Program Overview

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Overview

The Department of Mathematics at Columbia University offers a range of undergraduate programs, including majors in Mathematics, Applied Mathematics, Computer Science-Mathematics, and Economics-Mathematics, as well as minors in Mathematics and Mathematical Probability.

Major in Mathematics

The major in Mathematics requires 40-42 points, including:

• One of the following three calculus and linear algebra sequences:
  • MATH UN1101, MATH UN1102, MATH UN1201, MATH UN1202, and MATH UN2010
  • MATH UN1101, MATH UN1102, MATH UN1205, and MATH UN2010
  • MATH UN1207 and MATH UN1208
• 12 points in the following courses:
  • MATH GU4041: Intro Modern Algebra I
  • MATH GU4042: Intro Modern Algebra II
  • MATH GU4061: Intro Modern Analysis I
  • MATH GU4062: Intro Modern Analysis II
• 3 points in the following:
  • MATH UN3951: Undergraduate Seminars I
  • MATH UN3952: Undergraduate Seminars II
• 12 points from the following:
  • Courses offered by the department numbered 2000 or higher
  • Approved cognate courses

Major in Applied Mathematics

The major in Applied Mathematics requires 37-41 points, including:

• One of the following three calculus and linear algebra sequences:
  • MATH UN1101, MATH UN1102, MATH UN1201, MATH UN1202, and MATH UN2010
  • MATH UN1101, MATH UN1102, MATH UN1205, and MATH UN2010
  • MATH UN1207 and MATH UN1208
• One of the following three courses:
  • MATH UN2500: Analysis and Optimization
  • MATH GU4032: Fourier Analysis
  • MATH GU4061: Intro Modern Analysis I
• APMA E4901: Sem-Prob in Applied Math (junior year)
• APMA E4903: Sem-Prob in Applied Math (senior year)
• 18 points in electives, with at least 9 points in Track A electives or at least 9 points in Track B electives

Major in Computer Science-Mathematics

The major in Computer Science-Mathematics requires:

• 20 points in computer science
• 19-21 points in mathematics
• Two 3-point electives in either computer science or mathematics

Major in Economics-Mathematics

For a description of the joint major in Economics-Mathematics, see the relevant section of the bulletin.

Major in Mathematics-Statistics

The major in Mathematics-Statistics requires 38-43 points, including:

• Select one of the following sequences:
  • MATH UN1101, MATH UN1102, MATH UN1201, MATH UN2010, and MATH UN2500
  • MATH UN1101, MATH UN1102, MATH UN1205, MATH UN2010, and MATH UN2500
  • MATH UN1207, MATH UN1208, and MATH UN2500
• STAT UN1201: Calc-Based Intro to Statistics
• STAT GU4203: Probability Theory
• STAT GU4204: Statistical Inference
• STAT GU4205: Linear Regression Models
• Select one of the following courses:
  • STAT GU4207: Elementary Stochastic Process
  • STAT GU4262: Stochastic Processes for Finance
  • STAT GU4264: Stochastic Processes-Applications I
  • STAT GU4265: Stochastic Methods in Finance
• Select one of the following courses:
  • COMS W1004: Programming in Java
  • COMS W1005: Intro-Comp Sci/Prog-Matlab
  • ENGI E1006: Intro to Comp for Eng/App Sci
• An approved selection of three advanced courses in mathematics, statistics, applied mathematics, industrial engineering and operations research, computer science, or approved mathematical methods courses in a quantitative discipline

Minor in Mathematics

The minor in Mathematics requires 15-17 points, including:

• Multivariable calculus
• Linear Algebra
• Three approved elective courses (at least 9 points), two of which must be 2000+ level courses offered by the Mathematics department

Minor in Mathematical Probability

The minor in Mathematical Probability requires 15-17 points, including:

• Multivariable calculus
• Linear Algebra
• Probability Theory
• Two approved elective courses (at least 6 points), at least one of which is an approved course offered by the Mathematics Department

Courses

The department offers a range of courses, including:

• MATH UN1003: College Algebra-Anlytc Geomtry
• MATH UN1101: Calculus I
• MATH UN1102: Calculus II
• MATH UN1201: Calculus III
• MATH UN1202: Calculus IV
• MATH UN1205: Accelerated Multivariable Calc
• MATH UN1207: Honors Mathematics A
• MATH UN1208: Honors Mathematics B
• MATH UN2000: Intro to Higher Mathematics
• MATH UN2010: Linear Algebra
• MATH UN2015: Linear Algebra and Probability
• MATH UN2030: Ordinary Differential Equations
• MATH UN2500: Analysis and Optimization
• MATH UN3007: Complex Variables
• MATH UN3020: Number Theory and Cryptography
• MATH UN3025: Making, Breaking Codes
• MATH UN3028: Partial Differential Equations
• MATH UN3050: Discrete Time Models in Financ
• MATH UN3386: Differential Geometry
• MATH UN3901: Supervised Readings I
• MATH UN3902: Supervised Readings II
• MATH UN3951: Undergraduate Seminars I
• MATH UN3952: Undergraduate Seminars II
• MATH UN3994: Senior Thesis in Mathematics I
• MATH UN3995: Senior Thesis in Mathematics II
• MATH GU4007: Analytic Number Theory
• MATH GU4032: Fourier Analysis
• MATH GU4041: Intro Modern Algebra I
• MATH GU4042: Intro Modern Algebra II
• MATH GU4043: Algebraic Number Theory
• MATH GU4044: Representatns of Finite Groups
• MATH GU4045: Algebraic Curves
• MATH GU4051: Topology
• MATH GU4052: Introduction to Knot Theory
• MATH GU4053: Intro to Algebraic Topology
• MATH GU4061: Intro Modern Analysis I
• MATH GU4062: Intro Modern Analysis II
• MATH GU4065: Honors Complex Variables
• MATH GU4081: Intro-Differentiable Manifolds
• MATH GU4155: Probability Theory
• MATH GU4156: Advanced Probability Theory
• MATH GU4391: Intro to Quantum Mechanics
• MATH GU4392: Intro to Quantum Mechanics II

Faculty

The department has a diverse faculty with expertise in various areas of mathematics, including:

• Andrew Blumberg
• Simon Brendle
• Ivan Corwin
• Panagiota Daskalopoulos
• Aise Johan de Jong
• Daniela De Silva (Barnard Chair)
• Julien Dubedat
• Robert Friedman
• Soren Galatius
• Dorian Goldfeld
• Brian Greene
• Michael Harris
• Ioannis Karatzas
• Chiu-Chu Liu (Department Chair)
• Dusa McDuff (Barnard)
• Andrei Okounkov
• D. H. Phong
• Ovidiu Savin
• Michael Thaddeus
• Eric Urban
• Mu-Tao Wang

Associate Professors

• Chao Li
• Francesco Lin

Assistant Professors

• Marco Castronovo (Barnard)
• Elena Giorgi
• Alisa Knizel (Barnard)
• Giulia Sacca
• Mehtaab Sawhney

J.F. Ritt Assistant Professors

• Rostislav Akhmechet
• Deeparaj Bhat
• Tommaso Botta
• Jeanne Boursier
• Myungsin Cho
• Qiao He
• Sven Hirsch
• Andres Ibanez Nunez
• Yoonjoo Kim
• Tang-Kai Lee
• Gyujin Oh
• Dawei Shen
• Evan Sorensen
• Roger Van Peski
• Anh Duc Vo
• Yujie Xu
• Lucy Yang
• Tianqing Zhu

Senior Lecturers in Discipline

• Jaehyuk Choi
• Mikhail Smirnov
• Peter Woit

Lecturers in Discipline

• George Dragomir

On Leave

• Fall 2025: Profs. Okounkov, Phong, Sacca, Woit
• Spring 2026: Profs. Okounkov, Sacca, Urban

Guidance for Undergraduate Students in Mathematics

The department provides guidance for undergraduate students, including:

• Placement in the Calculus Sequences
• Transfer Inside the Calculus Sequences
• Grading
• Double Counting
• Planning Forms
• Course Numbering Structure

Guidance for First-Year Students

The department provides guidance for first-year students, including:

• The systematic study of mathematics begins with one of the following three alternative calculus and linear algebra sequences:
  • MATH UN1101, MATH UN1102, MATH UN1201, MATH UN1202, and MATH UN2010
  • MATH UN1101, MATH UN1102, MATH UN1205, and MATH UN2010
  • MATH UN1207 and MATH UN1208

Guidance for Transfer Students

The department provides guidance for transfer students, including:

• Consideration for AP, IB, and transfer credit
• Equivalent courses for MATH UN1101, MATH UN1102, and MATH UN1201

Undergraduate Programs of Study

The department offers various undergraduate programs of study, including:

• Major in Mathematics
• Major in Applied Mathematics
• Major in Computer Science-Mathematics
• Major in Economics-Mathematics
• Major in Mathematics-Statistics
• Minor in Mathematics
• Minor in Mathematical Probability

Concentration in Mathematics

The concentration in Mathematics requires:

• Multivariable calculus and linear algebra
• Additional courses in mathematics

Department Honors and Prizes

The department offers various honors and prizes, including:

• Department Honors
• Academic Prizes
  • Putnam Exam
  • Columbia Prizes
    • Professor Van Amringe Mathematical Prize
    • John Dash Van Buren Jr. Prize in Mathematics

Other Important Information

The department provides other important information, including:

• Student Advising
• Enrolling in Classes
• Preparing for Graduate Study
• Coursework Taken Outside of Columbia
• Advanced Placement
• Barnard College Courses
• Transfer Courses
• Study Abroad Courses
• Summer Courses
• Undergraduate Research and Senior Thesis
• Undergraduate Research Outside of Courses
• Department Honors and Prizes
• Other Important Information

For Students Who Entered Columbia in or Before the 2022-2023 Academic Year

The department provides information for students who entered Columbia in or before the 2022-2023 academic year, including:

• Concentration in Mathematics
• Major in Mathematics
• Major in Applied Mathematics
• Major in Computer Science-Mathematics
• Major in Economics-Mathematics
• Major in Mathematics-Statistics
• Minor in Mathematics
• Minor in Mathematical Probability