Chair:  Daniela De Silva (Professor)
Professors:  Dave Bayer, Daniela De Silva, Dusa McDuff (Helen Lyttle Kimmel Chair), Walter Neumann 
Term Assistant Professor: Lindsay Piechnik
Research Professor and Professor Emerita: Joan Birman

Links to other faculty of Columbia University offering courses in Mathematics:

Faculty by Rank:  http://www.math.columbia.edu/people/faculty-by-rank/

Alphabetical Faculty Listing:  http://www.math.columbia.edu/people/alphabetical-faculty-listing/

Requirements for the Major

The major programs in both Mathematics and Applied Mathematics are appropriate for students who plan to continue their training in graduate school. The major in Mathematical Sciences combines the elements of Mathematics, Computer Science and Statistics. It is designed to prepare students for employment in business, administration, and finance, and also give excellent background for someone planning graduate study in a social science field. Students who plan to obtain a teaching qualification in mathematics should plan their course of study carefully with an advisor, since courses that are too far from mathematics do not count towards certification.

For a major in Mathematics: 14 courses as follows:

Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit. Six courses in mathematics numbered at or above 2000, and four courses in any combination of mathematics and cognate courses. The courses in mathematics must include:

MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH GU4041INTRO MODERN ALGEBRA I (I)
MATH GU4042INTRO MODERN ALGEBRA II (II)
MATH GU4061INTRO MODERN ANALYSIS I (I)
MATH GU4062INTRO MODERN ANALYSIS II (II)
MATH UN3951Undergraduate Seminars in Mathematics I (at least one term)
or MATH UN3952 Undergraduate Seminars in Mathematics II

However, students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH GU4061 INTRO MODERN ANALYSIS I - MATH GU4062 INTRO MODERN ANALYSIS II by one or two of the following courses: MATH UN2500 ANALYSIS AND OPTIMIZATION, MATH UN3007 Complex Variables, or MATH GU4032 Fourier Analysis and may replace MATH GU4042 INTRO MODERN ALGEBRA II by one of MATH UN3020 Number Theory and Cryptography or MATH UN3025 Making, Breaking Codes. In exceptional cases, the chair will approve the substitution of certain more advanced courses for those mentioned above.

For a major in Applied Mathematics: 14 courses

Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit.

MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH GU4061INTRO MODERN ANALYSIS I
APMA E4901Seminar: Problem in Applied Mathematics
APMA E4903Seminar: Problems in Applied Mathematics
APMA E3900Undergraduate Research in Applied Mathematics (APMA E3900 may be replaced, with approval, by another technical elective for seniors that involves an undergraduate thesis or creative research report)

Additional electives, to be approved by the Applied Math Committee, e.g.:

MATH UN2500ANALYSIS AND OPTIMIZATION
MATH UN3007Complex Variables
or MATH GU4065 Honors Complex Variables
or APMA E4204 Functions of a Complex Variable
MATH UN3027Ordinary Differential Equations
or MATH UN2030 ORDINARY DIFFERENTIAL EQUATION
MATH UN3028PARTIAL DIFFERENTIAL EQUATIONS
or APMA E4200 Partial Differential Equations
MATH GU4032Fourier Analysis
APMA E4300Computational Math: Introduction to Numerical Methods
APMA E4101Introduction to Dynamical Systems
APMA E4150Applied Functional Analysis

For a major in Mathematical Sciences: 14 courses:

6 from Mathematics, 5 from a combination of Statistics and Computer Science and 3 electives from a combination of Mathematics, Statistics, Computer Science.

Mathematics
Six required courses:
MATH UN1101CALCULUS I
MATH UN1102CALCULUS II
MATH UN1201Calculus III
MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH UN2000INTRO TO HIGHER MATHEMATICS
MATH UN2030ORDINARY DIFFERENTIAL EQUATION
or MATH UN3027 Ordinary Differential Equations
Possible further courses selected from the following:
MATH UN1202CALCULUS IV
MATH UN2500ANALYSIS AND OPTIMIZATION
MATH UN3020Number Theory and Cryptography
MATH UN3025Making, Breaking Codes
Any 3 credit MATH course numbered 2000 or above
Statistics
Select at least one of the following:
STAT UN1101Introduction to Statistics
STAT UN1201Calculus-Based Introduction to Statistics
or equivalent
Other courses from the Statistics list (eg, STAT UN2102, STAT UN2103, STAT UN2104, STAT UN3105, STAT UN3106)
Computer Science
Select at least one of the following programming courses:
COMS W1002Computing in Context
COMS W1004Introduction to Computer Science and Programming in Java (preferred)
COMS W1005Introduction to Computer Science and Programming in MATLAB
COMS W1007Honors Introduction to Computer Science
Possible further courses selected from the following:
Other classes from the Computer Science Core
COMS W3203DISCRETE MATHEMATICS
COMS W3210Scientific Computation
ENGI E1006Introduction to Computing for Engineers and Applied Scientists

More generally, electives may be any course with a prerequisite of at least one semester of Calculus, Statistics or Computer Science with the prior approval of the Mathematics Chair.

The Capstone Experience can be fulfilled by a significant thesis written under the supervision of faculty of any one of the three departments or by the Undergraduate Seminar in Mathematics.

For a major in Mathematics-Statistics: 14 courses:

Mathematics
Select one of the following sequences:
MATH UN1101
 - MATH UN1102
 - MATH UN1201
 - MATH UN2010
 - MATH UN2500
CALCULUS I
and CALCULUS II
and Calculus III
and LINEAR ALGEBRA
and ANALYSIS AND OPTIMIZATION
MATH UN1207
 - MATH UN1208
 - MATH UN2500
Honors Mathematics A
and Honors Mathematics B
and ANALYSIS AND OPTIMIZATION
Statistics
Statistics required courses
STAT UN1201Calculus-Based Introduction to Statistics
STAT GU4203PROBABILITY THEORY
STAT GU4204Statistical Inference
STAT GU4205Linear Regression Models
And select one of the following courses:
STAT GU4207Elementary Stochastic Processes
STAT GU4262Stochastic Processes for Finance
STAT GU4264STOCHASTC PROCSSES-APPLIC
STAT GU4265Stochastic Methods in Finance
Computer Science
Select one of the following courses:
COMS W1004Introduction to Computer Science and Programming in Java
COMS W1005Introduction to Computer Science and Programming in MATLAB
COMS W1007Honors Introduction to Computer Science
ENGI E1006Introduction to Computing for Engineers and Applied Scientists
or an advanced Computer Science offering in programming
Electives
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. At least one elective must be a Mathematics Department course numbered 3000 or above.

Students should plan to include a senior thesis or the Undergraduate Seminar in Mathematics in their program, in consultation with their advisors.

Note: Students must obtain approval from an adviser in each of the two departments before selecting electives. Students should take MATH UN2010 LINEAR ALGEBRA in the second semester of the second year. 

For a major in Mathematics-Computer Science 15 courses:

Mathematics
Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit; and the 3 following courses:
MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH GU4041INTRO MODERN ALGEBRA I
MATH UN3951Undergraduate Seminars in Mathematics I (at least one term)
or MATH UN3952 Undergraduate Seminars in Mathematics II
Computer Science
COMS W1004Introduction to Computer Science and Programming in Java
COMS W3134Data Structures in Java
COMS W3157Advanced Programming
COMS W3203DISCRETE MATHEMATICS
COMS W3261Computer Science Theory
CSEE W3827Fundamentals of Computer Systems

Note A: AP Computer Science with a grade of 4 or 5 or similar experience (e.g., COMS W1004) is a prerequisite for COMS W1007

Electives: 2 of the following:
CSOR W4231Analysis of Algorithms I
COMS W4241Numerical Algorithms and Complexity
MATH UN3020Number Theory and Cryptography
MATH BC2006Combinatorics
MATH GU4061INTRO MODERN ANALYSIS I
MATH UN2500ANALYSIS AND OPTIMIZATION
MATH UN3007Complex Variables
MATH UN3386Differential Geometry
MATH GU4051Topology

Students seeking to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.

For a major in Economics and Mathematics, see the catalogue.

Requirement for the Minor in Mathematics

For a minor in Mathematics or Applied Mathematics: Six courses from any of the courses offered by the department except MATH UN1003 College Algebra and Analytic Geometry, MATH UN1101 CALCULUS I / MATH UN1102 CALCULUS II. Some cognate courses are also acceptable with prior approval from the department chair.

Requirements for the Minor in Mathematical Sciences

The minor in Mathematical Sciences comprises 6 courses, at least two from Mathematics and one from each of Statistics and Computer Science. There should be a minimum of three courses in Statistics and Computer Science. Eligible courses are any listed in the Mathematical Sciences Major with the exception of Calculus I and II.

MATH UN1003 College Algebra and Analytic Geometry. 3 points.

Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year or the appropriate grade on the General Studies Mathematics Placement Examination.

Columbia College students do not receive any credit for this course and must see their CSA advising dean. For students who wish to study calculus but do not know analytic geometry. 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.

Fall 2020: MATH UN1003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1003 001/11290 M W 6:10pm - 7:25pm
Online Only
Alexander Pieloch 3 19/30
MATH 1003 002/11291 T Th 2:40pm - 3:55pm
Online Only
Mrudul Thatte 3 18/30
Spring 2021: MATH UN1003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1003 001/12309 M W 1:10pm - 2:25pm
Online Only
Nguyen Dung 3 15/35
MATH 1003 002/12310 T Th 6:10pm - 7:25pm
Online Only
Shalin Parekh 3 17/35
MATH 1003 AU1/19220  
Nguyen Dung 3 0/5
MATH 1003 AU2/19221  
Shalin Parekh 3 0/5

MATH UN1101 CALCULUS I. 3.00 points.

Prerequisites: (see Courses for First-Year Students). Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed. (SC)

Fall 2020: MATH UN1101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1101 002/11292 M W 10:10am - 11:25am
Online Only
Daniele Alessandrini 3.00 28/116
MATH 1101 003/11293 M W 11:40am - 12:55pm
Online Only
Daniele Alessandrini 3.00 40/116
MATH 1101 004/11294 M W 1:10pm - 2:25pm
Online Only
Akash Sengupta 3.00 110/120
MATH 1101 005/11295 M W 2:40pm - 3:55pm
Online Only
Akash Sengupta 3.00 114/120
MATH 1101 006/11296 M W 4:10pm - 5:25pm
Online Only
Chung Hang Kwan 3.00 37/40
MATH 1101 007/11297 T Th 10:10am - 11:25am
Online Only
George Dragomir 3.00 79/110
MATH 1101 008/11298 T Th 2:40pm - 3:55pm
Online Only
Robin Zhang 3.00 33/40
MATH 1101 009/11299 T Th 1:10pm - 2:25pm
Online Only
George Dragomir 3.00 89/120
MATH 1101 012/21307 T Th 11:40am - 12:55pm
Online Only
Panagiota Daskalopoulos 3.00 69/100
Spring 2021: MATH UN1101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1101 001/12308 M W 2:40pm - 3:55pm
Online Only
Sayan Das 3.00 13/35
MATH 1101 002/12307 M W 4:10pm - 5:25pm
Online Only
Kevin Smith 3.00 16/35
MATH 1101 003/12306 T Th 10:10am - 11:25am
Online Only
Panagiota Daskalopoulos 3.00 89/100
MATH 1101 004/12305 T Th 11:40am - 12:55pm
Online Only
George Dragomir 3.00 87/100
MATH 1101 005/12304 T Th 4:10pm - 5:25pm
Online Only
0. FACULTY 3.00 37/100
MATH 1101 AU1/19222  
Sayan Das 3.00 0/5
MATH 1101 AU2/19223  
Kevin Smith 3.00 0/5
MATH 1101 AU3/19224  
Panagiota Daskalopoulos 3.00 0/5
MATH 1101 AU5/19225  
3.00 0/5

MATH UN1102 CALCULUS II. 3.00 points.

Prerequisites: MATH UN1101 or the equivalent.
Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Fall 2020: MATH UN1102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1102 001/11302 M W 11:40am - 12:55pm
Online Only
Maithreya Sitaraman 3.00 16/30
MATH 1102 002/11303 M W 2:40pm - 3:55pm
Online Only
Zachary Sylvan 3.00 94/100
MATH 1102 003/11304 M W 4:10pm - 5:25pm
Online Only
Zachary Sylvan 3.00 40/110
MATH 1102 005/00434 T Th 2:40pm - 3:55pm
Room TBA
Lindsay Piechnik 3.00 95/100
MATH 1102 006/11306 T Th 6:10pm - 7:25pm
Online Only
Elliott Stein 3.00 38/45
MATH 1102 007/21402 T Th 11:40am - 12:55pm
Online Only
Renata Picciotto 3.00 30/33
Spring 2021: MATH UN1102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1102 001/12303 M W 11:40am - 12:55pm
Online Only
Maithreya Sitaraman 3.00 13/35
MATH 1102 002/12302 M W 4:10pm - 5:25pm
Online Only
Yier Lin 3.00 8/35
MATH 1102 003/12301 T Th 11:40am - 12:55pm
Online Only
Evgeni Dimitrov 3.00 88/100
MATH 1102 004/12300 T Th 1:10pm - 2:25pm
Online Only
Evgeni Dimitrov 3.00 75/100
MATH 1102 AU1/19280  
Maithreya Sitaraman 3.00 0/5
MATH 1102 AU2/19281  
Yier Lin 3.00 0/5

MATH UN1201 Calculus III. 3 points.

Prerequisites: MATH UN1101 or the equivalent

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. (SC) 

Fall 2020: MATH UN1201
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1201 001/11389 M W 10:10am - 11:25am
Online Only
Konstantin Aleshkin 3 49/110
MATH 1201 002/11390 M W 11:40am - 12:55pm
Online Only
Konstantin Aleshkin 3 38/110
MATH 1201 003/11394 M W 1:10pm - 2:25pm
Online Only
Ovidiu Savin 3 45/110
MATH 1201 004/11398 T Th 10:10am - 11:25am
Online Only
Carolyn Abbott 3 110/116
MATH 1201 005/11402 T Th 11:40am - 12:55pm
Online Only
Evan Warner 3 84/116
MATH 1201 006/11407 T Th 2:40pm - 3:55pm
Online Only
Inbar Klang 3 98/100
MATH 1201 007/11412 T Th 4:10pm - 5:25pm
Online Only
Inbar Klang 3 98/100
Spring 2021: MATH UN1201
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1201 001/12299 M W 10:10am - 11:25am
Online Only
Nicholas Salter 3 57/100
MATH 1201 002/12298 M W 11:40am - 12:55pm
Online Only
Nicholas Salter 3 89/100
MATH 1201 003/12297 M W 1:10pm - 2:25pm
Online Only
Mu-Tao Wang 3 18/100
MATH 1201 004/12296 T Th 2:40pm - 3:55pm
Online Only
Andrew Ahn 3 48/100
MATH 1201 005/00082 T Th 4:10pm - 5:25pm
Room TBA
Lindsay Piechnik 3 100/100
MATH 1201 006/00083 T Th 6:10pm - 7:25pm
Room TBA
Lindsay Piechnik 3 88/100
MATH 1201 AU1/19226  
3 0/5
MATH 1201 AU3/19227  
Mu-Tao Wang 3 0/5
MATH 1201 AU4/19228  
Andrew Ahn 3 0/5

MATH UN1202 CALCULUS IV. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent Multiple integrals, Taylor's formula in several variables, line and surface integrals, calculus of vector fields, Fourier series. (SC)

Fall 2020: MATH UN1202
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1202 001/11421 T Th 10:10am - 11:25am
Online Only
Stephen Miller 3.00 33/64
MATH 1202 002/11424 M W 6:10pm - 7:25pm
Online Only
Mikhail Smirnov 3.00 26/116
Spring 2021: MATH UN1202
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1202 001/00084 T Th 10:10am - 11:25am
Room TBA
Daniela De Silva 3.00 37/100
MATH 1202 002/00085 T Th 1:10pm - 2:25pm
Room TBA
Daniela De Silva 3.00 52/100
MATH 1202 AU1/19282  
3.00 0/5
MATH 1202 AU2/19283  
Daniela De Silva 3.00 0/5

MATH UN1207 Honors Mathematics A. 4 points.

Prerequisites:  (see Courses for First-Year Students).  The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)

Fall 2020: MATH UN1207
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1207 001/11430 T Th 1:10pm - 2:25pm
Online Only
Evan Warner 4 55/110

MATH UN1208 Honors Mathematics B. 4 points.

Prerequisites: (see Courses for First-Year Students).

The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)

Spring 2021: MATH UN1208
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1208 001/12294 T Th 1:10pm - 2:25pm
Online Only
Evan Warner 4 41/100

MATH UN2000 INTRO TO HIGHER MATHEMATICS. 3.00 points.

Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)

Fall 2020: MATH UN2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2000 001/11446 M W 10:10am - 11:25am
Online Only
Dusa McDuff 3.00 32/49
Spring 2021: MATH UN2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2000 001/12293 M W 10:10am - 11:25am
Online Only
Gus Schrader 3.00 38/100
MATH 2000 AU1/19229  
Gus Schrader 3.00 0/5

MATH BC2001 Perspectives in Mathematics. 1 point.

Prerequisites: some calculus or the instructor's permission.

Intended as an enrichment to the mathemathics curriculum of the first years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.

MATH BC2006 Combinatorics. 3 points.

Corequisites: MATH V2010 is helpful as a corequisite, but not required.

Honors-level introductory course in enumerative combinatorics. Pigeonhole principle, binomial coefficients, permutations and combinations. Polya enumeration, inclusion-exclusion principle, generating functions and recurrence relations.

Spring 2021: MATH BC2006
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2006 001/00086 T Th 10:10am - 11:25am
Room TBA
David Bayer 3 29/40

MATH UN2010 LINEAR ALGEBRA. 3.00 points.

Prerequisites: MATH UN1201 or the equivalent.
Prerequisites: MATH UN1201 or the equivalent. Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

Fall 2020: MATH UN2010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2010 001/00117 T Th 8:40am - 9:55am
Room TBA
David Bayer 3.00 22/100
MATH 2010 002/00118 T Th 10:10am - 11:25am
Room TBA
David Bayer 3.00 34/100
MATH 2010 003/11450 M W 4:10pm - 5:25pm
Online Only
Francesco Lin 3.00 75/100
MATH 2010 004/11453 M W 11:40am - 12:55pm
Online Only
Kyle Hayden 3.00 90/100
MATH 2010 005/11455 M W 8:40am - 9:55am
Online Only
Giulia Sacca 3.00 44/100
Spring 2021: MATH UN2010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2010 001/12292 M W 10:10am - 11:25am
Online Only
Konstantin Aleshkin 3.00 29/100
MATH 2010 002/12291 M W 1:10pm - 2:25pm
Online Only
Gus Schrader 3.00 100/100
MATH 2010 003/12290 T Th 11:40am - 12:55pm
Online Only
Stephen Miller 3.00 88/100
MATH 2010 004/12289 T Th 1:10pm - 2:25pm
Online Only
Andrew Ahn 3.00 21/100
MATH 2010 005/12288 T Th 6:10pm - 7:25pm
Online Only
Elliott Stein 3.00 35/45
MATH 2010 AU1/19230  
Konstantin Aleshkin 3.00 0/5
MATH 2010 AU4/19231  
Andrew Ahn 3.00 0/5

MATH UN2020 Honors Linear Algebra. 3 points.

Not offered during 2020-21 academic year.

Prerequisites: MATH UN1201 A more extensive treatment of the material in MATH UN2010, with increased emphasis on proof. Not to be taken in addition to MATH UN2010 or MATH UN1207-MATH UN1208.

MATH UN2030 ORDINARY DIFFERENTIAL EQUATION. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.
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

Fall 2020: MATH UN2030
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2030 001/11457 M W 1:10pm - 2:25pm
Online Only
Florian Johne 3.00 48/116
MATH 2030 002/11461 M W 2:40pm - 3:55pm
Online Only
Florian Johne 3.00 29/116
Spring 2021: MATH UN2030
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2030 001/12287 M W 2:40pm - 3:55pm
Online Only
Igor Krichever 3.00 100/100
MATH 2030 002/12286 T Th 10:10am - 11:25am
Online Only
0. FACULTY 3.00 34/100
MATH 2030 AU2/19232  
3.00 0/5

MATH UN2500 ANALYSIS AND OPTIMIZATION. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010.
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010. 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. (SC)

Fall 2020: MATH UN2500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2500 001/11464 T Th 1:10pm - 2:25pm
Online Only
Kanstantsin Matetski 3.00 28/64
MATH 2500 002/11466 T Th 2:40pm - 3:55pm
Online Only
Kanstantsin Matetski 3.00 38/64
Spring 2021: MATH UN2500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2500 001/12285 M W 1:10pm - 2:25pm
Online Only
Yash Jhaveri 3.00 57/100
MATH 2500 002/12284 M W 2:40pm - 3:55pm
Online Only
Yash Jhaveri 3.00 51/100
MATH 2500 AU1/19233  
3.00 0/5
MATH 2500 AU2/19234  
3.00 0/5

MATH UN3007 Complex Variables. 3 points.

Prerequisites: MATH UN1202 An elementary course in functions of a complex variable.

Fundamental properties of the complex numbers, differentiability, Cauchy-Riemann equations. Cauchy integral theorem. Taylor and Laurent series, poles, and essential singularities. Residue theorem and conformal mapping.(SC)

Fall 2020: MATH UN3007
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3007 001/11470 M W 2:40pm - 3:55pm
Online Only
Nicholas Salter 3 57/64

MATH UN3020 Number Theory and Cryptography. 3 points.

Prerequisites: one year of calculus.

Prerequisite: One year of Calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications.

MATH UN3025 Making, Breaking Codes. 3 points.

Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and and MATH UN2010.

A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory.

Fall 2020: MATH UN3025
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3025 001/11471 T Th 1:10pm - 2:25pm
Online Only
Dorian Goldfeld 3 83/116

MATH UN3027 Ordinary Differential Equations. 3 points.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.
Corequisites: MATH UN2010

Equations of order one; systems of linear equations. Second-order equations. Series solutions at regular and singular points. Boundary value problems. Selected applications. 

Fall 2020: MATH UN3027
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3027 001/11478 T Th 11:40am - 12:55pm
Online Only
Simon Brendle 3 32/116

MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS. 3.00 points.

Prerequisites: MATH UN3027 and MATH UN2010 or the equivalent
Prerequisites: MATH UN3027 and MATH UN2010 or the equivalent Introduction to partial differential equations. First-order equations. Linear second-order equations; separation of variables, solution by series expansions. Boundary value problems

Spring 2021: MATH UN3028
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3028 001/12282 M W 1:10pm - 2:25pm
Online Only
Florian Johne 3.00 82/100
MATH 3028 AU1/19235  
Florian Johne 3.00 0/5

MATH UN3050 Discrete Time Models in Finance. 3 points.

Prerequisites: (MATH UN1102 and MATH UN1201) or (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH UN2010 Recommended: MATH UN3027 (or MATH UN2030 and SIEO W3600).

Elementary discrete time methods for pricing financial instruments, such as options. Notions of arbitrage, risk-neutral valuation, hedging, term-structure of interest rates.

Spring 2021: MATH UN3050
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3050 001/13870 M W 6:10pm - 7:25pm
312 Mathematics Building
Mikhail Smirnov 3 60/60

MATH UN3386 Differential Geometry. 3 points.

Prerequisites: MATH UN1202 or the equivalent.

Local and global differential geometry of submanifolds of Euclidiean 3-space. Frenet formulas for curves. Various types of curvatures for curves and surfaces and their relations. The Gauss-Bonnet theorem.

Fall 2020: MATH UN3386
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3386 001/11484 T Th 11:40am - 12:55pm
Online Only
Richard Hamilton 3 25/49

MATH UN3901 Supervised Readings in Mathematics I. 2-3 points.

Prerequisites: The written permission of the staff member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the Director of Undergraduate Studies.  The written permission must be deposited with the Director of Undergraduate Studies before registration is completed.  Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.

Fall 2020: MATH UN3901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3901 001/24553  
Dorian Goldfeld 2-3 1/2
MATH 3901 002/24556  
Dusa McDuff 2-3 2/2
MATH 3901 003/24704  
Francesco Lin 2-3 1/2
MATH 3901 004/24705  
Ivan Corwin 2-3 1/2
MATH 3901 005/24834  
David Bayer 2-3 1/1
MATH 3901 006/24915  
Ovidiu Savin 2-3 3/3
MATH 3901 007/25035  
Stephen Miller 2-3 2/1

MATH UN3902 Supervised Readings in Mathematics II. 2-3 points.

Prerequisites: The written permission of the staff member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the Director of Undergraduate Studies.  The written permission must be deposited with the Director of Undergraduate Studies before registration is completed.  Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.

Spring 2021: MATH UN3902
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3902 001/17763  
Dusa McDuff 2-3 1/1
MATH 3902 002/17765  
Francesco Lin 2-3 1/1
MATH 3902 003/19327  
Dorian Goldfeld 2-3 1/1
MATH 3902 004/19328  
Guillaume Remy 2-3 1/1
MATH 3902 005/19366  
Ivan Corwin 2-3 1/2

MATH UN3951 Undergraduate Seminars in Mathematics I. 3 points.

Prerequisites: Two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.

Fall 2020: MATH UN3951
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3951 001/00120  
Daniela De Silva 3 31/64
MATH 3951 002/00121 M W 6:10pm - 7:25pm
Room TBA
Lindsay Piechnik 3 7/15

MATH UN3952 Undergraduate Seminars in Mathematics II. 3 points.

Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow. Prerequisite: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

Spring 2021: MATH UN3952
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3952 001/00688  
David Bayer 3 30/60

MATH UN3997 Supervised Individual Research. 3 points.

Prerequisites: The written permission of the faculty member who agrees to act as a supervisor, and the permission of the Director of Undergraduate Studies.  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.

Fall 2020: MATH UN3997
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3997 001/00976  
Daniela De Silva 3 1/1

MATH UN3998 Supervised Individual Research. 3 points.

Prerequisites: The written permission of the faculty member who agrees to act as a supervisor, and the permission of the Director of Undergraduate Studies. 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.

MATH GU4007 Analytic Number Theory. 3 points.

Prerequisites: MATH UN3007

A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.

Spring 2021: MATH GU4007
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4007 001/12281 T Th 11:40am - 12:55pm
Online Only
Dorian Goldfeld 3 22/50

MATH GU4032 Fourier Analysis. 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. 

MATH GU4041 INTRO MODERN ALGEBRA I. 3 points.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent

The second term of this course may not be taken without the first. Groups, homomorphisms, rings, ideals, fields, polynomials, field extensions, Galois theory.

Fall 2020: MATH GU4041
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4041 001/11487 M W 2:40pm - 3:55pm
Online Only
Robert Friedman 3 65/110
Spring 2021: MATH GU4041
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4041 001/12280 M W 10:10am - 11:25am
Online Only
Daniele Alessandrini 3 42/100
MATH 4041 AU1/19290  
Daniele Alessandrini 3 0/5

MATH GU4042 INTRO MODERN ALGEBRA II. 3 points.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent.

The second term of this course may not be taken without the first. Rings, homomorphisms, ideals, integral and Euclidean domains, the division algorithm, principal ideal and unique factorization domains, fields, algebraic and transcendental extensions, splitting fields, finite fields, Galois theory.

Fall 2020: MATH GU4042
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4042 001/11488 M W 1:10pm - 2:25pm
Online Only
Mikhail Khovanov 3 12/35
Spring 2021: MATH GU4042
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4042 001/12279 M W 2:40pm - 3:55pm
Online Only
Inbar Klang 3 52/100
MATH 4042 AU1/19291  
Inbar Klang 3 0/5

MATH GU4043 Algebraic Number Theory. 3 points.

Prerequisites: MATH GU4041 and MATH GU4042 or the equivalent

Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function.

MATH GU4044 Representations of Finite Groups. 3 points.

Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent.

Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups.

Fall 2020: MATH GU4044
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4044 001/11490 T Th 1:10pm - 2:25pm
Online Only
Chao Li 3 10/19

MATH GU4045 Algebraic Curves. 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.

MATH W4046 Introduction to Category Theory. 3 points.

CC/GS: Partial Fulfillment of Science Requirement
Not offered during 2020-21 academic year.

Prerequisites: MATH W4041.

Categories, functors, natural transformations, adjoint functors, limits and colimits, introduction to higher categories and diagrammatic methods in algebra.

MATH GU4051 Topology. 3 points.

Prerequisites: (MATH UN1202 and MATH UN2010) and rudiments of group theory (e.g., MATH GU4041). MATH UN1208 or MATH GU4061 is recommended, but not required.

Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.

Fall 2020: MATH GU4051
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4051 001/11491 T Th 11:40am - 12:55pm
Online Only
Stephen Miller 3 27/64

MATH GU4052 Introduction to Knot Theory. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: MATH GU4051 Topology and / or MATH GU4061 Introduction To Modern Analysis I (or equivalents). Recommended (can be taken concurrently): MATH UN2010 linear algebra, or equivalent.

The study of algebraic and geometric properties of knots in R^3, including but not limited to knot projections and Reidemeister's theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants.

MATH GU4053 Introduction to Algebraic Topology. 3 points.

Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051

The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces.

MATH GU4061 INTRO MODERN ANALYSIS I. 3 points.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, Ascoli-Arzela theorem, Stone-Weierstrass theorem.

Fall 2020: MATH GU4061
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4061 001/11494 T Th 2:40pm - 3:55pm
Online Only
Henri Roesch 3 34/100
MATH 4061 002/11495 T Th 4:10pm - 5:25pm
Online Only
Henri Roesch 3 30/100
Spring 2021: MATH GU4061
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4061 001/12278 M W 1:10pm - 2:25pm
Online Only
Hui Yu 3 50/100
MATH 4061 002/12277 M W 4:10pm - 5:25pm
Online Only
Hui Yu 3 45/100

MATH GU4062 INTRO MODERN ANALYSIS II. 3.00 points.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Power series, analytic functions, Implicit function theorem, Fubini theorem, change of variables formula, Lebesgue measure and integration, function spaces

Fall 2020: MATH GU4062
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4062 001/11498 M W 4:10pm - 5:25pm
Online Only
Hui Yu 3.00 25/49
Spring 2021: MATH GU4062
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4062 001/12276 T Th 4:10pm - 5:25pm
Online Only
Henri Roesch 3.00 28/100

MATH GU4065 Honors Complex Variables. 3 points.

Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061

A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.

Fall 2020: MATH GU4065
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4065 001/11503 T Th 10:10am - 11:25am
Online Only
Julien Dubédat 3 17/45

MATH GU4071 Introduction to the Mathematics of Finance. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: MATH UN1202 and MATH UN3027 and STAT W4150 and SEIO W4150, or their equivalents.

The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the BlackûScholes formula, and binomial models.

MATH GU4081 Introduction to Differentiable Manifolds. 3 points.

Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010

Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sard's theorem.  Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stokes' theorem.

Spring 2021: MATH GU4081
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4081 001/00088 M W 10:10am - 11:25am
Room TBA
Dusa McDuff 3 25/40

MATH GU4155 Probability Theory. 3 points.

Prerequisites: MATH GU4061 or MATH UN3007

A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. Generating functions. Convergence in probability and in distribution. Discrete probability spaces, recurrence and transience of random walks. Infinite models, proof of the law of large numbers and the central limit theorem. Markov chains.

Spring 2021: MATH GU4155
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4155 001/12275 T Th 2:40pm - 3:55pm
Online Only
Ioannis Karatzas 3 29/55

MATH GU4392 INTRO TO QUANTUM MECHANICS II. 3.00 points.

Not offered during 2020-21 academic year.

Continuation of GU4391. This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant to be accessible to students with no previous formal training in quantum theory. The role of symmetry, groups and representations will be stressed

Spring 2021: MATH GU4392
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4392 001/12274 T Th 4:10pm - 5:25pm
Online Only
Peter Woit 3.00 6/40

Cross-Listed Courses

Computer Science

COMS S3251 Computational Linear Algebra. 3 points.

Not offered during 2020-21 academic year.

Prerequisites: two terms of calculus.

Computational linear algebra, solution of linear systems, sparse linear systems, least squares, eigenvalue problems, and numerical solution of other multivariate problems as time permits.

COMS W4203 Graph Theory. 3 points.

Lect: 3.

Prerequisites: (COMS W3203)

General introduction to graph theory. Isomorphism testing, algebraic specification, symmetries, spanning trees, traversability, planarity, drawings on higher-order surfaces, colorings, extremal graphs, random graphs, graphical measurement, directed graphs, Burnside-Polya counting, voltage graph theory.

COMS W3203 DISCRETE MATHEMATICS. 4.00 points.

Lect: 3.

Prerequisites: Any introductory course in computer programming.
Prerequisites: Any introductory course in computer programming. Logic and formal proofs, sequences and summation, mathematical induction, binomial coefficients, elements of finite probability, recurrence relations, equivalence relations and partial orderings, and topics in graph theory (including isomorphism, traversability, planarity, and colorings)

Fall 2020: COMS W3203
Course Number Section/Call Number Times/Location Instructor Points Enrollment
COMS 3203 001/11672 T Th 10:10am - 11:25am
Online Only
Ansaf Salleb-Aouissi 4.00 153/150
COMS 3203 002/11673 T Th 11:40am - 12:55pm
Online Only
Ansaf Salleb-Aouissi 4.00 147/150
Spring 2021: COMS W3203
Course Number Section/Call Number Times/Location Instructor Points Enrollment
COMS 3203 001/13030 M W 10:10am - 11:25am
Online Only
Ansaf Salleb-Aouissi 4.00 150/150

Industrial Engineering and Operations Research

CSOR E4010 Graph Theory: A Combinatorial View. 3 points.

Lect: 3.Not offered during 2020-21 academic year.

Prerequisites: Linear Algebra, or instructor's permission.

Graph Theory is an important part of the theoretical basis of operations research. A good understanding of the basic fundamentals of graph theory is necessary in order to apply the theory successfully in the future. This is an introductory course in graph theory with emphasis on its combinatorial aspects. It covers basic definitions, and some fundamental concepts in graph theory and its applications. Topics include trees and forests graph coloring, connectivity, matching theory and others. This course will provide a solid foundation for students in the IEOR department, on which further courses may build.