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Applied MathematicsAPPLIED 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 UN3411SYMBOLIC 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 must1take 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.Placement in the Calculus SequencesCalculus IStudents who have essentially mastered a precalculus course and thosewho have a score of 3 or less on an Advanced Placement (AP) exam
2Applied Mathematics(either AB or BC) should begin their study of calculus with MATH UN1101CALCULUS I. Panagiota DaskalopoulosCalculus II and III Daniela De Silva (Barnard Chair)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 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.GradingNo 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.Departmental Honors Aise Johan de Jong (Department 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 Professors Rostislav Akhmechet Konstantin Aleshkin Amadou Bah Marco Castronovo Sam Collingbourne Andres Fernandez-Herrero Florian JohneIn 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. Inbar KlangProfessors Xi Sisi Shen Mohammed Abouzaid David A. Bayer (Barnard) Andrew Blumberg Simon Brendle Ivan Corwin S. Michael Miller Eismeier Gyujin Oh Tudor Padurariu Akash SenguptaSenior Lecturers in Discipline Lars Nielsen Mikhail Smirnov Peter Woit
Applied MathematicsLecturers in Disciplinegraduate studies in mathematics are urged to obtain a reading knowledgeof one of the following languages: French, German, or Russian. George DragomirMajors are offered the opportunity to write an honors senior thesis underthe guidance of a faculty member. Interested students should contact thedirector of undergraduate studies. 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.**Only one section of the Undergraduate Seminar may count towards themajor requirements.***Additional courses may be selected only with prior written approval fromthe Director of Undergraduate Studies.The program of study should be planned with a departmental adviserbefore the end of the sophomore year. Majors who are planning onApproved CognateCourses 1Approved CognateCourses 2Approved CognateCourses 3APMA E4300 COMPUT ECON UN3025 Financial PHYS UN2601 Physics,MATH:INTROEconomicsIII: Classical andNUMERCL METHECON BC3035 IntermediateQuantum WavesAPMA E4302 METHODS Microeconomic Theory PHYS UN2801 AcceleratedIN COMPUTATIONALECON BC3038 InternationalPhysics ISCIMoney and FinancePHYS UN2802 AcceleratedCOMS W3134 DataECON UN3211 IntermediatePhysics IIStructures in JavaMicroeconomicsPHYS UN3003 MechanicsCOMS W3157 Advanced ECON UN3213 IntermediatePHYS UN3007 ElectricityProgrammingMacroeconomicsand MagnetismCOMS W3203 DISCRETEECON UN3265 MONEY PHYS UN3008 ElectromagneticMATHEMATICSAND BANKINGWaves and OpticsCOMS W3261 Computer ECON UN3412 IntroductionPHYS GU4011 ParticleScience TheoryTo EconometricsAstrophysics andCOMS W4111 INTRODUCTIONECON GU4020 EconomicsCosmologyTO DATABASESof Uncertainty andPHYS GU4018 SolidCOMS W4160 Computer InformationState PhysicsGraphicsECON GU4230 EconomicsPHYS GU4019 MathematicalCOMS W4162 Advanced of New York CityMethods of PhysicsComputer GraphicsECON GU4280 CORPORATEPHYS GU4021 QuantumCOMS W4203 GraphFINANCEMechanics ITheoryECON GU4415 GamePHYS GU4022 QuantumCOMS W4261 INTROTheoryMechanics IITO CRYPTOGRAPHYECON GU4710 FINANCE PHYS GU4023 ThermalCOMS W4460 Principles AND THE REALand Statistical Physicsof Innovation andECONOMYPHYS GU4040 IntroductionEntrepreneurshipEESC GU4008 Introductionto General RelativityCOMS W4701 Artificial to Atmospheric Science POLS GU4700 MATH #IntelligenceEESC GU4090 IntroductionSTATS FOR POLI SCICOMS W4771 Machine to Geochronology and STAT UN3106 APPLIEDLearningThermochronologyMACHINE LEARNINGCOMS W4773 Machine IEOR E3106 STOCHASTICSTAT GU4001 INTRODUCTIONLearning TheorySYSTEMS ANDTO PROBABILITY ANDCSEE W3827 FundamentalsAPPLICATIONSSTATISTICSof Computer Systems IEOR E3658 PROBABILITYSTAT GU4203 PROBABILITYCSOR W4231 Analysis FOR ENGINEERSTHEORYof Algorithms IIEOR E4700 INTROSTAT GU4204 StatisticalCSOR W4246 AlgorithmsTO FINANCIALInferencefor Data ScienceENGINEERINGSTAT GU4205 LinearCSPH G4801 MathematicalMSAE E3010 FOUNDATIONSRegression ModelsLogic IOF MATERIALSSTAT GU4206 StatisticalCSPH G4802 MathSCIENCEComputing andLogic II: Incompletness PHIL UN3411 SYMBOLICIntroduction to DataLOGICSciencePHIL GU4424 ModalSTAT GU4207 ElementaryLogicStochastic ProcessesPHIL GU4561 Probabilityand Decision TheoryPHIL GU4810 Latticesand Boolean Algebras
4Applied MathematicsMajor in Applied MathematicsComputer ScienceCOMS W1004The 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):MATH UN1101- MATH UN1102- MATH UN1201- MATH UN1202- MATH UN2010CALCULUS Iand CALCULUS IIand Calculus IIIand CALCULUS IVand LINEAR ALGEBRAMATH UN1101- MATH UN1102- MATH UN1205- MATH UN2010CALCULUS Iand CALCULUS IIand Accelerated Multivariable Calculusand LINEAR ALGEBRAMATH UN1101- MATH UN1102- MATH UN1207- MATH UN1208CALCULUS Iand CALCULUS IIand Honors Mathematics Aand HONORS MATHEMATICS BORORSelect one of the following three courses. The selected course may notcount as an elective.MATH UN2500ANALYSIS AND OPTIMIZATIONMATH GU4032Fourier AnalysisMATH GU4061INTRO MODERN ANALYSIS IAPMA E4901SEM-PROBLEMS IN APPLIED MATH(junior year)APMA E4903SEM-PROBLEMS 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.MATH UN2500ANALYSIS AND OPTIMIZATIONMATH UN2030ORDINARY DIFFERENTIAL EQUATIONSMATH UN3007Complex Variablesor MATH GU4065Honors Complex Variablesor APMA E4204FUNCTNS OF A COMPLEX VARIABLEMATH UN3028PARTIAL DIFFERENTIAL EQUATIONSor APMA E4200PARTIAL DIFFERENTIAL EQUATIONSor APMA E6301ANALYTIC METHODS FOR PDE'SMATH GU4032Fourier AnalysisAPMA E4300COMPUT MATH:INTRO-NUMERCL METHAPMA E4101APPL MATH III:DYNAMICAL SYSTMSAPMA E4150APPLIED FUNCTIONAL ANALYSISAPMA E4400INTRO TO BIOPHYSICAL MODELINGMajor in Computer Science–MathematicsThe goal of this interdepartmental major is to provide substantialbackground in each of these two disciplines, focusing on some of theparts of each which are closest to the other. Students intending to pursuea 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, 19-21 points inmathematics, and two 3-point electives in either computer science ormathematics.or COMS W1007COMS W3134or COMS W3137Introduction to Computer Science andProgramming in JavaHonors Introduction to Computer ScienceData Structures in JavaHonors Data Structures and AlgorithmsCOMS W3157Advanced ProgrammingCOMS 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 GU4041Undergraduate Seminars in Mathematics IIINTRO MODERN ALGEBRA IElectivesSelect 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.
Applied MathematicsMathematicsSelect one of the following sequences:MATH UN1101- MATH UN1102- MATH UN1201- MATH UN2010- MATH UN2500CALCULUS Iand CALCULUS IIand Calculus IIIand LINEAR ALGEBRAand ANALYSIS AND OPTIMIZATIONMATH 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)ORORStatisticsIntroductory 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 FinanceComputer ScienceSelect one of the following courses:COMS 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 .Concentration in MathematicsThe concentration requires the following:MathematicsSelect one of the following three multivariable calculus and linearalgebra sequences:MATH UN1201- MATH UN1202- MATH UN2010Calculus IIIand CALCULUS IVand LINEAR ALGEBRAMATH UN1205- MATH UN2010Accelerated Multivariable Calculusand LINEAR ALGEBRAMATH UN1207- MATH UN1208Honors Mathematics Aand HONORS MATHEMATICS BORORAdditional 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.*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 entM W 11:40am - 12:55pmKevin Smith3.0016/30David lmentM W 6:10pm - 7:25pmLindsay3.0012/30323 Milbank HallPiechnikT Th 2:40pm - 3:55pmLindsay3.0014/30207 Milbank HallPiechnik407 MathematicsBuildingMATH 1003002/11814T Th 6:10pm - 7:25pm407 MathematicsBuildingFall 2022: MATH UN1003CourseSection/CallNumberNumberMATH 1003001/00055MATH 1003002/000565
6Applied 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)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 2022: MATH UN1101Spring 2022: MATH UN1102CourseSection/CallNumberNumberMATH 1101001/00005MATH 1101MATH 1101002/00006003/11815Times/LocationInstructorM W 6:10pm - 7:25pmLindsayLl002 Milstein CenterPiechnikT Th 2:40pm - 3:55pmLindsayLl002 Milstein CenterPiechnikT Th 11:40am - 12:55pmXi Section/CallNumberNumberMATH 1102001/11826MATH 1102002/11827MATH 1102003/11829BuildingMATH 1101004/11818M W 10:10am - 11:25amHung Chiang3.00MATH 1102004/11831BuildingMATH 1101005/11822T Th 4:10pm - 5:25pmJingze Zhu3.00MATH 1102005/11833BuildingSection/CallNumberNumberMATH entM W 11:40am - 12:55pmDaniele3.0015/110203 MathematicsAlessandrini3.0018/64BuildingMATH 1101002/12746M W 1:10pm - 2:25pmMichael417 MathematicsThaddeusMATH erMATH 1102001/12761004/12749M W 2:40pm - 3:55pmAkash417 MathematicsSengupta3.00005/12751MATH 1102002/12763M W 4:10pm - 5:25pmAkash207 MathematicsSengupta3.00MATH 1102003/12765008/00057MATH 1101009/12756MATH 1101010/12758T Th 10:10am - 11:25amAmadou Bah3.00MATH 11023.0010/303.0030/303.0060/1163.0062/110M W 6:10pm - 7:25pmChaim Avram407 MathematicsZeffT Th 10:10am - 11:25amGerhardt407 MathematicsHinkleT Th 11:40am - 12:55pmGeorge312 MathematicsDragomirT Th 11:40am - 12:55pmGerhardt520 MathematicsHinkleLindsay405 Milbank HallPiechnikT Th 4:10pm - 5:25pm3.00004/12767825 Seeley W. structorPointsEnrollmentM W 1:10pm - 2:25pm0. FACULTY3.0010/1000. FACULTY3.0011/1003.0011/300. FACULTY3.0010/1000. FACULTY3.0020/1003.0015/30M W 2:40pm - 3:55pmM W 4:10pm - 5:25pmT Th 10:10am - 11:25amBuilding10/49MATH 11023.00005/12768T Th 11:40am - 12:55pmBuilding100/100MATH 11023.005/303.003/303.005/30BuildingT Th 2:40pm - 3:55pmEvan Warner,203 Mathematics312 MathematicsT Th 1:10pm - 2:25pmM W 6:10pm - 7:25pmT Th 2:40pm - 3:55pm312 Mathematics407 Mathematics012/1276019/110Building6/100414 Pupin LaboratoriesMATH 11013.00Padurariu407 MathematicsBuildingMATH 1101Tudor203 MathematicsBuilding27/100Building006/12752M W 2:40pm - 3:55pm203 Mathematics207 MathematicsMATH 110125/49Building29/64BuildingMATH 11013.00Daskalopoulos203 MathematicsBuildingMATH 1101Panagiota517 Hamilton HallFall 2022: MATH UN1102BuildingMATH 1101M W 1:10pm - 2:25pmBuildingFall 2022: MATH UN1101CourseEnrollmentBuilding27/30407 MathematicsPointsBuilding19/30407 MathematicsInstructorBuilding59/100203 MathematicsTimes/Location006/12771T Th 6:10pm - 7:25pm407 MathematicsBuilding
Applied MathematicsMATH 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)MATH 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 UN1201CourseSection/CallNumberNumberMATH entM W 10:10am - 11:25amKyle Hayden361/110M W 11:40am - 12:55pmKyle Hayden374/110207 MathematicsBuildingMATH 1201003/11840M W 1:10pm - 2:25pmKonstantin203 MathematicsAleshkin3004/11841T Th 1:10pm - 2:25pmChen-Chih Lai3T Th 2:40pm - 3:55pmStephen Miller 391/116Times/LocationInstructorPointsEnrollmentM W 10:10am - 11:25amTudor343/100207 MathematicsPadurariu369/100BuildingFall 2022: MATH UN1201Section/CallNumberNumberMATH 1201001/12774BuildingMATH 1201002/12776M W 11:40am - 12:55pmTudor207 MathematicsPadurariuBuildingMATH 1201003/12778001/00007M W 1:10pm - 2:25pm002/00008CourseSection/CallNumberNumberMATH 1202001/127860. FACULTY312/100M W 2:40pm - 3:55pm0. FACULTY324/100312 MathematicsBuildingMATH 1201005/12781T Th 11:40am - 12:55pmIlya Kofman342/1000. FACULTY322/1000. FACULTY314/100T Th 4:10pm - 5:25pmGeorge347/100312 MathematicsDragomirT Th 1:10pm - 2:25pmBuilding007/12784T Th 2:40pm - 3:55pm207 MathematicsBuildingMATH 1201008/127853.0041/100SilvaT Th 2:40pm - 3:55pmDaniela De3.0046/100Ll104 Diana tM W 6:10pm - 7:25pmMikhail3.0055/116312 MathematicsSmirnov3.007/55M W 2:40pm - 3:55pm0. FACULTYCourseSection/CallNumberNumberMATH entT Th 1:10pm - 2:25pmKanstantsin420/110203 MathematicsMatetskiFall 2022: MATH UN1205CourseSection/CallNumberNumberMATH entM W 1:10pm - 2:25pmMu-Tao Wang47/49520 MathematicsBuilding207 MathematicsMATH 1201Daniela De328 Milbank HallSpring 2022: MATH UN1205Building006/12783T Th 10:10am - 11:25amMATH 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 UN1202.207 MathematicsMATH ing002/15049312 MathematicsMATH 1201Instructor34/110312 MathematicsCourseMATH 1202Times/Location330 Uris HallBuilding005/12698NumberMATH 1202207 MathematicsMATH 1201Section/CallNumber64/110BuildingMATH 1201CourseFall 2022: MATH UN1202Building002/11837Spring 2022: MATH UN1202MATH 1202207 MathematicsMATH 12017MATH 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)BuildingFall 2022: MATH UN1207CourseSection/CallNumberNumberMATH 1207001/12791Times/LocationInstructorT Th 1:10pm - 2:25pmStephen Miller 4417 MathematicsBuildingPointsEnrollment9/64
8Applied MathematicsMATH 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 UN1208CourseSection/CallNumberNumberMATH 1208001/11854Times/LocationInstructorT Th 1:10pm - 2:25pmEvan Warner,417 ction/CallNumberMATH entT Th 1:10pm - 2:25pmGiulia Sacca3.0029/49NumberMATH 2000001/00058MATH entM W 10:10am - 11:25amAmadou Bah3.0050/110Amadou Bah3.0034/110Allen Yuan3.0092/116T Th 4:10pm - 5:25pmHenry3.0023/49520 MathematicsPinkhamElliott mentT Th 8:40am - 9:55amDavid Bayer3.0047/50David Bayer3.0051/50M W 10:10am - 11:25amMarco3.0032/100312 Ma
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
