Computer Science  Mathematics
The Department of Mathematics
Department website: http://www.math.columbia.edu
Office location: 410 Mathematics
Office contact: 2128542432
Director of Undergraduate Studies
Julien Dubedat, 601 Mathematics; 2128548806; jd2653@columbia.edu
Undergraduate Academic Coordinator
Shay Bailey, 410 Mathematics; 2128542432; sb3985@columbia.edu
The Study of Mathematics
The major in mathematics is an introduction to some of the highlights of the development of theoretical mathematics over the past four hundred years from a modern perspective. This study is also applied to many problems, both internal to mathematics and arising in other disciplines such as physics, cryptography, and finance.
Majors begin by taking either Honors mathematics or the calculus sequence. Students who do not take MATH UN1207 HONORS MATHEMATICS A and MATH UN1208 HONORS MATHEMATICS B normally take MATH UN2010 LINEAR ALGEBRA in the second year. Following this, majors begin to learn some aspects of the main branches of modern mathematics: algebra, analysis, and geometry; as well as some of their subdivisions and hybrids (e.g., number theory, differential geometry, and complex analysis). As the courses become more advanced, they also become more theoretical and prooforiented and less computational.
Aside from the courses offered by the Mathematics Department, cognate courses in areas such as astronomy, chemistry, physics, probability, logic, economics, and computer science can be used toward the major. A cognate course must be a 2000level (or higher) course and must be approved by the director of undergraduate studies. In general, a course not taught by the Mathematics Department is a cognate course for the mathematics major if either (a) it has at least two semesters of calculus as a stated prerequisite, or (b) the subject matter in the course is mathematics beyond an elementary level, such as PHIL UN3411 SYMBOLIC LOGIC, in the Philosophy Department, or COMS W3203 DISCRETE MATHEMATICS, in the Computer Science Department. A list of preapproved cognate courses can be found under the major requirements.
Another requirement for majors is participation in an undergraduate seminar, usually in the junior or senior year. Applied math majors must take the undergraduate applied math seminar sequence in both the junior and senior year. In these seminars, students gain experience in learning an advanced topic and lecturing on it. In order to be eligible for departmental honors, majors must write a senior thesis.
Student Advising
Director of Undergraduate Studies
Prof. Julien Dubedat, 601 Mathematics; 2128548806; jd2653@columbia.edu
Calculus Director
Prof. George Dragomir, 525 Mathematics; 2128542849; gd2572@columbia.edu
Computer ScienceMathematics Advisers
Computer Science: Dr. Jae Woo Lee, 715 CEPSR; 2129397066; jae@cs.columbia.edu
Mathematics: Prof. ChiuChu Melissa Liu, 623 Mathematics; 2128542499; ccliu@math.columbia.edu
EconomicsMathematics Advisers
Economics: Dr. Susan Elmes, 1006 International Affairs Building; 2128549124; se5@columbia.edu
Mathematics: Prof. Francesco Lin, 613 Mathematics; 2128542192; fl2550@columbia.edu
MathematicsStatistics Advisers
Mathematics: Prof. Andrew Blumberg, 607 Mathematics; 2128519307; ab4808@columbia.edu
Statistics: Dr. Ronald Neath, 612 Watson; 2128531398; rcn2112@columbia.edu
Enrolling in Classes
Most undergraduate level courses in Mathematics can be taken once the prerequisite courses have been completed. Any exceptions to waive a prerequisite requirement must be obtained by writing to the Director of Undergraduate Studies.
Students who wish to register for a section of either Supervised Readings and/or Senior Thesis must first identify a faculty sponsor, determine a suitable topic, and obtain written permission from the Director of Undergraduate Studies. Refer to the Undergraduate Research and Senior Thesis section, below.
Preparing for Graduate Study
Departmental advisors can offer advice about and help with graduate school applications. The Mathematics department also runs a Master’s degree program in mathematical finance and a Ph.D. program in mathematics.
Coursework Taken Outside of Columbia
Comprehensive information on college level coursework taken outside Columbia University are described on the College’s Academic Regulation website or the General Studies Transfer Credit website.
Advanced Placement
AP or IB calculus may count towards degree requirements, subject to completion of a higher level course:
 The department grants 3 credits for a score of 4 or 5 on the AP Calculus AB exam provided students complete MATH UN1102 CALCULUS II or MATH UN1201 CALCULUS III with a grade of C or better.
 The department grants 3 credits for a score of 4 on the AP Calculus BC exam provided students complete MATH UN1102 CALCULUS II or MATH UN1201 CALCULUS III with a grade of C or better.
 The department grants 6 credits for a score of 5 on the AP Calculus BC exam provided students complete MATH UN1201 CALCULUS III or MATH UN1205 ACCELERATED MULTIVARIABLE CALC or MATH UN1207 HONORS MATHEMATICS A with a grade of C or better.
Students can receive credit for only one calculus sequence. Other college level courses taken during high school may substitute for course prerequisites pending the approval of the Director of Undergraduate Studies, but will not confer credits.
Barnard College Courses
Any course offered by the Mathematics@Barnard department will count towards degree requirements.
Transfer Courses
Courses taken at other colleges or universities prior to matriculation at Columbia may be evaluated for transfer credit. A maximum of 16 transfer credits may be granted.
 Course equivalency requests for any Calculus level course, Linear Algebra, or Ordinary Differential Equations must be submitted to the Calculus Director for evaluation.
 Course equivalency requests for any other mathematics course must be submitted to the Director of Undergraduate Studies for evaluation.
Study Abroad Courses
Although study abroad is not an integral part of your studies in mathematics, it can provide you with exposure to a different culture and a different educational system, and, as such, can be very fulfilling. You may also want to participate in the Budapest Mathematical Seminar or similar programs in your junior year. Keep in mind, however, that study abroad requires careful planning. If you are seriously considering studying abroad, you should consult with the Director of Undergraduate Studies as early in your program as possible in order to plan your major accordingly and to incorporate study abroad courses that are compatible with your major in mathematics.
Summer Courses
Any mathematics or approved cognate course offered during the summer session will count towards the degree, with the exception of online only courses, which do not count towards degree requirements.
Undergraduate Research and Senior Thesis
Undergraduate Research in Courses
MATH UN3901 Supervised Readings I (fall term only)
MATH UN3902 Supervised Readings II (spring term only)
Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to fulltime 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 Director of Undergraduate Studies.
Senior Thesis Coursework and Requirements
A Senior Thesis in Mathematics is an original presentation of a subject in pure or applied mathematics from sources in the published literature. The thesis must demonstrate significant independent work of the author. A thesis is expected to be between 20 and 50 pages with complete references and must have a substantial expository component to be well received.
A student who is interested in writing a senior thesis needs to identify a faculty member in the Department of Mathematics as an advisor, determine an appropriate topic, and receive the written approval from the faculty advisor and the Director of Undergraduate Studies. The research of the thesis is conducted primarily during the fall term and the final paper is submitted to the Director of Undergraduate Studies by the end of March.
Students must register for MATH UN3994 SENIOR THESIS IN MATHEMATICS I (4 credits) in the fall semester of their senior year. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II (2 credits) is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper. Sections of Senior Thesis in Mathematics I and II do NOT count towards the major requirements, unless prior written approval is obtained from the Director of Undergraduate Studies.
Undergraduate Research Outside of Courses
The department runs several undergraduate research programs aimed at math majors. Opportunities are available during the academic year and summer terms.
The Undergraduate Mathematics Society is the department’s undergraduate club. Detailed information on membership, Societysponsored seminars and activities, and archival resources are available on the Society’s Web site. The department also sponsors workshops and weekly seminars in mathematics, and posts information about special lectures, conferences, and seminars at nearby schools.
In addition, the Association for Women in Mathematics Columbia Chapter connects students and professors interested in mathematics at Columbia University and Barnard College as part of a broader effort to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment of women and girls in the STEM fields.
Department Honors and Prizes
Department Honors
To be recommended to the College Committee on Honors, Awards, and Prizes, which makes the final decisions on all honors’ recipients, you must have a GPA of 3.63 in the major and have completed a senior thesis of merit. For more information on researching and writing the senior thesis and on departmental honors, you should consult with the Director of Undergraduate Studies. Normally no more than 10% of graduating majors receive departmental honors in a given academic year.
Academic Prizes
Putnam Exam
The Putnam exam is a nationwide competitive exam administered each year on the first Saturday in December. A faculty member conducts coaching sessions for students who are interested in competing.
Columbia Prizes
Several prizes for excellence in mathematics are awarded each year to undergraduates, based on performance on a prize exam scheduled each spring. These include:
 Professor Van Amringe Mathematical Prize
 This prize, established in 1910 by George G. Dewitt, Class of 1867, may be awarded to a first year, a sophomore, and a junior student in the College who are deemed most proficient in the mathematical subjects designated during the year of the award.
 John Dash Van Buren Jr. Prize in Mathematics
 Established in 1906 by Mrs. Louis T. Hoyt in memory of her nephew, John Dash Van Buren, Jr., Class of 1905, this prize may be awarded to a Columbia College senior degree candidate who writes the best examination in subjects prescribed by the Mathematics Department.
Other Important Information
Other helpful information may be found on the Department of Mathematics website.
Professors
 David A. Bayer (Barnard)
 Andrew Blumberg
 Simon Brendle
 Ivan Corwin
 Panagiota Daskalopoulos
 Aise Johan de Jong (Department Chair)
 Daniela De Silva (Barnard Chair)
 Julien Dubedat
 Robert Friedman
 Dorian Goldfeld
 Brian Greene
 Richard Hamilton
 Michael Harris
 Ioannis Karatzas
 Alisa Knizel (Barnard)
 ChiuChu Liu
 Dusa McDuff (Barnard)
 Andrei Okounkov
 D. H. Phong
 Ovidiu Savin
 Michael Thaddeus
 Eric Urban
 MuTao Wang
Associate Professors
 Amol Aggarwal
 Chao Li
 Francesco Lin
 Lindsay Piechnik (Barnard)
Assistant Professors
 Elena Giorgi
 Giulia Sacca
 Mehtaab Sawhney
J.F. Ritt Assistant Professors
 Rostislav Akhmechet
 Amadou Bah
 Deeparaj Bhat
 Jeanne Boursier
 Marco Castronovo
 Brian Harvie
 Qiao He
 Sven Hirsch
 Andres Ibanez Nunez
 Yoonjoo Kim
 Siddhi Krishna
 Gyujin Oh
 Marco Sangiovanni Vincentelli
 Dawei Shen
 Xi Sisi Shen
 Evan Sorensen
 Roger Van Peski
 Lucy Yang
Senior Lecturers in Discipline
 Mikhail Smirnov
 Peter Woit
Lecturers in Discipline
 George Dragomir
On Leave
 Fall 2024: Profs. Aggarwal, Bayer, Giorgi, Li, Sawhney, Shen, Wang
 Spring 2025: Profs. Aggarwal, Bayer, Li, Liu, Sawhney, Urban, Wang
Guidance for Undergraduate Students in Mathematics
Program Planning for all Students
Placement in the Calculus Sequences
Calculus I
Students who have essentially mastered a precalculus course and those who have a score of 3 or less on an Advanced Placement (AP) exam (either AB or BC) should begin their study of calculus with MATH UN1101 CALCULUS I.
Calculus II and III
Students with a score of 4 or 5 on the AB exam, 4 on the BC exam, or those with no AP score but with a grade of A in a full year of high school calculus may begin with either MATH UN1102 CALCULUS II or MATH UN1201 CALCULUS III. Note that such students who decide to start with Calculus III may still need to take Calculus II since it is a requirement or prerequisite for other courses. In particular, they MUST take Calculus II before going on to MATH UN1202 CALCULUS IV. Students with a score of 5 on the BC exam may begin with Calculus III and do not need to take Calculus II.
Those with a score of 4 or 5 on the AB exam or 4 on the BC exam may receive 3 points of AP credit upon completion of Calculus II with a grade of C or higher. Those students with a score of 5 on the BC exam may receive 6 points of AP credit upon completion of Calculus III with a grade of C or higher.
Accelerated Multivariable Calculus
Students with a score of 5 on the AP BC exam or 7 on the IB HL exam may begin with MATH UN1205 ACCELERATED MULTIVARIABLE CALC. Upon completion of this course with a grade of C or higher, they may receive 6 points of AP credit.
Honors Mathematics A
Students who want a prooforiented theoretical sequence and have a score of 5 on the BC exam may begin with MATH UN1207 HONORS MATHEMATICS A, which is especially designed for mathematics majors. Upon completion of this course with a grade of C or higher, they may receive 6 points of AP credit.
Transfer Inside the Calculus Sequences
Students who wish to transfer from one calculus course to another are allowed to do so beyond the date specified on the Academic Calendar. They are considered to be adjusting their level, not changing their program. However, students must obtain the approval of the new instructor and their advising dean prior to reporting to the Office of the Registrar.
Grading
No course with a grade of D or lower can count toward the major, interdepartmental major, minor, or concentration.
Double Counting
Students who are doing a double major should review the College Bulletin's policy on Double Counting Courses towards Requirements. In general, courses in the Calculus sequence may be counted towards both majors, with up to two additional MATH UN2xxx or higher level courses at the discretion of all approving departments. Students pursuing a minor may double count at most one additional MATH UN2xxx or higher level course.
Planning Forms
Planning forms for all programs are available on our website. These forms should be completed and approved by a department adviser early in the semester of the expected graduation date.
Course Numbering Structure
 10002000 Level courses are intended to be introductory courses (such as the Calculus sequence and Linear Algebra).
 30004000 Level courses cover more advanced mathematics, as well as supervised readings, undergraduate seminars, and senior theses.
 5000 Level courses are Master’s level courses.
 6000 Level and above are PhD level courses.
Guidance for FirstYear Students
The systematic study of mathematics begins with one of the following three alternative calculus and linear algebra sequences:
Code  Title  Points 

MATH UN1101  MATH UN1102  MATH UN1201  MATH UN1202  MATH UN2010  CALCULUS I and CALCULUS II and CALCULUS III and CALCULUS IV and LINEAR ALGEBRA  
OR  
MATH UN1101  MATH UN1102  MATH UN1205  MATH UN2010  CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA  
OR  
MATH UN1101  MATH UN1102  MATH UN1207  MATH UN1208  CALCULUS I and CALCULUS II and HONORS MATHEMATICS A and HONORS MATHEMATICS B 
Credit is allowed for only one calculus and linear algebra sequence.
Calculus I, II is a standard course in singlevariable differential and integral calculus; Calculus III, IV is a standard course in multivariable differential and integral calculus; Accelerated Multivariable Calculus is an accelerated course in multivariable differential and integral calculus.
While Calculus II is no longer a prerequisite for Calculus III, students are strongly urged to take it before taking Calculus III. In particular, students thinking of majoring or concentrating in mathematics or one of the joint majors involving mathematics should take Calculus II before taking Calculus III. Note that Calculus II is a prerequisite for Accelerated Multivariable Calculus, and both Calculus II and Calculus III are prerequisites for Calculus IV.
The third sequence, Honors Mathematics A/B, is for exceptionally wellqualified students who have strong Advanced Placement scores. It covers multivariable calculus (MATH UN1201 CALCULUS III  MATH UN1202 CALCULUS IV) and linear algebra (MATH UN2010 LINEAR ALGEBRA), with an emphasis on theory.
Guidance for Transfer Students
Consideration for AP, IB and transfer credit is as follows:
Equivalent to MATH UN1101 Calculus I:
 A score of 4 on the Calculus BC Advanced Placement exam.
 A score of 4 or 5 on the Calculus AB Advanced Placement exam.
 A score of 6 on the IB Mathematics: analysis and approaches HL exam (2021 or later) or a score of 6 on the IB HL Mathematics or Further Mathematics exams (2020 or earlier).
 A score of 6 or 7 on the IB Mathematics: applications and interpretation HL exam (2021 or later) or a score of 6 or 7 on the IB SL Mathematics exam (2020 or earlier). This does not include the IB “Mathematical Studies SL” exam.
 An A on the ALevel Mathematics exam or a B in ALevel Further Mathematics exam in the U.K.
 A grade of A in a full year of high school calculus.
Equivalent to MATH 1101 Calculus I and MATH 1102 Calculus II:
 A score of 5 on the Calculus BC Advanced Placement.
 A score of 7 on the IB Mathematics: analysis and approaches HL exam (2021 or later) or a score of 7 on the IB HL Mathematics or Further Mathematics exams (2020 or earlier).
 An A on the ALevel Further Mathematics exam in the U.K.
Undergraduate Programs of Study
Major in Mathematics
The major requires 4042 points as follows:
Code  Title  Points 

Select one of the following three calculus and linear algebra sequences (1315 points including Advanced Placement Credit):  
CALCULUS I and CALCULUS II and CALCULUS III and CALCULUS IV and LINEAR ALGEBRA ^{1}  
OR  
CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA ^{1}  
OR  
CALCULUS I and CALCULUS II and HONORS MATHEMATICS A and HONORS MATHEMATICS B  
12 points in the following courses:  
INTRO MODERN ALGEBRA I  
INTRO MODERN ALGEBRA II  
INTRO MODERN ANALYSIS I ^{2}  
INTRO MODERN ANALYSIS II ^{2}  
3 points in the following:  
UNDERGRADUATE SEMINARS I ^{3}  
or MATH UN3952  UNDERGRADUATE SEMINARS II  
12 points from the following:  
1) Courses offered by the department numbered 2000 or higher ^{3}  
2) Courses from the list of approved cognate courses below. A maximum of 6 credits may be taken from courses outside the department. ^{4} 
 ^{ 1 }
MATH UN2015 Linear Algebra and Probability does NOT replace MATH UN2010 LINEAR ALGEBRA as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015.
 ^{ 2 }
Students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH GU4061 MATH GU4062 by one or two of the following courses: MATH UN2500 ANALYSIS AND OPTIMIZATION, MATH UN3007 COMPLEX VARIABLES, MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS, or MATH GU4032 FOURIER ANALYSIS.
 ^{ 3 }
Only one Undergraduate Seminar may count towards the major requirements.
 ^{ 4 }
Additional courses may be selected only with prior written approval from the Director of Undergraduate Studies.
The program of study should be planned with a departmental adviser before the end of the sophomore year. Majors who are planning on graduate studies in mathematics are urged to obtain a reading knowledge of one of the following languages: French, German, or Russian.
Majors are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should refer to the "Undergraduate Research and Senior Thesis" section on the Overview tab for additional information.
Approved Cognate Courses 1  Approved Cognate Courses 2  Approved Cognate Courses 3 

APMA E2101 INTRO TO APPLIED MATHEMATICS APMA E3102 APPLIED MATHEMATICS II: PDE'S APMA E4300 COMPUT MATH:INTRONUMERCL METH APMA E4302 METHODS IN COMPUTATIONAL SCI APPH E6102 PLASMA PHYSICS II CBMF W4761 COMPUTATIONAL GENOMICS CHEM UN3079 PHYSICAL CHEMISTRY ILECTURES CHEM UN3080 PHYSICAL CHEMISTRY IILECTURES COMS W3134 Data Structures in Java COMS W3157 ADVANCED PROGRAMMING COMS W3203 DISCRETE MATHEMATICS COMS W3261 COMPUTER SCIENCE THEORY COMS W4111 INTRODUCTION TO DATABASES COMS W4160 COMPUTER GRAPHICS COMS W4162 Advanced Computer Graphics COMS W4203 Graph Theory COMS W4261 INTRO TO CRYPTOGRAPHY COMS W4460 PRININNOVATN/ENTREPRENEURSHIP COMS W4701 ARTIFICIAL INTELLIGENCE COMS W4705 NATURAL LANGUAGE PROCESSING COMS W4762 Machine Learning for Functional Genomics COMS W4771 MACHINE LEARNING COMS W4773 Machine Learning Theory CSEE W3827 FUNDAMENTALS OF COMPUTER SYSTS CSOR W4231 ANALYSIS OF ALGORITHMS I CSOR W4246 ALGORITHMS FOR DATA SCIENCE CSPH G4801 Mathematical Logic I CSPH G4802 Math Logic II: Incompletness 
ECON UN3025 FINANCIAL ECONOMICS ECON BC3035 INTERMEDTE MICROECONOMC THEORY ECON BC3038 INTERNATIONAL MONEY ＆ FINANCE ECON UN3211 INTERMEDIATE MICROECONOMICS ECON UN3213 INTERMEDIATE MACROECONOMICS ECON UN3265 MONEY AND BANKING ECON UN3412 INTRODUCTION TO ECONOMETRICS ECON GU4020 ECON OF UNCERTAINTY ＆ INFORMTN ECON GU4230 ECONOMICS OF NEW YORK CITY ECON GU4280 CORPORATE FINANCE ECON GU4415 GAME THEORY ECON GU4710 FINANCE AND THE REAL ECONOMY EEOR E6616 CONVEX OPTIMIZATION EESC UN3400 COMPUTATIONAL EARTH SCIENCE EESC GU4008 Introduction to Atmospheric Science EESC GU4090 INTRO TO GEOCHRONOLGY EESC GU4924 INTRO TO ATMOSPHERIC CHEMISTRY IEOR E3106 STOCHASTIC SYSTEMS AND APPLICATIONS IEOR E3658 PROBABILITY FOR ENGINEERS IEOR E4700 INTRO TO FINANCIAL ENGINEERING IEOR E6613 Optimization, I MSAE E3010 FOUNDATIONS OF MATERIALS SCIENCE MSAE E3111 THERMO/KINETIC THRY/STAT MECH PHIL UN3411 SYMBOLIC LOGIC PHIL GU4424 MODAL LOGIC PHIL GU4431 INTRODUCTION TO SET THEORY PHIL GU4561 PROBABILITY ＆ DECISION THEORY PHIL GU4810 LATTICES AND BOOLEAN ALGEBRA 
PHYS UN2601 PHYSICS III:CLASS/QUANTUM WAVE PHYS UN2801 ACCELERATED PHYSICS I PHYS UN2802 ACCELERATED PHYSICS II PHYS UN3003 MECHANICS PHYS UN3007 ELECTRICITYMAGNETISM PHYS UN3008 ELECTROMAGNETIC WAVES ＆ OPTICS PHYS GU4011 PARTICLE ASTROPHYS ＆ COSMOLOGY PHYS GU4018 SOLID STATE PHYSICS PHYS GU4019 MATHEMATICL METHODS OF PHYSICS PHYS GU4021 QUANTUM MECHANICS I PHYS GU4022 QUANTUM MECHANICS II PHYS GU4023 THERMAL ＆ STATISTICAL PHYSICS PHYS GU4040 INTRO TO GENERAL RELATIVITY PHYS GR6047 QUANTUM FIELD THEORY I PHYS GR6080 SCIENTIFIC COMPUTING POLS GU4700 MATH ＆ STATS FOR POLI SCI STAT UN3106 APPLIED MACHINE LEARNING STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS STAT GU4203 PROBABILITY THEORY STAT GU4204 STATISTICAL INFERENCE STAT GU4205 LINEAR REGRESSION MODELS STAT GU4206 STAT COMP ＆ INTRO DATA SCIENCE STAT GU4207 ELEMENTARY STOCHASTIC PROCESS 
Major in Applied Mathematics
The major requires 3741 points as follows:
Code  Title  Points 

Select one of the following three calculus and linear algebra sequences (1315 points including Advanced Placement Credit):  
CALCULUS I and CALCULUS II and CALCULUS III and CALCULUS IV and LINEAR ALGEBRA ^{1}  
OR  
CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA ^{1}  
OR  
CALCULUS I and CALCULUS II and HONORS MATHEMATICS A and HONORS MATHEMATICS B  
Select one of the following three courses. The selected course may not count as an elective.  
ANALYSIS AND OPTIMIZATION  
FOURIER ANALYSIS  
INTRO MODERN ANALYSIS I  
Take each of the following two required courses:  
SEMPROBLEMS IN APPLIED MATH (junior year)  
SEMPROBLEMS IN APPLIED MATH (senior year)  
18 points in electives, with at least 9 points from the following courses. A maximum of 9 points may be selected from courses outside this list, with prior written approval from the Director of Undergraduate Studies.  
ANALYSIS AND OPTIMIZATION  
ORDINARY DIFFERENTIAL EQUATIONS  
COMPLEX VARIABLES  
or MATH GU4065  HONORS COMPLEX VARIABLES  
or APMA E4204  FUNCTNS OF A COMPLEX VARIABLE  
PARTIAL DIFFERENTIAL EQUATIONS  
or APMA E4200  PARTIAL DIFFERENTIAL EQUATIONS  
or APMA E6301  ANALYTIC METHODS FOR PDE'S  
FOURIER ANALYSIS  
COMPUT MATH:INTRONUMERCL METH  
APPL MATH III:DYNAMICAL SYSTMS  
APPLIED FUNCTIONAL ANALYSIS  
INTRO TO BIOPHYSICAL MODELING 
 ^{ 1 }
MATH UN2015 Linear Algebra and Probability does NOT replace MATH UN2010 LINEAR ALGEBRA as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015.
Major in Computer Science–Mathematics
The goal of this interdepartmental major is to provide substantial background in each of these two disciplines, focusing on some of the parts of each which are closest to the other. Students intending to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.
The major requires 20 points in computer science, 1921 points in mathematics, and two 3point electives in either computer science or mathematics.
Code  Title  Points 

Computer Science  
COMS W1004  Introduction to Computer Science and Programming in Java  
or COMS W1007  
COMS W3134  Data Structures in Java  
or COMS W3137  HONORS DATA STRUCTURES ＆ ALGOL  
COMS W3157  ADVANCED PROGRAMMING  
COMS W3203  DISCRETE MATHEMATICS  
COMS W3261  COMPUTER SCIENCE THEORY  
CSEE W3827  FUNDAMENTALS OF COMPUTER SYSTS  
Mathematics  
Select one of the following three calculus and linear algebra sequences (1315 points including Advanced Placement Credit):  
MATH UN1101  MATH UN1102  MATH UN1201  MATH UN1202  MATH UN2010  CALCULUS I and CALCULUS II and CALCULUS III and CALCULUS IV and LINEAR ALGEBRA ^{1}  
OR  
MATH UN1101  MATH UN1102  MATH UN1205  MATH UN2010  CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA ^{1}  
OR  
MATH UN1101  MATH UN1102  MATH UN1207  MATH UN1208  CALCULUS I and CALCULUS II and HONORS MATHEMATICS A and HONORS MATHEMATICS B  
MATH UN3951  UNDERGRADUATE SEMINARS I  
or MATH UN3952  UNDERGRADUATE SEMINARS II  
MATH GU4041  INTRO MODERN ALGEBRA I  
Electives  
Select two of the following courses:  
COMBINATORICS  
ORDINARY DIFFERENTIAL EQUATIONS  
ANALYSIS AND OPTIMIZATION  
COMPLEX VARIABLES  
NUMBER THEORY AND CRYPTOGRAPHY  
MAKING, BREAKING CODES  
PARTIAL DIFFERENTIAL EQUATIONS  
DIFFERENTIAL GEOMETRY  
FOURIER ANALYSIS  
INTRO MODERN ALGEBRA II  
TOPOLOGY  
INTRO TO ALGEBRAIC TOPOLOGY  
INTRO MODERN ANALYSIS I  
INTRO MODERN ANALYSIS II  
INTRODUCTION TO DATABASES  
FUNDLARGESCALE DIST SYSTEMS  
PROGRAMMING LANG ＆ TRANSLATORS  
OPERATING SYSTEMS I  
COMPUTER NETWORKS  
Engineering SoftwareasaService  
ADVANCED SOFTWARE ENGINEERING  
COMPUTER GRAPHICS  
COMPUTER ANIMATION  
USER INTERFACE DESIGN  
SECURITY I  
ANALYSIS OF ALGORITHMS I  
INTROCOMPUTATIONAL COMPLEXITY  
ARTIFICIAL INTELLIGENCE  
NATURAL LANGUAGE PROCESSING  
Computer Vision I: First Principles  
COMPUTATIONAL ASPECTS OF ROBOTICS  
COMPUTATIONAL GENOMICS  
MACHINE LEARNING  
COMPUTER ARCHITECTURE  
SYSTEMONCHIP PLATFORMS 
 ^{ 1 }
MATH UN2015 Linear Algebra and Probability does NOT replace MATH UN2010 LINEAR ALGEBRA as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015.
Major in EconomicsMathematics
For a description of the joint major in economicsmathematics, see the Economics section of this bulletin.
Major in MathematicsStatistics
The program is designed to prepare the student for: (1) a career in industries such as finance and insurance that require a high level of mathematical sophistication and a substantial knowledge of probability and statistics, and (2) graduate study in quantitative disciplines. Students choose electives in finance, actuarial science, operations research, or other quantitative fields to complement requirements in mathematics, statistics, and computer science.
The major requires 3843 points as follows:
Code  Title  Points 

Mathematics  
Select one of the following sequences:  
CALCULUS I and CALCULUS II and CALCULUS III and LINEAR ALGEBRA and ANALYSIS AND OPTIMIZATION ^{1}  
OR  
CALCULUS I and CALCULUS II and ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA and ANALYSIS AND OPTIMIZATION ^{1}  
OR  
HONORS MATHEMATICS A and HONORS MATHEMATICS B and ANALYSIS AND OPTIMIZATION (with approval from the adviser)  
Statistics  
Introductory Course  
CALCBASED INTRO TO STATISTICS  
Required Courses  
PROBABILITY THEORY  
STATISTICAL INFERENCE  
LINEAR REGRESSION MODELS  
Select one of the following courses:  
ELEMENTARY STOCHASTIC PROCESS  
Stochastic Processes for Finance  
STOCHASTC PROCSSESAPPLICTNS I  
STOCHASTIC METHODS IN FINANCE  
Computer Science  
Select one of the following courses:  
Introduction to Computer Science and Programming in Java  
Introduction to Computer Science and Programming in MATLAB  
INTRO TO COMP FOR ENG/APP SCI  
COMS W1007  
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. 
 ^{ 1 }
MATH UN2015 Linear Algebra and Probability does NOT replace MATH UN2010 LINEAR ALGEBRA as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015.
Students interested in modeling applications are recommended to take MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS and MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS.
Students interested in finance are recommended to take MATH GR5010 INTRO TO THE MATH OF FINANCE, STAT GU4261 STATISTICAL METHODS IN FINANCE, and STAT GU4221 TIME SERIES ANALYSIS.
Students interested in graduate study in mathematics or in statistics are recommended to take MATH GU4061 INTRO MODERN ANALYSIS I and MATH GU4062 INTRO MODERN ANALYSIS II.
Students preparing for a career in actuarial science are encouraged to replace STAT GU4205 LINEAR REGRESSION MODELS with STAT GU4282 Linear Regression and Time Series Methods , and to take among their electives STAT GU4281 Theory of Interest .
Minor in Mathematics
The Minor in Mathematics aims to provide students with a solid foundation of mathematical concepts. The program focuses on essential coursework, including multivariable calculus and linear algebra.
The minor functions as a complement to a number of closely related majors, including physics, economics, and computer science. Designed for accessibility, the minor emphasizes foundational understanding rather than proofbased courses, distinguishing it from the comprehensive Mathematics major.
Students in economics, computer science, statistics, physics, and similar natural science programs such as biology and climate science may be particularly interested in the minor. However, its versatile skillset extends beyond these disciplines. Students in language programs, art, and other humanities can also benefit from the minor's quantitative proficiency, enhancing their studies and future career prospects.
Students start with the minor requirements, e.g. with advanced placement sufficient to start the Multivariable Calculus/Linear Algebra component. Upon completion of the minor, students will have acquired the skills and knowledge to carry out basic and advanced computations, formulate and solve problems, both internal to mathematics and arising from real world applications.
The minor consists of 1517 points, as follows:
 Multivariable calculus
 Linear Algebra

Three approved elective courses (at least 9 points), two of which must be 2000+ level courses offered by the Mathematics department. The third course may either be an additional course in Math, or selected from a list of approved cognate courses^{1}. Only one Undergraduate Seminar in Mathematics (MATH UN3951 UNDERGRADUATE SEMINARS I or MATH UN3952 UNDERGRADUATE SEMINARS II) may count towards the minor requirements.
Code  Title  Points 

Multivariable Calculus & Linear Algebra  
Select one of the following five multivariable and linear algebra sequences:  
CALCULUS IV and LINEAR ALGEBRA  
OR  
CALCULUS IV and Linear Algebra and Probability  
OR  
ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA  
OR  
ACCELERATED MULTIVARIABLE CALC and Linear Algebra and Probability  
OR  
HONORS MATHEMATICS A and HONORS MATHEMATICS B  
Electives  
Select three elective courses (at least 9 points), two of which must be 2000+ level courses offered by the Mathematics department. The third course may either be an additional course in Math, or selected from a list of approved cognate courses. ^{1}  
Only one Undergraduate Seminar in Mathematics (MATH UN3951 UNDERGRADUATE SEMINARS I or MATH UN3952 UNDERGRADUATE SEMINARS II) may count towards the minor requirements. 
 ^{ 1 }
See the list of approved cognate courses under the Major in Mathematics
Prerequisites
Prerequisites for the courses in (1) Multivariable calculus and (2) Linear Algebra are as follows:
 MATH UN1202 CALCULUS IV: requires MATH UN1102 CALCULUS II and MATH UN1201 CALCULUS III
 MATH UN1205 ACCELERATED MULTIVARIABLE CALC: requires MATH UN1101 CALCULUS I and MATH UN1102 CALCULUS II
 MATH UN2010 LINEAR ALGEBRA: MATH UN1201 CALCULUS III (strongly recommended)
 MATH UN2015 Linear Algebra and Probability: MATH UN1101 CALCULUS I (strongly recommended)
Minor in Mathematical Probability
Probability Theory is a core mathematical subject with deep connections to a wide variety of disciplines. Many fundamental probabilistic concepts and problems stem from such fruitful interactions, from material sciences (e.g. percolation) to social sciences and computer science (e.g. random networks).The Minor in Mathematical Probability is a focused minor aiming at providing students majoring in these disciplines with a solid mathematical foundation organized around the probabilistic concepts pertinent to their main program of study. The transversal nature of probability both in science at large, and in terms of university structure, is underlined by the option of satisfying some core and elective requirements in other departments, such as Statistics and Industrial Engineering and Operation Research.
The minor naturally complements programs of study in natural and social sciences. As a focused minor, it also provides students with precise guidance on choices of coursework with direct relevance to and synergy with their major.
Students start with the minor requirements, e.g. with advanced placement sufficient to start the Multivariable Calculus/Linear Algebra component. Upon completion of the minor, students will have acquired core mathematical skillsets motivated and illustrated by interactions with other disciplines, organized around theoretical and applied probability. The specialized structure and designation of the minor may also benefit career and professional development.
The minor consists of 1517 points, as follows:
 Multivariable calculus
 Linear Algebra
 Probability Theory
 Two approved elective courses (at least 6 points), at least one of which is an approved course offered by the Mathematics Department. The second course may either be an additional course in Math, or selected from the list of approved cognate courses.
Code  Title  Points 

Multivariable Calculus & Linear Algebra  
CALCULUS III and LINEAR ALGEBRA  
OR  
CALCULUS III and Linear Algebra and Probability  
OR  
ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA  
OR  
ACCELERATED MULTIVARIABLE CALC and Linear Algebra and Probability  
OR  
HONORS MATHEMATICS A and HONORS MATHEMATICS B  
Probability Theory  
PROBABILITY THEORY  
or STAT GU4203  PROBABILITY THEORY  
or IEOR E3658  PROBABILITY FOR ENGINEERS  
Electives  
Select two elective courses (at least 6 points), at least one of which is an approved course offered by the Mathematics Department. The second course may either be an additional course in Math, or selected from the list of approved cognate courses below.  
Approved Mathematics Electives  
ORDINARY DIFFERENTIAL EQUATIONS  
ANALYSIS AND OPTIMIZATION  
PARTIAL DIFFERENTIAL EQUATIONS  
DISCRETE TIME MODELS IN FINANC  
INTRO MODERN ANALYSIS I  
INTRO MODERN ANALYSIS II  
ADVANCED PROBABILITY THEORY  
Approved Cognate Electives  
DISCRETE MATHEMATICS  
STOCHASTIC SYSTEMS AND APPLICATIONS  
PROBABILITY ＆ DECISION THEORY  
THERMAL ＆ STATISTICAL PHYSICS  
STATISTICAL INFERENCE  
ELEMENTARY STOCHASTIC PROCESS  
Stochastic Processes for Finance  
STOCHASTC PROCSSESAPPLICTNS I 
Prerequisites
Prerequisites for the courses in (1) Multivariable calculus and (2) Linear Algebra are as follows:
 MATH UN1201 CALCULUS III: requires MATH UN1101 CALCULUS I
 MATH UN1205 ACCELERATED MULTIVARIABLE CALC: requires MATH UN1101 CALCULUS I and MATH UN1102 CALCULUS II
 MATH UN2010 LINEAR ALGEBRA: MATH UN1201 CALCULUS III (strongly recommended)
 MATH UN2015 Linear Algebra and Probability: MATH UN1101 CALCULUS I (strongly recommended)
Prerequisites for the courses in (3) Probability Theory are as follows:
 MATH GU4155 PROBABILITY THEORY: MATH GU4061 INTRO MODERN ANALYSIS I (approved elective)
 STAT GU4203 PROBABILITY THEORY: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201 CALCBASED INTRO TO STATISTICS, preferably) is strongly recommended
 IEOR E3658 PROBABILITY FOR ENGINEERS: Solid knowledge of calculus, including multiple variable integration
For students who entered Columbia in or before the 202324 academic year
Concentration in Mathematics
The concentration requires the following:
Code  Title  Points 

Mathematics  
Select one of the following three multivariable calculus and linear algebra sequences:  
CALCULUS III and CALCULUS IV and LINEAR ALGEBRA ^{1}  
OR  
ACCELERATED MULTIVARIABLE CALC and LINEAR ALGEBRA ^{1}  
OR  
HONORS MATHEMATICS A and HONORS MATHEMATICS B  
Additional Courses  
Select at least 12 additional points from any of the courses offered by the department numbered 2000 or higher. A maximum of 3 credits may be taken from courses outside the department. ^{2} 
 ^{ 1 }
MATH UN2015 Linear Algebra and Probability does NOT replace MATH UN2010 LINEAR ALGEBRA as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015.
 ^{ 2 }
For mathematics courses taken in other departments, consult with the Director of Undergraduate Studies.
Any course given by the Mathematics department fulfills the General Studies quantitative reasoning requirement when passed with a satisfactory letter grade.
MATH UN1003 COLLEGE ALGEBRAANLYTC 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
Spring 2024: MATH UN1003


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1003  001/12296  M W 11:40am  12:55pm 407 Mathematics Building 
Taeseok Lee  3.00  19/30 
MATH 1003  002/12298  T Th 6:10pm  7:25pm 407 Mathematics Building 
Baiqing Zhu  3.00  16/30 
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  17/56 
MATH UN1101 CALCULUS I. 3.00 points.
Prerequisites: (see Courses for FirstYear Students). Functions, limits, derivatives, introduction to integrals, or an understanding of precalculus will be assumed. (SC)
Spring 2024: MATH UN1101


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1101  001/00226  M W 6:10pm  7:25pm Ll002 Milstein Center 
Lindsay Piechnik  3.00  95/100 
MATH 1101  002/12300  T Th 10:10am  11:25am 413 Kent Hall 
Mrudul Thatte  3.00  42/100 
MATH 1101  003/12301  T Th 2:40pm  3:55pm 703 Hamilton Hall 
Alex Xu  3.00  25/30 
MATH 1101  004/12302  T Th 6:10pm  7:25pm 312 Mathematics Building 
Amal Mattoo  3.00  16/30 
MATH 1101  005/12303  M W 2:40pm  3:55pm 203 Mathematics Building 
Mrudul Thatte  3.00  48/100 
MATH 1101  006/12304  M W 4:10pm  5:25pm 203 Mathematics Building 
Jorge Pineiro Barcelo  3.00  44/100 
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  100/100 
MATH 1101  002/00082  T Th 2:40pm  3:55pm 405 Milbank Hall 
Lindsay Piechnik  3.00  100/100 
MATH 1101  003/11833  M W 10:10am  11:25am 203 Mathematics Building 
Marco Castronovo  3.00  17/100 
MATH 1101  004/11835  M W 11:40am  12:55pm 203 Mathematics Building 
Marco Castronovo  3.00  14/100 
MATH 1101  005/11837  M W 2:40pm  3:55pm 312 Mathematics Building 
George Dragomir  3.00  41/100 
MATH 1101  006/11838  M W 4:10pm  5:25pm 703 Hamilton Hall 
0. FACULTY  3.00  11/30 
MATH 1101  007/11840  M W 6:10pm  7:25pm 207 Mathematics Building 
Marco Sangiovanni Vincentelli  3.00  9/100 
MATH 1101  008/11841  T Th 10:10am  11:25am 520 Mathematics Building 
Soren Galatius  3.00  10/45 
MATH 1101  009/11842  T Th 11:40am  12:55pm 142 Uris Hall 
George Dragomir  3.00  34/100 
MATH 1101  010/11844  T Th 4:10pm  5:25pm 142 Uris Hall 
Marco Sangiovanni Vincentelli  3.00  7/100 
MATH 1101  011/11845  T Th 6:10pm  7:25pm 407 Mathematics Building 
0. FACULTY  3.00  1/30 
MATH 1101  012/00857  M W 1:10pm  2:25pm 408 Zankel 
0. FACULTY  3.00  11/100 
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)
Spring 2024: MATH UN1102


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1102  001/00227  T Th 2:40pm  3:55pm Ll103 Diana Center 
Lindsay Piechnik  3.00  57/60 
MATH 1102  002/12305  T Th 10:10am  11:25am 203 Mathematics Building 
Lucy Yang  3.00  34/100 
MATH 1102  003/12306  T Th 1:10pm  2:25pm 417 Mathematics Building 
Tomasz Owsiak  3.00  61/64 
MATH 1102  004/12307  T Th 6:10pm  7:25pm 520 Mathematics Building 
Fan Zhou  3.00  11/30 
MATH 1102  005/12308  M W 11:40am  12:55pm 520 Mathematics Building 
Davis Lazowski  3.00  23/30 
MATH 1102  006/12309  M W 2:40pm  3:55pm 312 Mathematics Building 
Andres Fernandez Herrero  3.00  33/100 
MATH 1102  007/12310  M W 4:10pm  5:25pm 312 Mathematics Building 
Andres Fernandez Herrero  3.00  12/100 
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  17/100 
MATH 1102  002/11848  M W 2:40pm  3:55pm 207 Mathematics Building 
Andres Ibanez Nunez  3.00  13/100 
MATH 1102  003/11849  M W 4:10pm  5:25pm 407 Mathematics Building 
0. FACULTY  3.00  13/30 
MATH 1102  004/11850  T Th 8:40am  9:55am 203 Mathematics Building 
Lucy Yang  3.00  9/100 
MATH 1102  005/11851  T Th 10:10am  11:25am 203 Mathematics Building 
Lucy Yang  3.00  8/100 
MATH 1102  006/11852  T Th 6:10pm  7:25pm 417 Mathematics Building 
Elliott Stein  3.00  22/64 
MATH UN1201 CALCULUS III. 3.00 points.
Prerequisites: MATH UN1101 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, vectorvalued functions of one variable, scalarvalued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)
Spring 2024: MATH UN1201


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1201  001/00228  M W 10:10am  11:25am 405 Milbank Hall 
Cristian Iovanov  3.00  87/100 
MATH 1201  002/00229  M W 11:40am  12:55pm 323 Milbank Hall 
Cristian Iovanov  3.00  57/60 
MATH 1201  003/12317  M W 1:10pm  2:25pm 207 Mathematics Building 
Ivan Horozov  3.00  94/106 
MATH 1201  004/12318  T Th 11:40am  12:55pm 312 Mathematics Building 
Shaoyun Bai  3.00  42/100 
MATH 1201  005/12320  T Th 2:40pm  3:55pm 207 Mathematics Building 
Jeanne Boursier  3.00  72/100 
MATH 1201  006/12322  T Th 4:10pm  5:25pm 207 Mathematics Building 
Jeanne Boursier  3.00  75/100 
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 
0. FACULTY  3.00  44/70 
MATH 1201  002/11853  M W 8:40am  9:55am 312 Mathematics Building 
Deeparaj Bhat  3.00  10/100 
MATH 1201  003/11854  M W 11:40am  12:55pm 312 Mathematics Building 
Brian Harvie  3.00  51/100 
MATH 1201  004/11855  M W 2:40pm  3:55pm 203 Mathematics Building 
Brian Harvie  3.00  47/100 
MATH 1201  005/11856  T Th 11:40am  12:55pm 203 Mathematics Building 
Gyujin Oh  3.00  100/100 
MATH 1201  006/11857  T Th 1:10pm  2:25pm 207 Mathematics Building 
Gyujin Oh  3.00  100/100 
MATH 1201  007/11861  T Th 2:40pm  3:55pm 207 Mathematics Building 
Yoonjoo Kim  3.00  24/100 
MATH 1201  008/11862  T Th 4:10pm  5:25pm 312 Mathematics Building 
Yoonjoo Kim  3.00  21/100 
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)
Spring 2024: MATH UN1202


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1202  001/12325  M W 4:10pm  5:25pm 417 Mathematics Building 
Qiao He  3.00  37/64 
MATH 1202  002/12327  T Th 2:40pm  3:55pm 417 Mathematics Building 
Qiao He  3.00  44/64 
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  52/50 
MATH 1202  002/11863  M W 6:10pm  7:25pm 203 Mathematics Building 
Mikhail Smirnov  3.00  54/100 
MATH UN1205 ACCELERATED MULTIVARIABLE CALC. 4.00 points.
Prerequisites: (MATH UN1101 and MATH UN1102)
Prerequisites: (MATH UN1101 and MATH UN1102) Vectors in dimensions 2 and 3, vectorvalued functions of one variable, scalarvalued functions of several variables, partial derivatives, gradients, optimization, Lagrange multipliers, double and triple integrals, line and surface integrals, vector calculus. This course is an accelerated version of MATH UN1201  MATH UN1202. Students taking this course may not receive credit for MATH UN1201 and MATH UN1202
Spring 2024: MATH UN1205


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1205  001/12328  T Th 11:40am  12:55pm 417 Mathematics Building 
Sam Collingbourne  4.00  28/64 
Fall 2024: MATH UN1205


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1205  001/11864  M W 1:10pm  2:25pm 417 Mathematics Building 
Dawei Shen  4.00  25/64 
MATH UN1207 HONORS MATHEMATICS A. 4.00 points.
Prerequisites: (see Courses for FirstYear 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 11:40am  12:55pm 417 Mathematics Building 
Giulia Sacca  4.00  10/64 
MATH UN1208 HONORS MATHEMATICS B. 4.00 points.
Prerequisites: (see Courses for FirstYear Students).
Prerequisites: (see Courses for FirstYear 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 2024: MATH UN1208


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 1208  001/12329  T Th 1:10pm  2:25pm 603 Hamilton Hall 
George Dragomir  4.00  31/50 
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)
Spring 2024: MATH UN2000


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2000  001/12330  T Th 1:10pm  2:25pm 520 Mathematics Building 
Giulia Sacca  3.00  21/44 
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  24/55 
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 2024: MATH BC2001


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2001  001/00231  W 1:10pm  2:00pm Ll103 Diana Center 
Dusa McDuff  1.00  17/28 
MATH UN2005 INTRODUCTION TO MATHEMATICS PROOFS. 0.00 points.
This is a seminar course that covers the basics of mathematical proofs and in particular the epsilondelta argument in single variable calculus. Students who have little experience with mathematical proofs are strongly encouraged to take this course concurrently with Honors Math, Into to Modern Algebra, or Intro to Modern Analysis
Spring 2024: MATH UN2005


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2005  001/12333  F 11:00am  1:00pm 417 Mathematics Building 
MuTao Wang  0.00  22/64 
Fall 2024: MATH UN2005


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2005  001/11866  F 11:00am  1:00pm 417 Mathematics Building 
0. FACULTY  0.00  24/64 
MATH BC2006 COMBINATORICS. 3.00 points.
Spring 2024: MATH BC2006


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2006  001/00254  T Th 10:10am  11:25am 328 Milbank Hall 
Alisa Knizel  3.00  42/56 
MATH UN2010 LINEAR ALGEBRA. 3.00 points.
Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
Spring 2024: MATH UN2010


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2010  001/12334  M W 10:10am  11:25am 312 Mathematics Building 
Amadou Bah  3.00  84/110 
MATH 2010  002/12335  M W 11:40am  12:55pm 312 Mathematics Building 
Amadou Bah  3.00  85/110 
MATH 2010  003/12336  T Th 11:40am  12:55pm 203 Mathematics Building 
Rostislav Akhmechet  3.00  105/110 
MATH 2010  004/12337  T Th 1:10pm  2:25pm 203 Mathematics Building 
Rostislav Akhmechet  3.00  108/110 
MATH 2010  005/12339  T Th 6:10pm  7:25pm 417 Mathematics Building 
Elliott Stein  3.00  42/64 
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  70/90 
MATH 2010  002/00015  M W 11:40am  12:55pm 405 Milbank Hall 
Cristian Iovanov  3.00  85/110 
MATH 2010  003/11867  M W 2:40pm  3:55pm 142 Uris Hall 
Siddhi Krishna  3.00  29/100 
MATH 2010  004/11868  T Th 10:10am  11:25am 312 Mathematics Building 
Amadou Bah  3.00  100/100 
MATH 2010  005/11869  T Th 1:10pm  2:25pm 203 Mathematics Building 
Amadou Bah  3.00  59/100 
MATH UN2015 Linear Algebra and Probability. 3.00 points.
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, the Spectral Theorem and singular value decompositions. 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 approaches to problem solving. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics. Math majors, joint majors, and math concentrators must take MATH UN2010 Linear Algebra, which focuses on linear algebra concepts and foundations that are needed for upperlevel math courses. MATH UN2015 (Linear Algebra and Probability) does NOT replace MATH UN2010 (Linear Algebra) as prerequisite requirements of math courses. Students may not receive full credit for both courses MATH UN2010 and MATH UN2015
Spring 2024: MATH UN2015


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2015  001/12340  M W 1:10pm  2:25pm 312 Mathematics Building 
ChenChih Lai  3.00  78/110 
Fall 2024: MATH UN2015


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2015  001/11870  T Th 11:40am  12:55pm 207 Mathematics Building 
Evan Sorensen  3.00  100/100 
MATH 2015  002/11871  T Th 1:10pm  2:25pm 142 Uris Hall 
Evan Sorensen  3.00  81/100 
MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS. 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
Spring 2024: MATH UN2030


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2030  001/12341  M W 10:10am  11:25am 203 Mathematics Building 
Ovidiu Savin  3.00  93/100 
MATH 2030  002/12346  T Th 11:40am  12:55pm 142 Uris Hall 
Yin Li  3.00  53/100 
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  100/100 
MATH 2030  002/11873  T Th 10:10am  11:25am 142 Uris Hall 
Jeanne Boursier  3.00  42/100 
MATH 2030  003/11874  T Th 1:10pm  2:25pm 520 Mathematics Building 
Jeanne Boursier  3.00  49/49 
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, KuhnTucker conditions. Elements of the calculus of variations and optimal control. (SC)
Spring 2024: MATH UN2500


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 2500  001/12347  T Th 11:40am  12:55pm 207 Mathematics Building 
Wenjian Liu  3.00  86/100 
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  64/64 
MATH 2500  002/11876  T Th 10:10am  11:25am 517 Hamilton Hall 
Roger Van Peski  3.00  75/75 
MATH UN3007 COMPLEX VARIABLES. 3.00 points.
Prerequisites: MATH UN1202 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, CauchyRiemann 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  83/100 
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 2024: MATH UN3020


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3020  001/12358  M W 10:10am  11:25am 207 Mathematics Building 
Yoonjoo Kim  3.00  70/100 
MATH UN3025 MAKING, BREAKING CODES. 3.00 points.
Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and and MATH UN2010.
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  98/100 
MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS. 3.00 points.
Prerequisites: MATH UN3027 and MATH UN2010 or the equivalent
Prerequisites: (MATH UN2010 and MATH UN2030) or the equivalent introduction to partial differential equations. Firstorder equations. Linear secondorder equations; separation of variables, solution by series expansions. Boundary value problems
Spring 2024: MATH UN3028


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3028  001/12359  T Th 1:10pm  2:25pm 312 Mathematics Building 
Simon Brendle  3.00  59/100 
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 Recommended: MATH UN3027 (or MATH UN2030 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, riskneutral valuation, hedging, termstructure of interest rates
Spring 2024: MATH UN3050


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3050  001/12360  M W 6:10pm  7:25pm 312 Mathematics Building 
Mikhail Smirnov  3.00  57/64 
MATH UN3386 DIFFERENTIAL GEOMETRY. 3.00 points.
Prerequisites: MATH UN1202 or the equivalent.
Local and global differential geometry of submanifolds of Euclidiean 3space. Frenet formulas for curves. Various types of curvatures for curves and surfaces and their relations. The GaussBonnet theorem.
MATH UN3901 SUPERVISED READINGS I. 1.003.00 points.
Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to fulltime 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  1.003.00  0/5 
MATH 3901  002/00791  
Daniela De Silva  1.003.00  0/5 
MATH 3901  003/17561  
Richard Hamilton  1.003.00  0/1 
MATH UN3902 SUPERVISED READINGS II. 1.003.00 points.
Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to fulltime 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 2024: MATH UN3902


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3902  001/18557  
Julien Dubedat  1.003.00  1/1 
MATH 3902  002/20706  
Amadou Bah  1.003.00  1/1 
MATH 3902  003/20734  
Andrew Blumberg  1.003.00  2/2 
MATH 3902  004/20960  
Simon Brendle  1.003.00  1/1 
MATH 3902  005/20967  
Francesco Lin  1.003.00  3/3 
MATH 3902  006/20991  
MuTao Wang  1.003.00  1/1 
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  48/64 
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 2024: MATH UN3952


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3952  001/00233  
Alisa Knizel  3.00  61/80 
MATH UN3994 SENIOR THESIS IN MATHEMATICS I. 4.00 points.
Majors in Mathematics are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should contact a faculty member to determine an appropriate topic, and receive written approval from the faculty advisor and the Director of Undergraduate Studies (faculty sponsorship is limited to fulltime instructors on the staff list). Research is conducted primarily during the fall term; the final paper is submitted to the Director of Undergraduate Studies during the subsequent spring term. MATH UN3994 SENIOR THESIS IN MATHEMATICS I must be taken in the fall term, during which period the student conducts primary research on the agreed topic. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper. Sections of SENIOR THESIS IN MATHEMATICS I and II do NOT count towards the major requirements, with the exception of an advanced written approval by the DUS
Fall 2024: MATH UN3994


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3994  001/17621  
Robert Friedman  4.00  0/1 
MATH UN3995 SENIOR THESIS IN MATHEMATICS II. 2.00 points.
Majors in Mathematics are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should contact a faculty member to determine an appropriate topic, and receive written approval from the faculty advisor and the Director of Undergraduate Studies (faculty sponsorship is limited to fulltime instructors on the staff list). Research is conducted primarily during the fall term; the final paper is submitted to the Director of Undergraduate Studies during the subsequent spring term. MATH UN3994 SENIOR THESIS IN MATHEMATICS I must be taken in the fall term, during which period the student conducts primary research on the agreed topic. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper. Sections of SENIOR THESIS IN MATHEMATICS I and II do NOT count towards the major requirements, with the exception of an advanced written approval by the DUS
Spring 2024: MATH UN3995


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 3995  001/20703  
Gyujin Oh  2.00  1/1 
MATH 3995  002/20726  
Xi Shen  2.00  1/1 
MATH 3995  003/20750  
Qiao He  2.00  1/1 
MATH 3995  004/20817  
Ioannis Karatzas  2.00  1/1 
MATH 3995  005/20818  
Daniela De Silva  2.00  1/1 
MATH 3995  006/20992  
MuTao Wang  2.00  1/1 
MATH GU4007 ANALYTIC NUMBER THEORY. 3.00 points.
Prerequisites: MATH UN3007
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 Lfunctions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper halfplane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, Lfunctions of modular forms
Spring 2024: MATH GU4007


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4007  001/12361  T Th 2:40pm  3:55pm 307 Mathematics Building 
Dorian Goldfeld  3.00  8/19 
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  47/49 
MATH GU4041 INTRO MODERN ALGEBRA I. 3.00 points.
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 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
Spring 2024: MATH GU4041


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4041  001/12362  M W 10:10am  11:25am 417 Mathematics Building 
Yujie Xu  3.00  55/64 
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  100/100 
MATH GU4042 INTRO MODERN ALGEBRA II. 3.00 points.
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 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
Spring 2024: MATH GU4042


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4042  001/12363  M W 2:40pm  3:55pm 417 Mathematics Building 
Konstantin Aleshkin  3.00  43/64 
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  31/49 
MATH GU4043 ALGEBRAIC NUMBER THEORY. 3.00 points.
Prerequisites: MATH GU4041 and MATH GU4042 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, padic numbers and Dedekind zeta function
Spring 2024: MATH GU4043


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4043  001/12364  T Th 4:10pm  5:25pm 307 Mathematics Building 
Gyujin Oh  3.00  8/20 
MATH GU4044 REPRESENTATNS OF FINITE GROUPS. 3.00 points.
Prerequisites: MATH UN2010 and MATH GU4041 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  30/30 
MATH GU4045 ALGEBRAIC CURVES. 3.00 points.
Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007
Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, RiemannRoch theorem
Spring 2024: MATH GU4045


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4045  001/12366  M W 2:40pm  3:55pm 307 Mathematics Building 
Nathan Chen  3.00  5/20 
MATH GU4051 TOPOLOGY. 3.00 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.
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  38/49 
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.
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 3manifold 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  13/20 
MATH GU4053 INTRO TO ALGEBRAIC TOPOLOGY. 3.00 points.
Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051
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 2024: MATH GU4053


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4053  001/12368  T Th 11:40am  12:55pm 407 Mathematics Building 
Lucy Yang  3.00  14/30 
MATH GU4061 INTRO MODERN ANALYSIS I. 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. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, AscoliArzela theorem, StoneWeierstrass theorem
Spring 2024: MATH GU4061


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4061  001/12541  M W 1:10pm  2:25pm 203 Mathematics Building 
Ivan Corwin  3.00  55/110 
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  61/64 
MATH 4061  002/11859  T Th 2:40pm  3:55pm 417 Mathematics Building 
3.00  53/64 
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.
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
Spring 2024: MATH GU4062


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4062  001/12540  T Th 4:10pm  5:25pm 417 Mathematics Building 
Nikolaos Apostolakis  3.00  14/50 
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  21/49 
MATH GU4065 HONORS COMPLEX VARIABLES. 3.00 points.
Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061
Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061 A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, CauchyRiemann 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  39/45 
MATH GU4081 INTRODIFFERENTIABLE MANIFOLDS. 3.00 points.
Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010
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. PoincareHopf theorem. Differential forms and Stokes theorem
Spring 2024: MATH GU4081


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4081  001/00234  M W 10:10am  11:25am Ll103 Diana Center 
Dusa McDuff  3.00  17/40 
MATH GU4155 PROBABILITY THEORY. 3.00 points.
Prerequisites: MATH GU4061 or MATH UN3007
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 2024: MATH GU4155


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4155  001/12373  T Th 2:40pm  3:55pm 520 Mathematics Building 
Ioannis Karatzas  3.00  27/49 
Fall 2024: MATH GU4155


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 4155  001/11860  T Th 2:40pm  3:55pm 717 Hamilton Hall 
Ivan Corwin  3.00  32/75 
MATH GU4156 ADVANCED PROBABILITY THEORY. 3.00 points.
This course will cover advance topics in probability, including: the theory of martingales in discrete and in continuous time; Brownian motion and its properties, stochastic integration, ordinary and partial stochastic differential equations; Applications to optimal filtering, stopping, control, and finance; Continuoustime Markov chains, systems of interacting particles, relative entropy dissipation, notions of information theory; Electrical networks, random walks on graphs and groups, percolation
MATH GU4200 MATHEMATICS AND THE HUMANITIES. 4.00 points.
This course is being taught by two senior faculty members who are theorists and practitioners in disciplines as different as mathematics and literary criticism. The instructors believe that in today's world, the different ways in which theoretical mathematics and literary criticism mold the imaginations of students and scholars, should be brought together, so that the robust ethical imagination that is needed to combat the disintegration of our world can be produced. Except for the length of novels, the reading is no more than 100 pages a week. Our general approach is to keep alive the disciplinary differences between literary/philosophical (humanities) reading and mathematical writing. Some preliminary questions we have considered are: the survival skills of the logicist school over against the Foundational Crisis of the early 20th century; by way of Wittgenstein and others, we ask, Are mathematical objects real? Or are they linguistic conventions? We will consider the literary/philosophical use of mathematics, often by imaginative analogy; and the role of the digital imagination in the humanities: Can socalled creative work as well as mathematics be written by machines? Guest faculty from other departments will teach with us to help students and instructors understand various topics. We will close with how a novel animates “science” in prose, stepping out of the silo of disciplinary mathematics to the arena where mathematics is considered a codename for science: Christine BrookeRose’s novel Subscript
MATH GU4391 INTRO TO QUANTUM MECHANICS. 3.00 points.
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
Fall 2024: MATH GU4391


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 

MATH 4391  001/11885  M W 2:40pm  3:55pm 417 Mathematics Building 
Peter Woit  3.00  43/64 
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.