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.

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

Summer 2022 Session Information

  • SESSION A (First Half Term) courses are May 23–July 1, 2022
  • SESSION B (Second Half Term) courses are July 5–August 12, 2022
  • SESSION X (Full Term) courses are May 23–August 12, 2022
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 001/10022 Session A 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 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10023 Session B Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Penka Marinova
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10024 Session A Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Georgy Gaitsgori
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 002/10025 Session B 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
Tomasz Owsiak
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 003/10026 X Summer Session 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
(no Adds or Drops)
In-Person
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 001/10027 Session A 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
Chuwen Wang
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 002/10028 Session B Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Emily Saunders
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10029 Session A Mo 01:00 PM–02:35 PM
Tu 01:00 PM–02:35 PM
We 01:00 PM–02:35 PM
Th 01:00 PM–02:35 PM

Instructor Points Enrollment Method of Instruction
Nikolaos Apostolakis
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 002/10030 Session B Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Roy Magen
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10031 Session A 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
Zoe Margaret Himwich
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 002/10032 Session B Mo 01:00 PM–02:35 PM
Tu 01:00 PM–02:35 PM
We 01:00 PM–02:35 PM
Th 01:00 PM–02:35 PM

Instructor Points Enrollment Method of Instruction
Luis Fernandez
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10033 Session A Mo 09:00 AM–10:35 AM
Tu 09:00 AM–10:35 AM
We 09:00 AM–10:35 AM
Th 09:00 AM–10:35 AM

Instructor Points Enrollment Method of Instruction
Lea Kenigsberg
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 002/10034 Session B 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
Alvaro Martinez Ruiz
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 003/10035 X Summer Session 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
(no Adds or Drops)
In-Person
Linear Algebra and Probability
MATH2015W001 3 points.

MATH UN2015 features linear algebra with a focus on probability and statistics. The course covers the standard linear algebra topics: systems of linear equations, matrices, determinants, vector spaces, bases, dimension, eigenvalues and eigenvectors. It also teaches applications of linear algebra to probability, statistics and dynamical systems giving a background sufficient for higher level courses in probability and statistics. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, probability distributions and the limit theorems, as well as Markov chains, curve fitting, regression, and pattern analysis. The course contains applications to life sciences, chemistry, and environmental life sciences. No a prior i background in the life sciences is assumed.

This course is best suited for students who wish to focus on applications and practical approach to problem solving, rather than abstract mathematics and mathematical proofs. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics. Students majoring in mathematics should take MATH UN2010 - Linear Algebra, which focuses on linear algebra concepts, and provides an introduction to writing mathematical proofs.

Course Number Section/Call Number Session Times/Location
MATH2015W001 001/10635 Session A Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
George Dragomir
3 Open for Enrollment
(auto-fill Wait List)
In-Person
ORDINARY DIFFERENTIAL EQUATIONS
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 001/10636 Session A 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
Tomasz Owsiak
3 Open for Enrollment
(auto-fill Wait List)
In-Person
ORDINARY DIFFERENTIAL EQUATIONS
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 002/10637 Session B 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
Tat Sang Fung
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10036 Session A Mo 09:00 AM–10:35 AM
Tu 09:00 AM–10:35 AM
We 09:00 AM–10:35 AM
Th 09:00 AM–10:35 AM

Instructor Points Enrollment Method of Instruction
Jorge Pineiro Barcelo
3 Open for Enrollment
(auto-fill Wait List)
In-Person
SUPERVISED READINGS I
MATH3901S001 3 points.
Course Number Section/Call Number Session Times/Location
MATH3901S001 001/12559 Session B
Instructor Points Enrollment Method of Instruction
Inbar Klang
3 Registration Block
(no Adds)
(self-man. Wait List)
In-Person
SUPERVISED READINGS I
MATH3901S002 3 points.
Course Number Section/Call Number Session Times/Location
MATH3901S002 002/13341 X Summer Session
Instructor Points Enrollment Method of Instruction
George Dragomir
3 Closed for Online Registration
(no Adds or Drops)
In-Person
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 001/10037 Session A Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Dobrin Marchev
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10038 Session B Mo 10:45 AM–12:20 PM
Tu 10:45 AM–12:20 PM
We 10:45 AM–12:20 PM
Th 10:45 AM–12:20 PM

Instructor Points Enrollment Method of Instruction
Peyam Tabrizian
3 Open for Enrollment
(auto-fill Wait List)
In-Person
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 001/10039 X Summer Session
Instructor Points Enrollment Method of Instruction
Lars Nielsen
Martyna Grazda
3 Closed for Online Registration
(no Adds or Drops)
In-Person