2024-2025 Edition

Mathematics

Chair
Daniela De Silva (Ann Whitney Olin Professor of Mathematics)

Professor
Dave Bayer, Dusa McDuff (Joan Lyttle Birman ’48 Chair of Mathematics)

Assistant Professor
Alisa Knizel

Term Associate Professors
Cristian Iovanov
Lindsay Piechnik 

Professors Emeriti
Joan Birman
Walter Neumann

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 (a minimum of 35 credits) as follows:

  • Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit.  A student who places out of Calc I/II with AP credits, will need to take a replacement course. 
  • Six courses in mathematics numbered at or above 2000. 
  • 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 I (at least one term)
or MATH UN3952 UNDERGRADUATE SEMINARS II
*

Note: It is strongly recommended that the sequences MATH GU4041 INTRO MODERN ALGEBRA I - MATH GU4062 INTRO MODERN ANALYSIS II and MATH GU4061 INTRO MODERN ANALYSIS I - MATH GU4062 INTRO MODERN ANALYSIS II be taken in separate years.

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 with one or two of the following courses:

and may replace MATH GU4042 INTRO MODERN ALGEBRA II with 

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 (a minimum of 35 credits)

Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit. A student that places out of Calc I/II with AP credits, will need to take a replacement course.

MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH GU4061INTRO MODERN ANALYSIS I
APMA E4901SEM-PROBLEMS IN APPLIED MATH
APMA E4903SEM-PROBLEMS IN APPLIED MATH
APMA E3900UNDERGRAD RES IN APPLIED MATH (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 FUNCTNS OF A COMPLEX VARIABLE
MATH UN3027Ordinary Differential Equations
or MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS
MATH UN3028PARTIAL DIFFERENTIAL EQUATIONS
or APMA E4200 PARTIAL DIFFERENTIAL EQUATIONS
MATH GU4032FOURIER ANALYSIS
APMA E4300COMPUT MATH:INTRO-NUMERCL METH
APMA E4101APPL MATH III:DYNAMICAL SYSTMS
APMA E4150APPLIED FUNCTIONAL ANALYSIS

For a major in Mathematical Sciences: 14 courses (a minimum of 38 credits):

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 EQUATIONS
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 UN1201CALC-BASED INTRO 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 W3107Clean Object-Oriented Design
Possible further courses selected from the following:
Other classes from the Computer Science Core
COMS W3203DISCRETE MATHEMATICS
COMS W3210Scientific Computation
ENGI E1006INTRO TO COMP FOR ENG/APP SCI

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.

NOTE: A student that places out of Calc I/II with AP credits, will need to take a replacement course.
NOTE: Students may not take for credit COMS W3107 if they already received credit for COMS W1007.

For a major in Mathematics-Statistics: 14 courses (a minimum of 38 credits):

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 UN1201CALC-BASED INTRO TO STATISTICS
STAT GU4203PROBABILITY THEORY
STAT GU4204STATISTICAL INFERENCE
STAT GU4205LINEAR REGRESSION MODELS
And select one of the following courses:
STAT GU4207ELEMENTARY STOCHASTIC PROCESS
STAT GU4262Stochastic Processes for Finance
STAT GU4264STOCHASTC PROCSSES-APPLICTNS I
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 W3107Clean Object-Oriented Design
ENGI E1006INTRO TO COMP FOR ENG/APP SCI
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. 

NOTE: A student that places out of Calc I/II with AP credits, will need to take a replacement course.

NOTE: Students may not take for credit COMS W3107 if they already received credit for COMS W1007.

For a major in Mathematics-Computer Science 15 courses (a minimum of 38 credits):

Mathematics
Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit. A student that places out of Calc I/II with AP credits, will need to take a replacement course; and the 3 following courses:
MATH UN2010LINEAR ALGEBRA (also satisfied by Honors Math A-B)
MATH GU4041INTRO MODERN ALGEBRA I
MATH UN3951UNDERGRADUATE SEMINARS I (at least one term)
or MATH UN3952 UNDERGRADUATE SEMINARS 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 SYSTS

Note A: AP Computer Science with a grade of 4 or 5 or similar experience is a prerequisite for COMS W1007.

Electives: Two additional electives from computer science or math should be included. At least one should be level 3000 or higher; the second should be level 2000 or higher. With adviser approval, appropriate electives from other departments can be considered, such as Statistics or Applied Math.
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-ANLYTC GEOMTRY, 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-ANLYTC GEOMTRY. 3.00 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. 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. This course may not be taken for credit after the successful completion of any course in the Calculus sequence

Fall 2024: MATH UN1003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1003 001/00010 M W 6:10pm - 7:25pm
323 Milbank Hall
Lindsay Piechnik 3.00 51/56
Spring 2025: MATH UN1003
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1003 001/15269 M W 11:40am - 12:55pm
407 Mathematics Building
Jiahe Shen 3.00 14/30
MATH 1003 002/15270 T Th 6:10pm - 7:25pm
407 Mathematics Building
Xiaorun Wu 3.00 7/30

MATH UN1101 CALCULUS I. 3.00 points.

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

Fall 2024: MATH UN1101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1101 001/00081 T Th 1:10pm - 2:25pm
263 Macy Hall
Lindsay Piechnik 3.00 97/100
MATH 1101 002/00082 Th 2:40pm - 3:55pm
405 Milbank Hall
Lindsay Piechnik 3.00 98/100
MATH 1101 003/11833 M W 10:10am - 11:25am
203 Mathematics Building
Marco Castronovo 3.00 49/100
MATH 1101 004/11835 M W 11:40am - 12:55pm
203 Mathematics Building
Marco Castronovo 3.00 65/100
MATH 1101 005/11837 M W 2:40pm - 3:55pm
312 Mathematics Building
George Dragomir 3.00 92/106
MATH 1101 006/11838 M W 4:10pm - 5:25pm
703 Hamilton Hall
Alex Scheffelin 3.00 29/30
MATH 1101 007/11840 M W 6:10pm - 7:25pm
207 Mathematics Building
Marco Sangiovanni Vincentelli 3.00 19/100
MATH 1101 008/11841 T Th 10:10am - 11:25am
520 Mathematics Building
Soren Galatius 3.00 43/45
MATH 1101 009/11842 T Th 11:40am - 12:55pm
142 Uris Hall
George Dragomir 3.00 105/108
MATH 1101 010/11844 T Th 4:10pm - 5:25pm
142 Uris Hall
Marco Sangiovanni Vincentelli 3.00 24/100
MATH 1101 011/11845 T Th 6:10pm - 7:25pm
407 Mathematics Building
Matthew Hase-Liu 3.00 31/30
MATH 1101 012/00857 M W 1:10pm - 2:25pm
152 Horace Mann Hall
Wenjian Liu 3.00 37/60
Spring 2025: MATH UN1101
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1101 001/00472 M W 1:10pm - 2:25pm
263 Macy Hall
Dusa McDuff 3.00 90/90
MATH 1101 002/15277 M W 4:10pm - 5:25pm
407 Mathematics Building
Qiyao Yu 3.00 30/30
MATH 1101 003/15278 M W 6:10pm - 7:25pm
312 Mathematics Building
Brian Harvie 3.00 20/100
MATH 1101 004/15280 T Th 10:10am - 11:25am
614 Schermerhorn Hall
Roger Van Peski 3.00 32/100
MATH 1101 005/15281 T Th 1:10pm - 2:25pm
207 Mathematics Building
Roger Van Peski 3.00 38/100
MATH 1101 006/15282 T Th 4:10pm - 5:25pm
407 Mathematics Building
Che Shen 3.00 30/30

MATH UN1102 CALCULUS II. 3.00 points.

Prerequisites: MATH UN1101 MATH V1101 or the equivalent.
Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Fall 2024: MATH UN1102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1102 001/11847 M W 1:10pm - 2:25pm
207 Mathematics Building
Andres Ibanez Nunez 3.00 85/100
MATH 1102 002/11848 M W 2:40pm - 3:55pm
207 Mathematics Building
Andres Ibanez Nunez 3.00 53/100
MATH 1102 004/11850 T Th 8:40am - 9:55am
203 Mathematics Building
Lucy Yang 3.00 48/100
MATH 1102 005/11851 T Th 10:10am - 11:25am
203 Mathematics Building
Lucy Yang 3.00 43/100
MATH 1102 006/11852 T Th 6:10pm - 7:25pm
417 Mathematics Building
Elliott Stein 3.00 62/64
Spring 2025: MATH UN1102
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1102 001/00477 T Th 2:40pm - 3:55pm
Ll002 Milstein Center
Lindsay Piechnik 3.00 90/90
MATH 1102 002/15285 M W 10:10am - 11:25am
312 Mathematics Building
Evan Sorensen 3.00 48/100
MATH 1102 003/00493 M W 11:40am - 12:55pm
263 Macy Hall
0. FACULTY 3.00 25/100
MATH 1102 004/15287 M W 4:10pm - 5:25pm
606 Martin Luther King Building
Jingbo Wan 3.00 23/30
MATH 1102 005/15289 T Th 10:10am - 11:25am
417 Mathematics Building
Peter Woit 3.00 25/64
MATH 1102 006/15291 T Th 11:40am - 12:55pm
203 Mathematics Building
Dawei Shen 3.00 32/100
MATH 1102 007/15294 T Th 1:10pm - 2:25pm
312 Mathematics Building
Andres Ibanez Nunez 3.00 12/100

MATH UN1201 CALCULUS III. 3.00 points.

Prerequisites: MATH UN1101 MATH V1101 or the equivalent.
Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers 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 2024: MATH UN1201
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1201 001/00011 M W 10:10am - 11:25am
504 Diana Center
Wenjian Liu 3.00 63/70
MATH 1201 002/11853 M W 8:40am - 9:55am
312 Mathematics Building
Deeparaj Bhat 3.00 57/100
MATH 1201 003/11854 M W 11:40am - 12:55pm
312 Mathematics Building
Brian Harvie 3.00 97/100
MATH 1201 004/11855 M W 2:40pm - 3:55pm
203 Mathematics Building
Brian Harvie 3.00 89/100
MATH 1201 005/11856 T Th 11:40am - 12:55pm
203 Mathematics Building
Gyujin Oh 3.00 97/100
MATH 1201 006/11857 T Th 1:10pm - 2:25pm
207 Mathematics Building
Gyujin Oh 3.00 101/100
MATH 1201 007/11861 T Th 2:40pm - 3:55pm
207 Mathematics Building
Yoonjoo Kim 3.00 88/100
MATH 1201 008/11862 T Th 4:10pm - 5:25pm
312 Mathematics Building
Yoonjoo Kim 3.00 82/100
Spring 2025: MATH UN1201
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1201 001/00494 M W 10:10am - 11:25am
263 Macy Hall
Cristian Iovanov 3.00 49/90
MATH 1201 002/00496 M W 11:40am - 12:55pm
405 Milbank Hall
Cristian Iovanov 3.00 55/90
MATH 1201 003/15298 M W 2:40pm - 3:55pm
312 Mathematics Building
Deeparaj Bhat 3.00 75/100
MATH 1201 004/15300 T Th 1:10pm - 2:25pm
203 Mathematics Building
Deeparaj Bhat 3.00 74/100
MATH 1201 005/15301 T Th 4:10pm - 5:25pm
203 Mathematics Building
Rostislav Akhmechet 3.00 100/100
MATH 1201 006/15302 T Th 6:10pm - 7:25pm
203 Mathematics Building
Rostislav Akhmechet 3.00 100/100

MATH UN1202 CALCULUS IV. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 MATH V1102, MATH V1201, 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 2024: MATH UN1202
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1202 001/00012 M W 10:10am - 11:25am
Ll001 Milstein Center
Daniela De Silva 3.00 38/50
MATH 1202 002/11863 M W 6:10pm - 7:25pm
203 Mathematics Building
Mikhail Smirnov 3.00 52/100
Spring 2025: MATH UN1202
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1202 001/15304 M W 4:10pm - 5:25pm
417 Mathematics Building
Ovidiu Savin 3.00 57/64
MATH 1202 002/15306 T Th 1:10pm - 2:25pm
417 Mathematics Building
Marco Sangiovanni Vincentelli 3.00 62/64

MATH UN1207 HONORS MATHEMATICS A. 4.00 points.

Prerequisites: (see Courses for First-Year Students).
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 2024: MATH UN1207
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1207 001/11865 T Th 1:10pm - 2:25pm
140 Uris Hall
Giulia Sacca 4.00 45/52

MATH UN1208 HONORS MATHEMATICS B. 4.00 points.

Prerequisites: (see Courses for First-Year Students).
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 2025: MATH UN1208
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 1208 001/15314 T Th 1:10pm - 2:25pm
330 Uris Hall
Jeanne Boursier 4.00 33/64

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 2024: MATH UN2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2000 001/00013 M W 10:10am - 11:25am
328 Milbank Hall
Dusa McDuff 3.00 28/55
Spring 2025: MATH UN2000
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2000 001/15319 T Th 1:10pm - 2:25pm
520 Mathematics Building
Giulia Sacca 3.00 41/49

MATH BC2001 PERSPECTIVES IN MATHEMATICS. 1.00 point.

Prerequisites: some calculus or the instructor's permission. Intended as an enrichment to the mathematics 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

Spring 2025: MATH BC2001
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2001 001/00904 W 2:40pm - 3:30pm
140 Horace Mann Hall
Dusa McDuff 1.00 0/30

MATH BC2006 COMBINATORICS. 3.00 points.

Spring 2025: MATH BC2006
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2006 001/00860 T Th 10:10am - 11:25am
408 Zankel
Alisa Knizel 3.00 34/60

MATH UN2010 LINEAR ALGEBRA. 3.00 points.

Prerequisites: MATH V1201, or the equivalent.

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

Fall 2024: MATH UN2010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2010 001/00014 M W 10:10am - 11:25am
Ll002 Milstein Center
Cristian Iovanov 3.00 81/90
MATH 2010 002/00015 M W 11:40am - 12:55pm
405 Milbank Hall
Cristian Iovanov 3.00 97/110
MATH 2010 003/11867 M W 2:40pm - 3:55pm
142 Uris Hall
Siddhi Krishna 3.00 38/100
MATH 2010 004/11868 T Th 10:10am - 11:25am
312 Mathematics Building
Amadou Bah 3.00 80/100
MATH 2010 005/11869 T Th 1:10pm - 2:25pm
203 Mathematics Building
Amadou Bah 3.00 78/100
Spring 2025: MATH UN2010
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2010 001/00487 M W 8:40am - 9:55am
263 Macy Hall
0. FACULTY 3.00 69/100
MATH 2010 002/00491 M W 2:40pm - 3:55pm
Ll002 Milstein Center
Lindsay Piechnik 3.00 90/90
MATH 2010 003/15325 T Th 10:10am - 11:25am
312 Mathematics Building
Qiao He 3.00 48/100
MATH 2010 004/15328 T Th 11:40am - 12:55pm
312 Mathematics Building
Qiao He 3.00 90/100
MATH 2010 005/15331 T Th 4:10pm - 5:25pm
312 Mathematics Building
Elliott Stein 3.00 64/64

MATH UN2020 Honors Linear Algebra. 3 points.

Not offered during 2023-2024 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 EQUATIONS. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 MATH V1102-MATH V1201 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 2024: MATH UN2030
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2030 001/11872 M W 1:10pm - 2:25pm
312 Mathematics Building
Panagiota Daskalopoulos 3.00 83/100
MATH 2030 002/11873 T Th 10:10am - 11:25am
142 Uris Hall
Jeanne Boursier 3.00 49/100
MATH 2030 003/11874 T Th 1:10pm - 2:25pm
520 Mathematics Building
Jeanne Boursier 3.00 30/49
Spring 2025: MATH UN2030
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2030 001/15344 M W 10:10am - 11:25am
207 Mathematics Building
Dawei Shen 3.00 88/100
MATH 2030 002/15345 T Th 11:40am - 12:55pm
207 Mathematics Building
Panagiota Daskalopoulos 3.00 100/100

MATH UN2500 ANALYSIS AND OPTIMIZATION. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1201 MATH V1102-MATH V1201 or the equivalent and MATH V2010.
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 2024: MATH UN2500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2500 001/11875 M W 4:10pm - 5:25pm
417 Mathematics Building
Qiao He 3.00 48/64
MATH 2500 002/11876 T Th 10:10am - 11:25am
517 Hamilton Hall
Roger Van Peski 3.00 50/75
Spring 2025: MATH UN2500
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 2500 001/15346 T Th 10:10am - 11:25am
203 Mathematics Building
Xi Shen 3.00 100/100

MATH UN3007 COMPLEX VARIABLES. 3.00 points.

Prerequisites: MATH UN1202 MATH V1202. An elementary course in functions of a complex variable.
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 2024: MATH UN3007
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3007 001/11877 T Th 11:40am - 12:55pm
312 Mathematics Building
Ovidiu Savin 3.00 56/100

MATH UN3020 NUMBER THEORY AND CRYPTOGRAPHY. 3.00 points.

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

Spring 2025: MATH UN3020
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3020 001/15349 M W 10:10am - 11:25am
203 Mathematics Building
Siddhi Krishna 3.00 56/100

MATH UN3025 MAKING, BREAKING CODES. 3.00 points.

Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH V1101, MATH V1102, MATH V1201 and MATH V2010.
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 2024: MATH UN3025
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3025 001/11878 T Th 1:10pm - 2:25pm
312 Mathematics Building
Dorian Goldfeld 3.00 94/100

MATH UN3027 Ordinary Differential Equations. 3 points.

Prerequisites: MATH UN1102 and MATH UN1201 MATH V1102-MATH V1201 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. 

MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS. 3.00 points.

Prerequisites: MATH UN3027 and MATH UN2010 MATH V3027 and MATH V2010 or the equivalent
Prerequisites: (MATH UN2010 and MATH UN2030) 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 2025: MATH UN3028
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3028 001/15351 T Th 2:40pm - 3:55pm
417 Mathematics Building
Simon Brendle 3.00 64/64

MATH UN3050 DISCRETE TIME MODELS IN FINANC. 3.00 points.

Prerequisites: (MATH UN1102 and MATH UN1201) or (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH UN2010 MATH V1102, MATH V1201 (or MATH V1101, MATH V1102, MATH V1201), MATH V2010. Recommended: MATH V3027 (or MATH V2030) and SIEO W3600.
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 2025: MATH UN3050
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3050 001/15353 M W 6:10pm - 7:25pm
417 Mathematics Building
Mikhail Smirnov 3.00 37/64

MATH UN3386 DIFFERENTIAL GEOMETRY. 3.00 points.

Prerequisites: MATH UN1202 MATH V1202 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.

MATH UN3901 SUPERVISED READINGS I. 1.00-3.00 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 director of undergraduate studies' permission. The written permission must be deposited with the director of undergraduate studies before registration is completed.
Prerequisites: The written permission of the faculty 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. Supervising Readings do NOT count towards major requirements, with the exception of an advanced written approval by the DUS

Fall 2024: MATH UN3901
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3901 001/00790  
Dusa McDuff 1.00-3.00 1/5
MATH 3901 002/00791  
Daniela De Silva 1.00-3.00 0/5
MATH 3901 003/17561  
Richard Hamilton, Simon Brendle 1.00-3.00 1/1
MATH 3901 004/19472  
Elena Giorgi 1.00-3.00 2/2
MATH 3901 005/20931  
Peter Woit 1.00-3.00 1/1
MATH 3901 006/21153  
Chiu-Chu Liu 1.00-3.00 1/1
MATH 3901 007/21214  
Robert Friedman 1.00-3.00 1/1
MATH 3901 008/21255  
Dorian Goldfeld 1.00-3.00 1/1

MATH UN3902 SUPERVISED READINGS II. 1.00-3.00 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 director of undergraduate studies' permission. The written permission must be deposited with the director of undergraduate studies before registration is completed.
Prerequisites: The written permission of the faculty 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. Supervising Readings do NOT count towards major requirements, with the exception of an advanced written approval by the DUS

Spring 2025: MATH UN3902
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3902 001/18893  
Julien Dubedat 1.00-3.00 0/1

MATH UN3951 UNDERGRADUATE SEMINARS I. 3.00 points.

Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.
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 2024: MATH UN3951
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3951 001/00078  
Cristian Iovanov 3.00 49/64

MATH UN3952 UNDERGRADUATE SEMINARS II. 3.00 points.

Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.
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 2025: MATH UN3952
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3952 001/00804  
Alisa Knizel 3.00 44/80

MATH UN3997 SUPERVISED INDIVIDUAL RESEARCH. 1.00-4.00 points.

Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies' permission.
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

Fall 2024: MATH UN3997
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 3997 001/00079  
Dusa McDuff 1.00-4.00 1/5

MATH UN3998 SUPERVISED INDIVIDUAL RESEARCH. 3.00 points.

Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies' permission.

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. 3.00 points.

Prerequisites: MATH UN3007 MATH V3007.
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 2025: MATH GU4007
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4007 001/15355 T Th 2:40pm - 3:55pm
307 Mathematics Building
Amadou Bah 3.00 14/20

MATH GU4032 FOURIER ANALYSIS. 3.00 points.

Prerequisites: three terms of calculus and linear algebra or four terms of calculus.
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

Fall 2024: MATH GU4032
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4032 001/11879 T Th 10:10am - 11:25am
603 Hamilton Hall
Simon Brendle 3.00 30/49

MATH GU4041 INTRO MODERN ALGEBRA I. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 MATH V1102-MATH V1202 and MATH V2010, or the equivalent.
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, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, finitely generated abelian groups

Fall 2024: MATH GU4041
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4041 001/11904 M W 1:10pm - 2:25pm
203 Mathematics Building
Robert Friedman 3.00 68/110
Spring 2025: MATH GU4041
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4041 001/15358 M W 2:40pm - 3:55pm
417 Mathematics Building
Michael Thaddeus 3.00 64/64

MATH GU4042 INTRO MODERN ALGEBRA II. 3.00 points.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 MATH V1102-MATH V1202 and MATH V2010, or the equivalent.
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 2024: MATH GU4042
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4042 001/11846 M W 10:10am - 11:25am
417 Mathematics Building
Michael Thaddeus 3.00 17/49
Spring 2025: MATH GU4042
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4042 001/15360 M W 2:40pm - 3:55pm
520 Mathematics Building
Robert Friedman 3.00 47/49

MATH GU4043 ALGEBRAIC NUMBER THEORY. 3.00 points.

Prerequisites: MATH GU4041 and MATH GU4042 MATH W4041-MATH W4042 or the equivalent.
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

Spring 2025: MATH GU4043
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4043 001/15362 T Th 4:10pm - 5:25pm
307 Mathematics Building
Yujie Xu 3.00 0/20

MATH GU4044 REPRESENTATNS OF FINITE GROUPS. 3.00 points.

Prerequisites: MATH UN2010 and MATH GU4041 MATH V2010 and MATH W4041 or the equivalent.
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 2024: MATH GU4044
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4044 001/11880 T Th 1:10pm - 2:25pm
407 Mathematics Building
Andrei Okounkov 3.00 15/30

MATH GU4045 ALGEBRAIC CURVES. 3.00 points.

Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 MATH W4041, MATH W4042 and MATH V3007.
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

Spring 2025: MATH GU4045
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4045 001/15365 M W 11:40am - 12:55pm
307 Mathematics Building
Yoonjoo Kim 3.00 14/20

MATH W4046 Introduction to Category Theory. 3 points.

CC/GS: Partial Fulfillment of Science Requirement
Not offered during 2023-2024 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. 3.00 points.

Prerequisites: (MATH UN1202 and MATH UN2010) and MATH V1202, MATH V2010, and rudiments of group theory (e.g., MATH W4041). MATH V1208 or MATH W4061 is recommended, but not required.
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 2024: MATH GU4051
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4051 001/11881 T Th 6:10pm - 7:25pm
520 Mathematics Building
Rostislav Akhmechet 3.00 17/49

MATH GU4052 INTRODUCTION TO KNOT THEORY. 3.00 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 Reidemeisters 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

Fall 2024: MATH GU4052
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4052 001/11882 M W 11:40am - 12:55pm
307 Mathematics Building
Siddhi Krishna 3.00 10/20

MATH GU4053 INTRO TO ALGEBRAIC TOPOLOGY. 3.00 points.

Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051 MATH V2010, MATH W4041, MATH W4051.
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

Spring 2025: MATH GU4053
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4053 001/15367 T Th 11:40am - 12:55pm
307 Mathematics Building
Soren Galatius 3.00 20/20

MATH GU4061 INTRO MODERN ANALYSIS I. 3.00 points.

Prerequisites: MATH UN1202 MATH V1202 or the equivalent, and MATH V2010. 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 2024: MATH GU4061
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4061 001/11858 T Th 1:10pm - 2:25pm
417 Mathematics Building
Sven Hirsch 3.00 53/64
MATH 4061 002/11859 T Th 2:40pm - 3:55pm
417 Mathematics Building
3.00 61/64
Spring 2025: MATH GU4061
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4061 001/15369 M W 1:10pm - 2:25pm
614 Schermerhorn Hall
Julien Dubedat 3.00 89/100

MATH GU4062 INTRO MODERN ANALYSIS II. 3.00 points.

Prerequisites: MATH UN1202 MATH V1202 or the equivalent, and MATH V2010. The second term of this course may not be taken without the first.
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 2024: MATH GU4062
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4062 001/11883 M W 11:40am - 12:55pm
520 Mathematics Building
Milind Hegde 3.00 12/49
Spring 2025: MATH GU4062
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4062 001/15370 T Th 4:10pm - 5:25pm
520 Mathematics Building
Francesco Lin 3.00 49/49

MATH GU4065 HONORS COMPLEX VARIABLES. 3.00 points.

Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061 MATH V1207 and MATH V1208 or MATH W4061.
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 2024: MATH GU4065
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4065 001/11884 T Th 11:40am - 12:55pm
520 Mathematics Building
Francesco Lin 3.00 35/45

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

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: MATH UN1202 and MATH UN3027 and

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 INTRO-DIFFERENTIABLE MANIFOLDS. 3.00 points.

Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010 MATH W4051 or MATH W4061 and MATH V2010.
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 Sards theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stokes theorem

Spring 2025: MATH GU4081
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4081 001/15373 M W 10:10am - 11:25am
520 Mathematics Building
Sven Hirsch 3.00 30/49

MATH GU4155 PROBABILITY THEORY. 3.00 points.

Prerequisites: MATH GU4061 or MATH UN3007 MATH W4061 or MATH V3007.
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

Fall 2024: MATH GU4155
Course Number Section/Call Number Times/Location Instructor Points Enrollment
MATH 4155 001/11860 T Th 2:40pm - 3:55pm
507 Mathematics Building
Ivan Corwin 3.00 12/26

MATH GU4392 INTRO TO QUANTUM MECHANICS II. 3.00 points.

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.

SIEO W3600 INTRO PROBABILITY/STATISTICS. 4.00 points.

SIEO W4150 INTRO-PROBABILITY & STATISTICS. 3.00 points.

Cross-Listed Courses

Computer Science

COMS S3251 Computational Linear Algebra. 3 points.

Not offered during 2023-2024 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) 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.
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 2024: COMS W3203
Course Number Section/Call Number Times/Location Instructor Points Enrollment
COMS 3203 001/11935 M W 4:10pm - 5:25pm
301 Pupin Laboratories
Tony Dear 4.00 196/270
Spring 2025: COMS W3203
Course Number Section/Call Number Times/Location Instructor Points Enrollment
COMS 3203 001/13386 M W 2:40pm - 3:55pm
501 Northwest Corner
Tony Dear 4.00 164/164

Industrial Engineering and Operations Research

CSOR E4010 GRAPH THEORY: COMBINATL VIEW. 3.00 points.

Lect: 3.Not offered during 2023-2024 academic year.

Prerequisites: Linear algebra, or instructor’s permission.
An introductory course in graph theory with emphasis on its combinatorial aspects. Basic definitions, and some fundamental topics in graph theory and its applications. Topics include trees and forests graph coloring, connectivity, matching theory and others