Computer Science  Mathematics
Departmental Undergraduate Office: 410 Mathematics; 2128542432
http://www.math.columbia.edu/
Director of Undergraduate Studies: Prof. MuTao Wang, 514 Mathematics; 2128543052; mtwang@math.columbia.edu
Calculus Director: Prof. George Dragomir, 525 Mathematics; 2128542849; gd2572@columbia.edu
Computer ScienceMathematics Adviser:
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:
Mathematics: Prof. Julien Dubedat, 601 Mathematics; 2128548806; jd2653@columbia.edu
Economics: Dr. Susan Elmes, 1006 International Affairs Building; 2128549124; se5@columbia.edu
MathematicsStatistics Advisers:
Mathematics: Prof. Julien Dubedat, 601 Mathematics; 2128548806; dubedat@math.columbia.edu
Statistics: Ronald Neath, 612 Watson; 2128531398; rcn2112@columbia.edu
Statistics: Gabriel Young, 610 Watson; 2128531395; gjy2107@columbia.edu

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.
Another requirement for majors is participation in an undergraduate seminar, usually in the junior or senior year. Applied math majors must take the undergraduate seminar 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.
Courses 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.
Advanced Placement
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 MATH UN1207 HONORS MATHEMATICS A with a grade of C or better. Students can receive credit for only one calculus sequence.
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.
Transfers 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, or concentration. Students who are doing a double major cannot double count courses for their majors.
Senior Thesis and Departmental Honors
In order to be eligible for departmental honors, majors must write a senior thesis. Normally no more than 10% of graduating majors receive departmental honors in a given academic year.
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 DUS. The research of the thesis is conducted primarily during the fall term and the final paper is submitted to the DUS 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, with the exception of an advanced written approval by the DUS.
Professors
 Mohammed Abouzaid
 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
 Mikhail Khovanov
 ChiuChu Liu
 Dusa McDuff (Barnard)
 Andrei Okounkov
 D. H. Phong
 Henry Pinkham
 Ovidiu Savin
 Michael Thaddeus
 Eric Urban
 MuTao Wang
Associate Professors
 Amol Aggarwal
 Chao Li
 Lindsay Piechnik (Barnard)
 Will Sawin
Assistant Professors
 Elena Giorgi
 Francesco Lin
 Giulia Sacca
J.F. Ritt Assistant Professors
 Rostislav Akhmechet
 Konstantin Aleshkin
 Amadou Bah
 Marco Castronovo
 Sam Collingbourne
 Andres FernandezHerrero
 Florian Johne
 Inbar Klang
 S. Michael Miller Eismeier
 Gyujin Oh
 Tudor Padurariu
 Akash Sengupta
 Xi Sisi Shen
Senior Lecturers in Discipline
 Lars Nielsen
 Mikhail Smirnov
 Peter Woit
Lecturers in Discipline
 George Dragomir
 Gerhardt Hinkle
On Leave
 Profs. Aggarwal, Corwin, Giorgi, Klang, Krichever, Okounkov (Fall 2022)
 Profs. Abouzaid, Aggarwal, Brendle, Friedman, Goldfeld, Oh, Okounkov (Spring 2023)
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  
15 points in the following courses:  
INTRO MODERN ALGEBRA I  
INTRO MODERN ALGEBRA II  
INTRO MODERN ANALYSIS I ^{2}  
INTRO MODERN ANALYSIS II ^{2}  
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  
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 }
UN2015 (Linear Algebra and Probability) does NOT replace 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 section of the 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 contact the director of undergraduate studies.
Approved Cognate Courses 1  Approved Cognate Courses 2  Approved Cognate Courses 3 

APMA E4300 COMPUT MATH:INTRONUMERCL METH APMA E4302 METHODS IN COMPUTATIONAL SCI 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 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 EESC GU4008 Introduction to Atmospheric Science EESC GU4090 INTRO TO GEOCHRONOLGY IEOR E3106 STOCHASTIC SYSTEMS AND APPLICATIONS IEOR E3658 PROBABILITY FOR ENGINEERS IEOR E4700 INTRO TO FINANCIAL ENGINEERING MSAE E3010 FOUNDATIONS OF MATERIALS SCIENCE PHIL UN3411 SYMBOLIC LOGIC PHIL GU4424 MODAL LOGIC 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 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  
APMA E4901  SEMPROBLEMS IN APPLIED MATH (junior year)  
APMA E4903  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 }
UN2015 (Linear Algebra and Probability) does NOT replace 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  Honors Introduction to Computer Science  
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:  
ANALYSIS OF ALGORITHMS I  
Numerical Algorithms and Complexity  
COMBINATORICS  
ANALYSIS AND OPTIMIZATION  
COMPLEX VARIABLES  
NUMBER THEORY AND CRYPTOGRAPHY  
DIFFERENTIAL GEOMETRY  
TOPOLOGY  
INTRO MODERN ANALYSIS I 
 ^{ 1 }
UN2015 (Linear Algebra and Probability) does NOT replace 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.
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  
Honors Introduction to Computer Science  
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 }
UN2015 (Linear Algebra and Probability) does NOT replace 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 .
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 }
UN2015 (Linear Algebra and Probability) does NOT replace 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 2023: MATH UN1003


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

MATH 1003  001/12007  M W 11:40am  12:55pm 407 Mathematics Building 
Gerhardt Hinkle  3.00  19/30 
MATH 1003  002/12008  T Th 6:10pm  7:25pm 407 Mathematics Building 
Gerhardt Hinkle  3.00  9/30 
Fall 2023: MATH UN1003


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1003  001/00080  M W 6:10pm  7:25pm 328 Milbank Hall 
Lindsay Piechnik  3.00  3/30 
MATH 1003  002/00081  T Th 2:40pm  3:55pm 207 Milbank Hall 
Lindsay Piechnik  3.00  6/30 
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 2023: MATH UN1101


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

MATH 1101  001/00020  M W 6:10pm  7:25pm Ll002 Milstein Center 
Lindsay Piechnik  3.00  98/100 
MATH 1101  002/12019  M W 10:10am  11:25am 402 Chandler 
Marco Castronovo  3.00  44/110 
MATH 1101  003/12020  M W 2:40pm  3:55pm 407 Mathematics Building 
KuanWen Chen  3.00  15/30 
MATH 1101  004/12021  T Th 11:40am  12:55pm 312 Mathematics Building 
Rostislav Akhmechet  3.00  58/110 
MATH 1101  005/12022  T Th 2:40pm  3:55pm 203 Mathematics Building 
Luis Fernandez  3.00  43/110 
MATH 1101  006/12023  T Th 4:10pm  5:25pm 407 Mathematics Building 
Chilin Zhang  3.00  5/30 
Fall 2023: MATH UN1101


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1101  001/10629  M W 10:10am  11:25am Room TBA 
Amadou Bah  3.00  11/100 
MATH 1101  002/10630  M W 11:40am  12:55pm Room TBA 
Nathan Chen  3.00  27/100 
MATH 1101  003/10631  M W 1:10pm  2:25pm Room TBA 
Nathan Chen  3.00  19/100 
MATH 1101  004/10632  M W 2:40pm  3:55pm Room TBA 
Yin Li  3.00  8/100 
MATH 1101  005/10633  M W 4:10pm  5:25pm Room TBA 
Qiao He  3.00  4/100 
MATH 1101  006/10634  M W 6:10pm  7:25pm Room TBA 
3.00  7/30  
MATH 1101  007/10635  T Th 10:10am  11:25am Room TBA 
Qiao He  3.00  9/100 
MATH 1101  008/10636  T Th 11:40am  12:55pm Room TBA 
James Hotchkiss  3.00  4/100 
MATH 1101  009/10637  T Th 1:10pm  2:25pm Room TBA 
James Hotchkiss  3.00  10/100 
MATH 1101  010/10638  T Th 4:10pm  5:25pm Room TBA 
3.00  7/30  
MATH 1101  011/10639  T Th 6:10pm  7:25pm Room TBA 
3.00  1/30 
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 2023: MATH UN1102


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

MATH 1102  001/00021  T Th 2:40pm  3:55pm 304 Barnard Hall 
Lindsay Piechnik  3.00  99/100 
MATH 1102  002/12024  M W 1:10pm  2:25pm 407 Mathematics Building 
Ryuichi Haney  3.00  17/30 
MATH 1102  003/12025  M W 2:40pm  3:55pm 417 Mathematics Building 
Richard Hamilton  3.00  11/64 
MATH 1102  004/12026  M W 6:10pm  7:25pm 417 Mathematics Building 
Elliott Stein  3.00  47/64 
MATH 1102  005/12027  T Th 10:10am  11:25am 203 Mathematics Building 
Allen Yuan  3.00  43/100 
MATH 1102  006/12028  T Th 11:40am  12:55pm 203 Mathematics Building 
Andres Fernandez Herrero  3.00  15/100 
MATH 1102  007/12029  T Th 6:10pm  7:25pm 417 Mathematics Building 
Patrick Lei  3.00  7/30 
Fall 2023: MATH UN1102


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1102  001/10640  M W 1:10pm  2:25pm Room TBA 
Yoonjoo Kim  3.00  14/100 
MATH 1102  002/10641  M W 2:40pm  3:55pm Room TBA 
Yoonjoo Kim  3.00  5/100 
MATH 1102  003/10642  M W 4:10pm  5:25pm Room TBA 
0. FACULTY  3.00  9/64 
MATH 1102  004/10643  T Th 10:10am  11:25am Room TBA 
3.00  12/30  
MATH 1102  005/10644  T Th 2:40pm  3:55pm Room TBA 
3.00  15/30  
MATH 1102  006/10645  T Th 6:10pm  7:25pm Room TBA 
Elliott Stein  3.00  13/64 
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 2023: MATH UN1201


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

MATH 1201  001/12030  M W 10:10am  11:25am 207 Mathematics Building 
Xi Shen  3.00  46/100 
MATH 1201  002/12031  M W 11:40am  12:55pm 312 Mathematics Building 
ChenChih Lai  3.00  56/100 
MATH 1201  003/12032  M W 1:10pm  2:25pm 203 Mathematics Building 
Xi Shen  3.00  79/100 
MATH 1201  004/12033  T Th 1:10pm  2:25pm 207 Mathematics Building 
Inbar Klang  3.00  107/100 
MATH 1201  005/12034  T Th 2:40pm  3:55pm 207 Mathematics Building 
Inbar Klang  3.00  112/100 
MATH 1201  006/19536  M W 6:10pm  7:25pm 203 Mathematics Building 
Tomasz Owsiak  3.00  36/100 
Fall 2023: MATH UN1201


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1201  001/00082  T Th 10:10am  11:25am Ll002 Milstein Center 
Alisa Knizel  3.00  38/80 
MATH 1201  002/10646  M W 8:40am  9:55am Room TBA 
Gyujin Oh  3.00  20/100 
MATH 1201  003/10647  M W 10:10am  11:25am Room TBA 
Gyujin Oh  3.00  100/100 
MATH 1201  004/10648  M W 2:40pm  3:55pm Room TBA 
Konstantin Aleshkin  3.00  66/100 
MATH 1201  005/10649  T Th 11:40am  12:55pm Room TBA 
Shaoyun Bai  3.00  11/100 
MATH 1201  006/10650  T Th 1:10pm  2:25pm Room TBA 
Shaoyun Bai  3.00  18/100 
MATH 1201  007/10651  T Th 6:10pm  7:25pm Room TBA 
Lucy Yang  3.00  16/100 
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 2023: MATH UN1202


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

MATH 1202  001/00022  T Th 2:40pm  3:55pm 504 Diana Center 
Daniela De Silva  3.00  47/60 
MATH 1202  002/00023  T Th 4:10pm  5:25pm 328 Milbank Hall 
Daniela De Silva  3.00  42/60 
Fall 2023: MATH UN1202


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1202  001/00083  M W 10:10am  11:25am 504 Diana Center 
Daniela De Silva  3.00  42/60 
MATH 1202  002/10652  M W 6:10pm  7:25pm Room TBA 
Mikhail Smirnov  3.00  29/100 
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 2023: MATH UN1205


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

MATH 1205  001/12492  T Th 1:10pm  2:25pm 141 Uris Hall 
Sam Collingbourne  4.00  29/50 
Fall 2023: MATH UN1205


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 1205  001/10653  M W 1:10pm  2:25pm Room TBA 
MuTao Wang  4.00  14/64 
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 2023: MATH UN1207


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

MATH 1207  001/10654  T Th 11:40am  12:55pm Room TBA 
George Dragomir  4.00  7/100 
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 2023: MATH UN1208


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

MATH 1208  001/12494  T Th 1:10pm  2:25pm 407 Mathematics Building 
Stephen Miller  4.00  32/64 
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)
Spring 2023: MATH UN2000


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

MATH 2000  001/12495  T Th 1:10pm  2:25pm 520 Mathematics Building 
Francesco Lin  3.00  24/50 
Fall 2023: MATH UN2000


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2000  001/00084  M W 10:10am  11:25am Ll104 Diana Center 
Dusa McDuff  3.00  20/55 
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 2023: MATH UN2005


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

MATH 2005  001/19598  F 11:00am  1:00pm 622 Mathematics Building 
MuTao Wang  0.00  4/20 
Fall 2023: MATH UN2005


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2005  001/10961  F 11:00am  1:00pm Room TBA 
MuTao Wang  0.00  17/64 
MATH BC2006 COMBINATORICS. 3.00 points.
Spring 2023: MATH BC2006


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

MATH 2006  001/00024  T Th 10:10am  11:25am 328 Milbank Hall 
David Bayer  3.00  60/56 
MATH UN2010 LINEAR ALGEBRA. 3.00 points.
Prerequisites: MATH UN1201 or the equivalent.
Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
Spring 2023: MATH UN2010


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

MATH 2010  001/12504  M W 10:10am  11:25am 203 Mathematics Building 
Amadou Bah  3.00  81/100 
MATH 2010  002/12541  M W 11:40am  12:55pm 203 Mathematics Building 
Amadou Bah  3.00  85/100 
MATH 2010  003/12543  T Th 1:10pm  2:25pm 312 Mathematics Building 
Jie Jun Morris Ang  3.00  72/100 
MATH 2010  004/12546  T Th 4:10pm  5:25pm 203 Mathematics Building 
Konstantin Aleshkin  3.00  56/100 
MATH 2010  005/12563  T Th 6:10pm  7:25pm 203 Mathematics Building 
Konstantin Aleshkin  3.00  29/100 
Fall 2023: MATH UN2010


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2010  001/00085  M W 10:10am  11:25am Ll103 Diana Center 
Daniele Alessandrini  3.00  56/56 
MATH 2010  002/00086  M W 11:40am  12:55pm 328 Milbank Hall 
Daniele Alessandrini  3.00  56/56 
MATH 2010  003/10962  M W 2:40pm  3:55pm Room TBA 
Siddhi Krishna  3.00  81/100 
MATH 2010  004/10963  T Th 8:40am  9:55am Room TBA 
Andrew Blumberg  3.00  19/100 
MATH 2010  005/10964  T Th 4:10pm  5:25pm Room TBA 
Marco Castronovo  3.00  100/100 
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 2023: MATH UN2015


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

MATH 2015  001/12568  T Th 11:40am  12:55pm 207 Mathematics Building 
George Dragomir  3.00  38/100 
Fall 2023: MATH UN2015


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2015  001/10965  M W 1:10pm  2:25pm Room TBA 
George Dragomir  3.00  100/100 
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 2023: MATH UN2030


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

MATH 2030  001/12573  T Th 10:10am  11:25am 312 Mathematics Building 
Timothy Large  3.00  75/110 
MATH 2030  002/12584  T Th 11:40am  12:55pm 614 Schermerhorn Hall 
Florian Johne  3.00  30/110 
Fall 2023: MATH UN2030


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2030  001/10966  M W 1:10pm  2:25pm Room TBA 
Elena Giorgi  3.00  70/100 
MATH 2030  002/10967  M W 4:10pm  5:25pm Room TBA 
Konstantin Aleshkin  3.00  75/100 
MATH 2030  003/10968  T Th 6:10pm  7:25pm Room TBA 
Jeanne Boursier  3.00  21/100 
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 2023: MATH UN2500


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

MATH 2500  001/12587  M W 1:10pm  2:25pm 207 Mathematics Building 
Julien Dubedat  3.00  20/100 
MATH 2500  002/12594  M W 2:40pm  3:55pm 207 Mathematics Building 
Ivan Horozov  3.00  66/100 
Fall 2023: MATH UN2500


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 2500  001/10969  T Th 8:40am  9:55am Room TBA 
Xi Shen  3.00  29/100 
MATH 2500  002/10970  T Th 10:10am  11:25am Room TBA 
Xi Shen  3.00  79/100 
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 2023: MATH UN3007


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

MATH 3007  001/10971  T Th 11:40am  12:55pm Room TBA 
Ovidiu Savin  3.00  50/50 
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 2023: MATH UN3020


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

MATH 3020  001/12598  M W 10:10am  11:25am 312 Mathematics Building 
Daniele Alessandrini  3.00  78/100 
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 2023: MATH UN3025


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

MATH 3025  001/10972  T Th 1:10pm  2:25pm Room TBA 
Dorian Goldfeld  3.00  100/100 
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 2023: MATH UN3028


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

MATH 3028  001/12600  T Th 1:10pm  2:25pm 203 Mathematics Building 
Elena Giorgi  3.00  78/110 
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 2023: MATH UN3050


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

MATH 3050  001/12604  M W 6:10pm  7:25pm 312 Mathematics Building 
Mikhail Smirnov  3.00  56/64 
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.
Fall 2023: MATH UN3386


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

MATH 3386  001/10973  M W 2:40pm  3:55pm Room TBA 
Richard Hamilton  3.00  27/50 
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 2023: MATH UN3901


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

MATH 3901  001/15172  
Peter Woit  1.003.00  0/4 
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 2023: MATH UN3902


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

MATH 3902  001/17996  
Ioannis Karatzas  1.003.00  6/3 
MATH 3902  002/18614  
George Dragomir  1.003.00  1/1 
MATH 3902  003/19430  
Elena Giorgi  1.003.00  1/1 
MATH 3902  004/19825  
Siddhi Krishna  1.003.00  2/2 
MATH 3902  005/20057  
Florian Johne  1.003.00  1/1 
MATH 3902  006/20071  
Tudor Padurariu  1.003.00  1/1 
MATH 3902  007/20158  
Mikhail Khovanov  1.003.00  2/2 
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 2023: MATH UN3951


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

MATH 3951  001/00757  
Daniele Alessandrini  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 2023: MATH UN3952


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

MATH 3952  001/00025  
David Bayer, Stephen Miller  3.00  73/80 
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 2023: MATH UN3994


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

MATH 3994  001/14137  
Peter Woit  4.00  1/1 
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 2023: MATH UN3995


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

MATH 3995  001/19826  
Stephen Miller  2.00  1/1 
MATH 3995  002/19941  
Andrew Blumberg  2.00  1/1 
MATH 3995  003/20039  
Dusa McDuff  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 2023: MATH GU4007


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

MATH 4007  001/12608  T Th 11:40am  12:55pm 520 Mathematics Building 
William Sawin  3.00  4/30 
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 2023: MATH GU4032


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

MATH 4032  001/10974  M W 10:10am  11:25am Room TBA 
Simon Brendle  3.00  50/50 
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 2023: MATH GU4041


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

MATH 4041  001/12610  T Th 10:10am  11:25am 417 Mathematics Building 
Nathan Chen  3.00  52/64 
Fall 2023: MATH GU4041


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 4041  001/10975  T Th 10:10am  11:25am Room TBA 
Michael Harris  3.00  76/100 
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 2023: MATH GU4042


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

MATH 4042  001/12613  M W 2:40pm  3:55pm 602 Hamilton Hall 
Tudor Padurariu  3.00  34/100 
Fall 2023: MATH GU4042


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 4042  001/10976  T Th 10:10am  11:25am Room TBA 
Aise Johan de Jong  3.00  23/50 
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 2023: MATH GU4043


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

MATH 4043  001/12618  T Th 1:10pm  2:25pm 307 Mathematics Building 
Aise Johan de Jong  3.00  8/19 
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 2023: MATH GU4044


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

MATH 4044  001/10977  T Th 1:10pm  2:25pm Room TBA 
Chao Li  3.00  19/19 
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 2023: MATH GU4045


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

MATH 4045  001/12621  M W 4:10pm  5:25pm 507 Mathematics Building 
Akash Sengupta  3.00  13/19 
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 2023: MATH GU4051


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

MATH 4051  001/10978  M W 4:10pm  5:25pm Room TBA 
Michael Thaddeus  3.00  39/50 
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 2023: MATH GU4052


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

MATH 4052  001/10979  M W 4:10pm  5:25pm Room TBA 
Rostislav Akhmechet  3.00  1/19 
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 2023: MATH GU4053


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

MATH 4053  001/12625  T Th 2:40pm  3:55pm 417 Mathematics Building 
Mikhail Khovanov  3.00  14/35 
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 2023: MATH GU4061


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

MATH 4061  001/12628  M W 2:40pm  3:55pm 203 Mathematics Building 
Pfeffer Joshua  3.00  61/100 
Fall 2023: MATH GU4061


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 4061  001/10980  T Th 11:40am  12:55pm Room TBA 
Sam Collingbourne  3.00  55/64 
MATH 4061  002/10981  T Th 1:10pm  2:25pm Room TBA 
Sam Collingbourne  3.00  37/64 
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.
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Power series, analytic functions, Implicit function theorem, Fubini theorem, change of variables formula, Lebesgue measure and integration, function spaces
Spring 2023: MATH GU4062


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

MATH 4062  001/12629  T Th 4:10pm  5:25pm 207 Mathematics Building 
Jorge Pineiro Barcelo  3.00  25/110 
Fall 2023: MATH GU4062


Course Number  Section/Call Number  Times/Location  Instructor  Points  Enrollment 
MATH 4062  001/10982  M W 6:10pm  7:25pm Room TBA 
Milind Hegde  3.00  22/50 
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 2023: MATH GU4065


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

MATH 4065  001/10983  T Th 11:40am  12:55pm Room TBA 
Eric Urban  3.00  18/35 
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 2023: MATH GU4081


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

MATH 4081  001/00026  M W 10:10am  11:25am 207 Milbank Hall 
Dusa McDuff  3.00  19/40 
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 2023: MATH GU4155


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

MATH 4155  001/12633  T Th 1:10pm  2:25pm 417 Mathematics Building 
Ioannis Karatzas  3.00  25/64 
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
Fall 2023: MATH GU4156


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

MATH 4156  001/10984  T Th 2:40pm  3:55pm Room TBA 
Ioannis Karatzas  3.00  38/50 
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
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.