
MATH3901S001 3 points.
Course Number Section/Call Number Session Times/Location
MATH3901S001 001/12966 Full Trm Crs
Instructor Points Enrollment Method of Instruction
Ivan Corwin
3 Closed for Online Registration On-Line Only
SUPERVISED READINGS I
MATH3901S002 3 points.
Course Number Section/Call Number Session Times/Location
MATH3901S002 002/14300 Summer A Subterm
Instructor Points Enrollment Method of Instruction
Ivan Corwin
3 Closed for Online Registration On-Line Only
SUPERVISED INDIVIDUAL RESEARCH
MATH3997V001 3 points.

Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies permission. For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member.

Course Number Section/Call Number Session Times/Location
MATH3997V001 001/00255 Summer B Subterm
Instructor Points Enrollment Method of Instruction
David Bayer
3 Closed for Online Registration
FOURIER ANALYSIS
MATH4032W001 3 points.
Prerequisites: three terms of calculus and linear algebra or four terms of calculus. Prerequisite: three terms of calculus and linear algebra or four terms of calculus. Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines.
Course Number Section/Call Number Session Times/Location
MATH4032W001 001/10281 Summer A Subterm Mo 02:45 PM–04:20 PM
Tu 02:45 PM–04:20 PM
We 02:45 PM–04:20 PM
Th 02:45 PM–04:20 PM

Instructor Points Enrollment Method of Instruction
Yash Jhaveri
3 Closed for Online Registration On-Line Only
ALGEBRAIC CURVES
MATH4045W001 3 points.
Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.
Course Number Section/Call Number Session Times/Location
MATH4045W001 001/10282 Summer A Subterm Th 10:45 AM–12:20 PM
Mo 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Akash Sengupta
3 Closed for Online Registration On-Line Only
INTRO TO MODERN ANALYSIS I
MATH4061S001 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 Session Times/Location
MATH4061S001 001/10923 Summer A Subterm Mo 09:00 AM–10:35 AM
Th 09:00 AM–10:35 AM
Tu 09:00 AM–10:35 AM
We 09:00 AM–10:35 AM

Instructor Points Enrollment Method of Instruction
Dobrin Marchev
3 Closed for Online Registration On-Line Only
INTRO TO MODERN ANALYSIS I
MATH4061S002 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 Session Times/Location
MATH4061S002 002/10929 Full Trm Crs Tu 06:15 PM–07:50 PM
Th 06:15 PM–07:50 PM

Instructor Points Enrollment Method of Instruction
Fabio Nironi
3 Closed for Online Registration On-Line Only
INTRO TO MODERN ANALYSIS II
MATH4062S001 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 Session Times/Location
MATH4062S001 001/10955 Summer B Subterm Mo 09:00 AM–10:35 AM
Th 09:00 AM–10:35 AM
Tu 09:00 AM–10:35 AM
We 09:00 AM–10:35 AM

Instructor Points Enrollment Method of Instruction
Dobrin Marchev
3 Open for Enrollment
(auto-fill waitlist)
On-Line Only
MAFN FIELDWORK
MATH5510G001 3 points.

Prerequisites: all 6 MAFN core courses, at least 6 credits of approved electives, and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.

Course Number Section/Call Number Session Times/Location
MATH5510G001 001/12288 Full Trm Crs
Instructor Points Enrollment Method of Instruction
Lars Nielsen
3 Closed for Online Registration On-Line Only