Mathematics
The Mathematics Department offers introductory and advanced level courses during the summer term.
Please note, it is not necessary to complete prerequisites at Columbia University. Students are expected to meet prerequisite requirements prior to registration.
Check the Directory of Classes for the most uptodate 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
BASIC MATHEMATICS
MATH0065S001 0 points.
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 (autofill Wait List) 
InPerson 
COLLEGE ALGEBRAANLYTC 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 (autofill Wait List) 
InPerson 
CALCULUS I
MATH1101S001 3 points.
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 (autofill Wait List) 
InPerson 
CALCULUS I
MATH1101S002 3 points.
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 (autofill Wait List) 
InPerson 
CALCULUS I
MATH1101S003 3 points.
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) 
InPerson 
CALCULUS II
MATH1102S001 3 points.
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 (autofill Wait List) 
InPerson 
CALCULUS II
MATH1102S002 3 points.
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 (autofill Wait List) 
InPerson 
CALCULUS III
MATH1201S001 3 points.
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 (autofill Wait List) 
InPerson 
CALCULUS III
MATH1201S002 3 points.
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 (autofill Wait List) 
InPerson 
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 (autofill Wait List) 
InPerson 
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 (autofill Wait List) 
InPerson 
LINEAR ALGEBRA
MATH2010S001 3 points.
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 (autofill Wait List) 
InPerson 
LINEAR ALGEBRA
MATH2010S002 3 points.
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 (autofill Wait List) 
InPerson 
LINEAR ALGEBRA
MATH2010S003 3 points.
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) 
InPerson 
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 (autofill Wait List) 
InPerson 
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 (autofill Wait List) 
InPerson 
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 (autofill Wait List) 
InPerson 
ANALYSIS AND OPTIMIZATION
MATH2500S001 3 points.
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 (autofill Wait List) 
InPerson 
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) (selfman. Wait List) 
InPerson 
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) 
InPerson 
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 (autofill Wait List) 
InPerson 
INTRO TO MODERN ANALYSIS II
MATH4062S001 3 points.
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 (autofill Wait List) 
InPerson 
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 offcampus 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) 
InPerson 