Geometry And Discrete Mathematics 1202
Departmental Undergraduate Office: 410 Mathematics; 212-854-2432Director of Undergraduate Studies: Prof. Ovidiu Savin, 409 Mathematics; 212-854-8233;Calculus Director: Prof. Michael Woodbury; 525 Mathematics; 212-854-2849;Computer Science-Mathematics Adviser: Prof.
Eric Urban, 608 Mathematics; 212-854-6362;Economics-Mathematics Advisers: Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806; Economics: Dr. Susan Elmes, 1006 International Affairs Building; 212-854-9124;Mathematics-Statistics Advisers: Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806; Statistics: Prof. Banu Baydil, 611 Watson; 212-851-2132;-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 Honors Mathematics A and Honors Mathematics B normally take Linear Algebra in the second year. Timeshare program reviews. 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 proof-oriented 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 2000-level (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 Symbolic Logic, in the Philosophy Department, or Discrete Mathematics: Introduction to Combinatorics and Graph Theory, in the Computer Science Department.Another requirement for majors is participation in an undergraduate seminar, usually in the junior or 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. Professors. Mohammed Abouzaid.
The originators of the basic concepts of Discrete Mathematics, the mathematics of finite structures, were the Hindus, who knew the formulae for the number of permutations of a set of n elements, and for the number of subsets of cardinality k in a set of n elements already in the sixth century. The beginning of Combinatorics as we know it today.
David A. Bayer (Barnard). Simon Brendle.
Ivan Corwin. Panagiota Daskalopoulos. Aise Johan de Jong. Robert Friedman. Dorian Goldfeld.
Brian Greene. Richard Hamilton. Michael Harris.
Discrete Mathematics Definition
Ioannis Karatzas. Mikhail Khovanov. Igor Krichever. Chiu-Chu Liu. Dusa McDuff (Barnard). Walter Neumann (Barnard).
Andrei Okounkov. D. Phong. Henry Pinkham. Ovidiu Savin.
Michael Thaddeus (Department Chair). Eric Urban. Mu-Tao WangAssociate Professors. Daniela De Silva (Barnard). Julien DubedatAssistant Professors.
Chao Li. Francesco Lin. Giulia Sacca.
Will SawinJ.F. Ritt Assistant Professors. Konstantin Aleshkin. Evgeni Dimitrov. Nathan Dowlin. Alexandra Florea.
Florian Johne. Inbar Klang. Shotaro Makisumi. Konstantin Matetski. S. Michael Miller. Henri Roesch.
Nicholas Salter. Gus Schrader. Akash Sengupta. Kyler Siegel. Yi Sun.
Evan Warner. Hui Yu. Yihang ZhuSenior Lecturers in Discipline. Lars Nielsen. Mikhail Smirnov.
Peter WoitLecturers in Discipline. Michael WoodburyOn Leave. Profs. Florea, Krichever, Neumann, Roesch, Sacca, Salter, Sawin (Fall 2019). Profs. Abouzaid, Hamilton, Neumann, Roesch, Sacca, Salter, Sawin (Spring 2020).
Introduction To Modern Analysis I and Introduction To Modern Analysis II12 points in any combination of mathematics and cognate courses. Introduction to Biophysical ModelingMajor in Computer Science–MathematicsThe 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, 19-21 points in mathematics, and two 3-point electives in either computer science or mathematics. Introduction To Modern Analysis IMajor in Economics-MathematicsFor a description of the joint major in economics-mathematics, see the section of this bulletin.For a description of the joint major in economics-mathematics, see the section of this bulletin. Major in Mathematics-StatisticsThe 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.
Course List CodeTitlePointsMathematicsSelect one of the following sequences. Or an advanced computer science offering in programmingElectivesAn 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. MATH UN1003 College Algebra and Analytic Geometry. 3 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.Columbia College students do not receive any credit for this course and must see their CSA advising dean. 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 2019: MATH UN1101Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 115M W 10:10am - 11:25am407 Mathematics BuildingYang An328/30MATH 112M W 4:10pm - 5:25pm207 Mathematics BuildingJacob Shapiro354/100MATH 110M W 6:10pm - 7:25pm407 Mathematics BuildingDmitrii Pirozhkov327/30MATH 110T Th 11:40am - 12:55pmRoom TBAWenhua Yu318/30MATH 111T Th 1:10pm - 2:25pm407 Mathematics BuildingHuaxin Liu331/30MATH 116T Th 2:40pm - 3:55pm417 Mathematics BuildingAlexander Cowan342/50. Spring 2019: MATH UN1102Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 115M W 4:10pm - 5:25pm203 Mathematics BuildingHenri Roesch347/100MATH 110M W 6:10pm - 7:25pm203 Mathematics BuildingHenri Roesch38/100MATH 110T Th 11:40am - 12:55pm417 Mathematics BuildingPak Hin Lee333/36MATH 113T Th 2:40pm - 3:55pm407 Mathematics BuildingRaymond Cheng327/36MATH 118T Th 4:10pm - 5:25pmRoom TBABeomjun Choi318/30.
Fall 2019: MATH UN1102Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 119M W 1:10pm - 2:25pm417 Mathematics BuildingYi Sun359/64MATH 118T Th 10:10am - 11:25am417 Mathematics BuildingPeter Woit320/64MATH 119T Th 4:10pm - 5:25pm203 Mathematics BuildingNathan Dowlin397/100MATH 110T Th 6:10pm - 7:25pm203 Mathematics BuildingNathan Dowlin348/100MATH 111M W 4:10pm - 5:25pm407 Mathematics BuildingXuan Wu319/30MATH 112T Th 11:40am - 12:55pm407 Mathematics BuildingDonghan Kim333/36. Spring 2019: MATH UN1201Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 129M W 10:10am - 11:25am312 Mathematics BuildingIgor Krichever397/116MATH 122M W 2:40pm - 3:55pm203 Mathematics BuildingLinh Truong388/100MATH 124M W 4:10pm - 5:25pm312 Mathematics BuildingGiulia Sacca364/100MATH 129M W 6:10pm - 7:25pmRoom TBATeng Fei355/100MATH 120T Th 11:40am - 12:55pm203 Mathematics BuildingYoel Groman324/100. Spring 2019: MATH UN2010Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 203M W 11:40am - 12:55pm312 Mathematics BuildingBianca Santoro389/116MATH 207M W 1:10pm - 2:25pm312 Mathematics BuildingJoshua Sussan393/100MATH 204T Th 10:10am - 11:25am312 Mathematics BuildingNicholas Salter362/100MATH 205T Th 11:40am - 12:55pm312 Mathematics BuildingNicholas Salter381/100MATH 207T Th 6:10pm - 7:25pmRoom TBAElliott Stein350/100. Fall 2019: MATH UN2010Course NumberSection/Call NumberTimes/LocationInstructorPointsEnrollmentMATH 200M W 11:40am - 12:55pm203 Mathematics BuildingFrancesco Lin388/100MATH 201M W 4:10pm - 5:25pm203 Mathematics BuildingKyle Hayden3102/102MATH 202T Th 10:10am - 11:25am520 Mathematics BuildingHenry Pinkham317/49MATH 203T Th 4:10pm - 5:25pm312 Mathematics BuildingMichael Thaddeus355/100MATH 204T Th 6:10pm - 7:25pm312 Mathematics BuildingBianca Santoro361/100.