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Computer Science - MathematicsCOMPUTER SCIENCE MATHEMATICSDepartmental Undergraduate Office: 410 Mathematics; 212-854-2432http://www.math.columbia.edu/Director of Undergraduate Studies: Prof. Mu-Tao Wang, 514 Mathematics;212-854-3052; mtwang@math.columbia.eduCalculus Director: Prof. George Dragomir, 525 Mathematics;212-854-2849; gd2572@columbia.eduComputer Science-Mathematics Adviser:Computer Science: Dr. Jae Woo Lee, 715 CEPSR;212-939-7066; jae@cs.columbia.eduMathematics: Prof. Chiu-Chu Melissa Liu, 623 Mathematics;212-854-2499; c liu@math.columbia.edu)Economics-Mathematics Advisers:Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806;jd2653@columbia.eduEconomics: Dr. Susan Elmes, 1006 International Affairs Building;212-854-9124; se5@columbia.eduMathematics-Statistics Advisers:Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806;dubedat@math.columbia.eduStatistics: Ronald Neath, 612 Watson; 212-853-1398;rcn2112@columbia.eduStatistics: Gabriel Young, 610 Watson; 212-853-1395;gjy2107@columbia.edu---The major in mathematics is an introduction to some of the highlights ofthe development of theoretical mathematics over the past four hundredyears from a modern perspective. This study is also applied to manyproblems, both internal to mathematics and arising in other disciplinessuch as physics, cryptography, and finance.Majors begin by taking either Honors mathematics or the calculussequence. Students who do not take MATH UN1207 Honors MathematicsA and MATH UN1208 HONORS MATHEMATICS B normally takeMATH UN2010 LINEAR ALGEBRA in the second year. Following this,majors begin to learn some aspects of the main branches of modernmathematics: algebra, analysis, and geometry; as well as some of theirsubdivisions and hybrids (e.g., number theory, differential geometry, andcomplex analysis). As the courses become more advanced, they alsobecome more theoretical and proof-oriented and less computational.Aside from the courses offered by the Mathematics Department, cognatecourses 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 2000-level (or higher) course and must beapproved by the director of undergraduate studies. In general, a coursenot taught by the Mathematics Department is a cognate course forthe mathematics major if either (a) it has at least two semesters ofcalculus as a stated prerequisite, or (b) the subject matter in the courseis mathematics beyond an elementary level, such as PHIL UN34111SYMBOLIC LOGIC, in the Philosophy Department, or COMS W3203DISCRETE MATHEMATICS, in the Computer Science Department.Another requirement for majors is participation in an undergraduateseminar, usually in the junior or senior year. Applied math majors musttake the undergraduate seminar in both the junior and senior year. Inthese seminars, students gain experience in learning an advanced topicand lecturing on it. In order to be eligible for departmental honors, majorsmust write a senior thesis.Courses for First-Year StudentsThe systematic study of mathematics begins with one of the followingthree alternative calculus and linear algebra sequences:MATH UN1101- MATH UN1102- MATH UN1201- MATH UN1202- MATH UN2010CALCULUS Iand CALCULUS IIand Calculus IIIand CALCULUS IVand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1205- MATH UN2010CALCULUS Iand CALCULUS IIand Accelerated Multivariable Calculusand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1207- MATH UN1208CALCULUS Iand CALCULUS IIand Honors Mathematics Aand HONORS MATHEMATICS BCredit is allowed for only one calculus and linear algebra sequence.Calculus I, II is a standard course in single-variable differential andintegral calculus; Calculus III, IV is a standard course in multivariabledifferential and integral calculus; Accelerated Multivariable Calculus is anaccelerated course in multivariable differential and integral calculus.While Calculus II is no longer a prerequisite for Calculus III, studentsare strongly urged to take it before taking Calculus III. In particular,students thinking of majoring or concentrating in mathematics orone of the joint majors involving mathematics should take CalculusII before taking Calculus III. Note that Calculus II is a prerequisite forAccelerated Multivariable Calculus, and both Calculus II and Calculus IIIare prerequisites for Calculus IV.The third sequence, Honors Mathematics A- B, is for exceptionally wellqualified students who have strong Advanced Placement scores. Itcovers multivariable calculus (MATH UN1201 Calculus III- MATH UN1202CALCULUS IV) and linear algebra (MATH UN2010 LINEAR ALGEBRA), withan emphasis on theory.Advanced PlacementThe department grants 3 credits for a score of 4 or 5 on the AP CalculusAB exam provided students complete MATH UN1102 CALCULUS II orMATH UN1201 Calculus III with a grade of C or better. The departmentgrants 3 credits for a score of 4 on the AP Calculus BC exam providedstudents complete MATH UN1102 CALCULUS II or MATH UN1201Calculus III with a grade of C or better. The department grants 6 creditsfor a score of 5 on the AP Calculus BC exam provided students completeMATH UN1201 Calculus III or MATH UN1205 Accelerated MultivariableCalculus MATH UN1207 Honors Mathematics A with a grade of C orbetter. Students can receive credit for only one calculus sequence.
2Computer Science - MathematicsPlacement in the Calculus SequencesCalculus IProfessors Mohammed AbouzaidStudents who have essentially mastered a precalculus course and thosewho 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 UN1101CALCULUS I. David A. Bayer (Barnard)Calculus II and III Panagiota DaskalopoulosStudents 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 highschool calculus may begin with either MATH UN1102 CALCULUS II orMATH UN1201 Calculus III. Note that such students who decide to startwith Calculus III may still need to take Calculus II since it is a requirementor prerequisite for other courses. In particular, they MUST take Calculus IIbefore going on to MATH UN1202 CALCULUS IV. Students with a scoreof 5 on the BC exam may begin with Calculus III and do not need to takeCalculus II.Those with a score of 4 or 5 on the AB exam or 4 on the BC exam mayreceive 3 points of AP credit upon completion of Calculus II with a gradeof C or higher. Those students with a score of 5 on the BC exam mayreceive 6 points of AP credit upon completion of Calculus III with a gradeof C or higher.Accelerated Multivariable CalculusStudents with a score of 5 on the AP BC exam or 7 on the IB HL exammay begin with MATH UN1205 Accelerated Multivariable Calculus. Uponcompletion of this course with a grade of C or higher, they may receive 6points of AP credit.Honors Mathematics AStudents who want a proof-oriented theoretical sequence and havea score of 5 on the BC exam may begin with MATH UN1207 HonorsMathematics A, which is especially designed for mathematics majors.Upon completion of this course with a grade of C or higher, they mayreceive 6 points of AP credit.Transfers Inside the Calculus SequencesStudents who wish to transfer from one calculus course to another areallowed to do so beyond the date specified on the Academic Calendar.They are considered to be adjusting their level, not changing theirprogram. However, students must obtain the approval of the newinstructor and their advising dean prior to reporting to the Office of theRegistrar.Grading Andrew Blumberg Simon Brendle Ivan Corwin 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 Igor Krichever Chiu-Chu Liu Dusa McDuff (Barnard) Andrei Okounkov D. H. Phong Henry Pinkham Ovidiu Savin Michael Thaddeus Eric Urban Mu-Tao WangAssociate Professors Amol Aggarwal Chao Li Lindsay Piechnik (Barnard)Assistant Professors Elena Giorgi Francesco Lin Giulia Sacca Will SawinJ.F. Ritt Assistant ProfessorsNo course with a grade of D or lower can count toward the major,interdepartmental major, or concentration. Students who are doing adouble major cannot double count courses for their majors. Rostislav AkhmechetDepartmental Honors Marco CastronovoIn order to be eligible for departmental honors, majors must write a seniorthesis. To write a senior thesis, students must register for MATH UN3999Senior Thesis in Mathematics in the fall semester of their senior year.Normally no more than 10% of graduating majors receive departmentalhonors in a given academic year. Andres Fernandez-Herrero Konstantin Aleshkin Amadou Bah Sam Collingbourne Florian Johne Inbar Klang S. Michael Miller Eismeier Gyujin Oh Tudor Padurariu
Computer Science - Mathematics Akash Sengupta**Only one section of the Undergraduate Seminar may count towards themajor requirements. Xi Sisi ShenSenior Lecturers in Discipline***Additional courses may be selected only with prior written approval fromthe Director of Undergraduate Studies. Lars Nielsen Mikhail Smirnov Peter WoitThe program of study should be planned with a departmental adviserbefore the end of the sophomore year. Majors who are planning ongraduate studies in mathematics are urged to obtain a reading knowledgeof one of the following languages: French, German, or Russian.Lecturers in Discipline George Dragomir Gerhardt HinkleOn Leave Profs. Aggarwal, Corwin, Giorgi, Klang, Krichever, Okounkov (Fall2022) Profs. Aggarwal, Brendle, Friedman, Goldfeld, Oh, Okounkov (Spring2023)Major in MathematicsThe major requires 40-42 points as follows:Select one of the following three calculus and linear algebra sequences(13-15 points including Advanced Placement Credit):MATH UN1101- MATH UN1102- MATH UN1201- MATH UN1202- MATH UN2010CALCULUS Iand CALCULUS IIand Calculus IIIand CALCULUS IVand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1205- MATH UN2010CALCULUS Iand CALCULUS IIand Accelerated Multivariable Calculusand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1207- MATH UN1208CALCULUS Iand CALCULUS IIand Honors Mathematics Aand HONORS MATHEMATICS B15 points in the following courses:MATH GU4041INTRO MODERN ALGEBRA IMATH GU4042INTRO MODERN ALGEBRA IIMATH GU4061INTRO MODERN ANALYSIS IMATH GU4062INTRO MODERN ANALYSIS IIMATH UN3951Undergraduate Seminars in Mathematics**Ior MATH UN39523**Undergraduate Seminars in Mathematics II12 points from the following:1) Courses offered by the department numbered 2000 or higher2) Courses from the list of approved cognate courses below. Amaximum of 6 credits may be taken from courses outside the***department.*Students who are not contemplating graduate study in mathematics mayreplace one or both of the two terms of MATH GU4061- MATH GU4062by one or two of the following courses: MATH UN2500 ANALYSIS ANDOPTIMIZATION, MATH UN3007 Complex Variables, MATH UN3028PARTIAL DIFFERENTIAL EQUATIONS, or MATH GU4032 Fourier Analysis.Majors are offered the opportunity to write an honors senior thesis underthe guidance of a faculty member. Interested students should contact thedirector of undergraduate studies.
4Computer Science - MathematicsApproved CognateCourses 1Approved CognateCourses 2Approved CognateCourses 3MATH UN1101- MATH UN1102- MATH UN1201- MATH UN1202- MATH UN2010CALCULUS Iand CALCULUS IIand Calculus IIIand CALCULUS IVand LINEAR ALGEBRAAPMA E4300 COMPUT ECON UN3025 Financial PHYS UN2601 Physics,MATH:INTROEconomicsIII: Classical andORNUMERCL METHECON BC3035 IntermediateQuantum WavesMATH UN1101CALCULUS IAPMA E4302 METHODS Microeconomic Theory PHYS UN2801 AcceleratedMATHUN1102and CALCULUS IIIN COMPUTATIONALECON BC3038 InternationalPhysics I- MATH UN1205and Accelerated Multivariable CalculusSCIMoney and FinancePHYS UN2802 Accelerated- MATH UN2010and LINEAR ALGEBRACOMS W3134 DataECON UN3211 IntermediatePhysics IIORStructures in JavaMicroeconomicsPHYS UN3003 MechanicsMATH UN1101CALCULUS ICOMS W3157 Advanced ECON UN3213 IntermediatePHYS UN3007 Electricity- MATH UN1102and CALCULUS IIProgrammingMacroeconomicsand Magnetism- MATH UN1207and Honors Mathematics ACOMS W3203 DISCRETEECON UN3265 MONEY PHYS UN3008 Electromagnetic- MATH UN1208and HONORS MATHEMATICS BMATHEMATICSAND BANKINGWaves and OpticsSelect one of the following three courses. The selected course may notCOMS W3261 Computer ECON UN3412 IntroductionPHYS GU4011 Particlecount as an elective.Science TheoryTo EconometricsAstrophysics andMATH UN2500ANALYSIS AND OPTIMIZATIONCOMS W4111 INTRODUCTIONECON GU4020 EconomicsCosmologyMATH GU4032Fourier AnalysisTO DATABASESof Uncertainty andPHYS GU4018 SolidMATHGU4061INTRO MODERN ANALYSIS ICOMS W4160 Computer InformationState PhysicsAPMA E4901SEM-PROBLEMS IN APPLIED MATHGraphicsECON GU4230 EconomicsPHYS GU4019 Mathematical(junior year)COMS W4162 Advanced of New York CityMethods of PhysicsAPMAE4903SEM-PROBLEMS IN APPLIED MATHComputer GraphicsECON GU4280 CORPORATEPHYS GU4021 Quantum(senior year)COMS W4203 GraphFINANCEMechanics I18 points in electives, with at least 9 points from the following courses.TheoryECON GU4415 GamePHYS GU4022 QuantumA maximum of 9 points may be selected from courses outside this list,COMS W4261 INTROTheoryMechanics IIwith prior written approval from the Director of Undergraduate Studies.TO CRYPTOGRAPHYECON GU4710 FINANCE PHYS GU4023 ThermalMATH UN2500ANALYSIS AND OPTIMIZATIONCOMS W4460 Principles AND THE REALand Statistical PhysicsORDINARY DIFFERENTIAL EQUATIONSof Innovation andECONOMYPHYS GU4040 Introduction MATH UN2030MATH UN3007Complex VariablesEntrepreneurshipEESC GU4008 Introductionto General RelativityCOMS W4701 Artificial to Atmospheric Science POLS GU4700 MATH #or MATH GU4065Honors Complex VariablesIntelligenceEESC GU4090 IntroductionSTATS FOR POLI SCIor APMA E4204FUNCTNS OF A COMPLEX VARIABLECOMS W4771 Machine to Geochronology and STAT UN3106 APPLIEDMATH UN3028PARTIAL DIFFERENTIAL EQUATIONSLearningThermochronologyMACHINE LEARNINGor APMA E4200PARTIAL DIFFERENTIAL EQUATIONSCOMS W4773 Machine IEOR E3106 STOCHASTICSTAT GU4001 INTRODUCTIONor APMA E6301ANALYTIC METHODS FOR PDE'SLearning TheorySYSTEMS ANDTO PROBABILITY ANDMATH GU4032Fourier AnalysisCSEE W3827 FundamentalsAPPLICATIONSSTATISTICSAPMA E4300COMPUT MATH:INTRO-NUMERCL METHof Computer Systems IEOR E3658 PROBABILITYSTAT GU4203 PROBABILITYAPMA E4101APPL MATH III:DYNAMICAL SYSTMSCSOR W4231 Analysis FOR ENGINEERSTHEORYAPMAE4150APPLIED FUNCTIONAL ANALYSISof Algorithms IIEOR E4700 INTROSTAT GU4204 StatisticalAPMA E4400INTRO TO BIOPHYSICAL MODELINGCSOR W4246 AlgorithmsTO FINANCIALInferencefor Data ScienceENGINEERINGSTAT GU4205 LinearCSPH G4801 MathematicalMSAE E3010 FOUNDATIONSRegression ModelsLogic IOF MATERIALSSTAT GU4206 StatisticalCSPH G4802 MathSCIENCEComputing andThe goal of this interdepartmental major is to provide substantialLogic II: Incompletness PHIL UN3411 SYMBOLICIntroduction to Databackground in each of these two disciplines, focusing on some of theLOGICScienceparts of each which are closest to the other. Students intending to pursuePHIL GU4424 ModalSTAT GU4207 Elementarya Ph.D. program in either discipline are urged to take additional courses,LogicStochastic Processesin consultation with their advisers.PHIL GU4561 Probabilityand Decision TheoryThe major requires 20 points in computer science, 19-21 points inPHIL GU4810 Latticesmathematics, and two 3-point electives in either computer science orand Boolean Algebrasmathematics.Major in Computer Science–MathematicsMajor in Applied MathematicsThe major requires 37-41 points as follows:Select one of the following three calculus and linear algebra sequences(13-15 points including Advanced Placement Credit):Computer ScienceCOMS W1004or COMS W1007COMS W3134or COMS W3137COMS W3157Introduction to Computer Science andProgramming in JavaHonors Introduction to Computer ScienceData Structures in JavaHonors Data Structures and AlgorithmsAdvanced Programming
Computer Science - MathematicsCOMS W3203DISCRETE MATHEMATICSCOMS W3261Computer Science TheoryCSEE W3827Fundamentals of Computer SystemsMathematicsSelect one of the following three calculus and linear algebra sequences(13-15 points including Advanced Placement Credit):MATH UN1101- MATH UN1102- MATH UN1201- MATH UN1202- MATH UN2010CALCULUS Iand CALCULUS IIand Calculus IIIand CALCULUS IVand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1205- MATH UN2010CALCULUS Iand CALCULUS IIand Accelerated Multivariable Calculusand LINEAR ALGEBRAORMATH UN1101- MATH UN1102- MATH UN1207- MATH UN1208CALCULUS Iand CALCULUS IIand Honors Mathematics Aand HONORS MATHEMATICS BMATH UN3951Undergraduate Seminars in MathematicsIor MATH UN3952MATH GU4041MATH UN1101- MATH UN1102- MATH UN1205- MATH UN2010- MATH UN2500CALCULUS Iand CALCULUS IIand Accelerated Multivariable Calculusand LINEAR ALGEBRAand ANALYSIS AND OPTIMIZATIONMATH UN1207- MATH UN1208- MATH UN2500Honors Mathematics Aand HONORS MATHEMATICS Band ANALYSIS AND OPTIMIZATION (withapproval from the adviser)ORStatisticsIntroductory CourseSTAT UN1201Calculus-Based Introduction to StatisticsRequired CoursesSTAT GU4203PROBABILITY THEORYSTAT GU4204Statistical InferenceSTAT GU4205Linear Regression ModelsSelect one of the following courses:STAT GU4207Elementary Stochastic ProcessesSTAT GU4262Stochastic Processes for FinanceSTAT GU4264STOCHASTC PROCSSES-APPLICSTAT GU4265Stochastic Methods in FinanceUndergraduate Seminars in Mathematics IIComputer ScienceINTRO MODERN ALGEBRA ISelect one of the following courses:ElectivesSelect two of the following courses:CSOR W4231Analysis of Algorithms ICOMS W4241Numerical Algorithms and ComplexityMATH BC2006CombinatoricsMATH UN2500ANALYSIS AND OPTIMIZATIONMATH UN3007Complex VariablesMATH UN3020Number Theory and CryptographyMATH UN3386Differential GeometryMATH GU4051TopologyMATH GU4061INTRO MODERN ANALYSIS IMajor in Economics-MathematicsFor a description of the joint major in economics-mathematics, seethe Economics section of this bulletin.Major in Mathematics-StatisticsThe program is designed to prepare the student for: (1) a career inindustries such as finance and insurance that require a high level ofmathematical sophistication and a substantial knowledge of probabilityand statistics, and (2) graduate study in quantitative disciplines. Studentschoose electives in finance, actuarial science, operations research, orother quantitative fields to complement requirements in mathematics,statistics, and computer science.MathematicsCOMS W1004Introduction to Computer Science andProgramming in JavaCOMS W1005Introduction to Computer Science andProgramming in MATLABENGI E1006INTRO TO COMP FOR ENG/APP SCICOMS W1007Honors Introduction to ComputerScienceor an advanced computer science offering in programmingElectivesAn approved selection of three advanced courses in mathematics,statistics, applied mathematics, industrial engineering and operationsresearch, computer science, or approved mathematical methodscourses in a quantitative discipline. At least one elective must be aMathematics Department course numbered 3000 or above.Students interested in modeling applications are recommended totake MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS andMATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS.Students interested in finance are recommended to take MATH GR5010Introduction to the Mathematics of Finance, STAT GU4261 StatisticalMethods in Finance, and STAT GU4221 Time Series Analysis.Students interested in graduate study in mathematics or in statistics arerecommended to take MATH GU4061 INTRO MODERN ANALYSIS I andMATH GU4062 INTRO MODERN ANALYSIS II.Students preparing for a career in actuarial science are encouraged toreplace STAT GU4205 Linear Regression Models with STAT GU4282Linear Regression and Time Series Methods , and to take among theirelectives STAT GU4281 Theory of Interest .Select one of the following sequences:MATH UN1101- MATH UN1102- MATH UN1201- MATH UN2010- MATH UN2500ORCALCULUS Iand CALCULUS IIand Calculus IIIand LINEAR ALGEBRAand ANALYSIS AND OPTIMIZATIONConcentration in MathematicsThe concentration requires the following:5
6Computer Science - MathematicsMATH UN1101 CALCULUS I. 3.00 points.Prerequisites: (see Courses for First-Year Students). Functions, limits,derivatives, introduction to integrals, or an understanding of pre-calculuswill be assumed. (SC)MathematicsSelect one of the following three multivariable calculus and linearalgebra sequences:MATH UN1201- MATH UN1202- MATH UN2010Calculus IIIand CALCULUS IVand LINEAR ALGEBRASpring 2022: MATH UN1101ORMATH UN1205- MATH UN2010Accelerated Multivariable Calculusand LINEAR ALGEBRASection/CallNumberNumberMATH 1101001/00005MATH 1101ORMATH UN1207- MATH UN1208CourseMATH 1101Honors Mathematics Aand HONORS MATHEMATICS nrollmentM W 6:10pm - 7:25pmLindsay3.0074/100Ll002 Milstein CenterPiechnikT Th 2:40pm - 3:55pmLindsay3.0094/100Ll002 Milstein CenterPiechnikT Th 11:40am - 12:55pmXi Shen3.0059/100Hung Chiang3.0019/30Jingze ntM W 11:40am - 12:55pmDaniele3.0015/110203 0Amadou Bah3.006/100T Th 11:40am - 12:55pmGerhardt3.0010/49520 30203 MathematicsBuildingAdditional CoursesSelect at least 12 additional points from any of the courses offeredby the department numbered 2000 or higher. A maximum of 3 credits*may be taken from courses outside the department.MATH 1101004/11818M W 10:10am - 11:25am407 MathematicsBuildingMATH 1101005/11822T Th 4:10pm - 5:25pm407 Mathematics*For mathematics courses taken in other departments, consult with thedirector of undergraduate studies.Any course given by the Mathematics department fulfills the GeneralStudies quantitative reasoning requirement when passed with asatisfactory letter grade.MATH UN1003 COLLEGE ALGEBRA-ANLYTC GEOMTRY. 3.00 points.Prerequisites: score of 550 on the mathematics portion of the SATcompleted within the last year, or the appropriate grade on the GeneralStudies Mathematics Placement Examination. For students whowish to study calculus but do not know analytic geometry. Algebrareview, graphs and functions, polynomial functions, rational functions,conic sections, systems of equations in two variables, exponentialand logarithmic functions, trigonometric functions and trigonometricidentities, applications of trigonometry, sequences, series, and limitsSpring 2022: MATH UN1003CourseSection/CallNumberNumberMATH /CallNumberNumberMATH 1101001/12744BuildingMATH 1101M W 11:40am - 12:55pmKevin Smith3.00T Th 6:10pm - 7:25pm002/12746003/12748004/12749NumberMATH 1003001/00055MATH 1003002/00056M W 2:40pm - 3:55pmAkash417 MathematicsSenguptaM W 4:10pm - 5:25pmAkash207 MathematicsSengupta005/12751T Th 10:10am - 11:25am207 MathematicsBuildingMATH 1101006/12752BuildingMATH 1101008/00057009/12756T Th 1:10pm - 2:25pmLindsay405 Milbank HallPiechnikM W 6:10pm - 7:25pm414 Pupin LaboratoriesDavid Marcil3.0019/30MATH 1101010/12758T Th 4:10pm - 5:25pm407 MathematicsBuildingFall 2022: MATH UN1003NumberThaddeusBuildingMATH 1101BuildingSection/CallMichael417 MathematicsBuildingMATH 110116/30407 MathematicsCourseM W 1:10pm - 2:25pmBuildingMATH 1101MATH 1101Building002/11814CourseEnrollment407 MathematicsMATH 1003BuildingFall 2022: MATH UN1101MATH 1101Times/LocationInstructorPointsEnrollmentM W 6:10pm - 7:25pmLindsay3.0012/30323 Milbank HallPiechnikT Th 2:40pm - 3:55pmLindsay3.0014/30207 Milbank HallPiechnik012/12760T Th 2:40pm - 3:55pm825 Seeley W. MuddBuilding
Computer Science - MathematicsMATH 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 2022: MATH UN1102CourseSection/CallNumberNumberMATH 1102001/11826MATH entM W 1:10pm - 2:25pmPanagiota3.0025/49517 Hamilton HallDaskalopoulosM W 2:40pm - 3:55pmTudor3.0019/110203 MathematicsPadurariu003/11829M W 6:10pm - 7:25pmChaim Avram407 MathematicsZeff3.0010/30004/11831T Th 10:10am - 11:25amGerhardt407 MathematicsHinkle3.0030/30005/11833T Th 11:40am - 12:55pmGeorge312 MathematicsDragomir3.0060/116006/11834T Th 2:40pm - 3:55pmEvan Warner,203 /CallNumberNumberMATH 1102001/12761Times/LocationInstructorPointsMATH 1201002/11837MATH 1201003/11840MATH 1201004/11841005/12698M W 1:10pm - 2:25pm0. FACULTY3.0010/100M W 2:40pm - 3:55pm0. H 1201001/12774M W 4:10pm - 5:25pm3.0011/30MATH 1201002/12776T Th 10:10am - 11:25am0. FACULTY3.0010/100374/110M W 1:10pm - 2:25pmKonstantin364/110203 MathematicsAleshkin334/110Stephen Miller 391/116Times/LocationInstructorPointsEnrollmentM W 10:10am - 11:25amTudor343/100207 MathematicsPadurariu369/1000. FACULTY312/1000. FACULTY324/100Ilya Kofman342/1000. FACULTY322/1000. FACULTY314/100T Th 4:10pm - 5:25pmGeorge347/100312 MathematicsDragomirT Th 1:10pm - 2:25pmChen-Chih LaiT Th 2:40pm - 3:55pmT Th 11:40am - 12:55pmT Th 6:10pm - 7:25pm003/12778Tudor207 MathematicsPadurariuM W 1:10pm - 2:25pm312 Mathematics0. FACULTY3.0020/100MATH 1201004/12779M W 2:40pm - 3:55pm312 MathematicsBuilding3.0015/30MATH 1201005/12781T Th 11:40am - 12:55pm207 Mathematics407 MathematicsBuildingM W 11:40am - 12:55pmBuildingBuilding006/12771Kyle HaydenM W 11:40am - 12:55pmBuildingMATH 1201312 MathematicsMATH 110261/110BuildingBuilding005/127683Building312 MathematicsMATH 1102Kyle HaydenFall 2022: MATH UN1201Building004/12767M W 10:10am - 11:25am207 Mathematics407 MathematicsMATH 1102Enrollment207 MathematicsEnrollmentBuilding003/12765Points207 Mathematics203 MathematicsMATH 1102Instructor312 nBuilding203 MathematicsMATH 1102MATH 1201MATH 1201Fall 2022: MATH UN1102CourseNumberBuildingBuildingMATH 1102Section/CallNumberBuildingBuildingMATH 1102CourseBuildingBuildingMATH 1102MATH UN1201 Calculus III. 3 points.Prerequisites: MATH UN1101 or the equivalentVectors in dimensions 2 and 3, complex numbers and the complexexponential function with applications to differential equations, Cramer'srule, vector-valued functions of one variable, scalar-valued functions ofseveral variables, partial derivatives, gradients, surfaces, optimization, themethod of Lagrange multipliers. (SC)Spring 2022: MATH UN1201BuildingMATH 11027BuildingMATH 1201006/12783T Th 1:10pm - 2:25pm207 MathematicsBuildingMATH 1201007/12784T Th 2:40pm - 3:55pm207 MathematicsBuildingMATH 1201008/12785Building
8Computer Science - MathematicsMATH UN1202 CALCULUS IV. 3.00 points.Prerequisites: MATH UN1102 and MATH UN1201 or the equivalentPrerequisites: MATH UN1102 and MATH UN1201 or the equivalentMultiple integrals, Taylor's formula in several variables, line and surfaceintegrals, calculus of vector fields, Fourier series. (SC)Spring 2022: MATH UN1202CourseSection/CallNumberNumberMATH 1202001/00007MATH entT Th 10:10am - 11:25amDaniela De3.0041/100328 Milbank HallSilvaT Th 2:40pm - 3:55pmDaniela DeLl104 Diana tM W 6:10pm - 7:25pmMikhail3.0055/116312 MathematicsSmirnov3.007/55MATH UN1208 HONORS MATHEMATICS B. 4.00 points.Prerequisites: (see Courses for First-Year Students).Prerequisites: (see Courses for First-Year Students). The second termof this course may not be taken without the first. Multivariable calculusand linear algebra from a rigorous point of view. Recommended formathematics majors. Fulfills the linear algebra requirement for the major.(SC)Spring 2022: MATH UN12083.0046/100CourseSection/CallNumberNumberMATH 1208001/11854Fall 2022: MATH UN1202CourseSection/CallNumberNumberMATH 1202001/12786BuildingMATH 1202002/15049M W 2:40pm - 3:55pm0. FACULTY330 Uris HallMATH UN1205 Accelerated Multivariable Calculus. 4 points.Prerequisites: (MATH UN1101 and MATH UN1102)Vectors in dimensions 2 and 3, vector-valued functions of one variable,scalar-valued functions of several variables, partial derivatives, gradients,optimization, Lagrange multipliers, double and triple integrals, line andsurface integrals, vector calculus. This course is an accelerated versionof MATH UN1201 - MATH UN1202. Students taking this course may notreceive credit for MATH UN1201 and MATH UN1202.Spring 2022: MATH UN1205CourseSection/CallNumberNumberMATH entT Th 1:10pm - 2:25pmKanstantsin420/110203 MathematicsMatetskiBuildingFall 2022: MATH UN1205CourseSection/CallNumberNumberMATH entM W 1:10pm - 2:25pmMu-Tao Wang47/49520 MathematicsBuildingMATH UN1207 Honors Mathematics A. 4 points.Prerequisites: (see Courses for First-Year Students). The second term ofthis course may not be taken without the first. Multivariable calculusand linear algebra from a rigorous point of view. Recommended formathematics majors. Fulfills the linear algebra requirement for the major.(SC)Fall 2022: MATH UN1207CourseSection/CallNumberNumberMATH 1207001/12791Times/LocationInstructorT Th 1:10pm - 2:25pmStephen Miller 4417 ionInstructorPointsEnrollmentT Th 1:10pm - 2:25pmEvan Warner,4.0033/64417 MathematicsGeorgeBuildingDragomirMATH UN2000 INTRO TO HIGHER MATHEMATICS. 3.00 points.Introduction to understanding and writing mathematical proofs.Emphasis on precise thinking and the presentation of mathematicalresults, both in oral and in written form. Intended for students who areconsidering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of GeneralEduca
212-854-9124; se5@columbia.edu Mathematics-Statistics Advisers: Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806; . Money and Finance ECON UN3211 Intermediate Microeconomics ECON UN3213 Intermediate SCIENCE Science Major in Computer Science-Mathematics
