Professors: David A. Bayer (Chair), Dusa McDuff (Helen Lyttle Kimmel Chair), Walter D. Neumann
Assistant Professors: Dylan Thurston
Visiting Assistant Professor: Daniela De Silva
Research Professor and Professor Emerita: Joan Birman
Other officers of the University offering courses in Mathematics:
Visiting Professor: Andrei Okounkov
Professors: Panagiota Daskalopoulos, Aise Johan de Jong, Patrick X. Gallagher, Dorian Goldfeld, Brian Greene, Richard Hamilton, Hervé M. Jacquet, Troels Jørgensen, Ioannis Karatzas, Igor Krichever, John W. Morgan, Peter S. Ozsváth, D. H. Phong, Henry Pinkham, Shou-Wu Zhang
Associate Professors: Peter Bank, Melissa Liu, Ovidiu Savin, Michael Thaddeus, Eric Urban, Mu-Tao Wang
Assistant Professors: Joel Bëllaïche, Mirela Ciperiani, Julien Dubdat, Aaron Lauda, Xiaoqing Li, Xiaobo Liu, Ciprian Manolescu, Mihai Sîrbu, Kenneth Tignor
Ritt Assistant Professors: Anar Akmedov, Maksym Fedorchuk, Yakov Kerzhner, Adam C. Knapp, Nam Q. Le, Max Lipyanskiy, Ovidiu Munteanu, Emmanuel Schertzer, Gabor Szekelyhidi, Weizhe Zheng
NSF Postdoctoral Fellows: Jarod Alper, Oren Ben-Basat, Elisenda Grigsby, Robert Lipshitz, Kimball Martin, Robert W. Neel, Nicholas Proudfoot
For a complete list of
faculty on leave see:
http://www.barnard.edu/provost/facleavelist.html
GENERAL INFORMATION
Students who have special placement problems, or are unclear about their level, should make an appointment with a faculty member or the chair.
Two help rooms, one in 404 Mathematics and one in 333 Milbank, will be open all term (hours will be posted on the door and the Web) for students seeking individual help and counseling from the instructors and teaching assistants. No appointments are necessary. However, resources are limited and students who seek individual attention should make every effort to come during the less popular hours and to avoid the periods just before midterm and final exams.
COURSES FOR FIRST-YEAR
STUDENTS
The systematic study of Mathematics begins with one of the following alternative sequences: Calculus I, II, III, IV (Math V 1101–2, V 1201–2); Honors Math A-B (Math V 1207–8).
Credit is allowed for only one of the calculus sequences. The calculus sequence is a standard course in differential and integral calculus. Honors Mathematics III–IV is for exceptionally well-qualified students who have strong advanced placement scores. It covers second-year Calculus (Math V 1201–2) and Linear Algebra (MathV 2010), with an emphasis on theory.
Calculus II is NOT a prerequisite for Calculus III, so students who plan to take only one year of calculus may choose between I and II or I and III. The latter requires a B or better in Calculus I and is a recommended option for some majors.
Introduction to Higher Mathematics (MATH V 2000) is a course that can be taken in their first or second year by students with an aptitude for mathematics who would like to practice writing and understanding mathematical proofs.
PLACEMENT IN THE CALCULUS
SEQUENCE
College Algebra and Analytical Geometry is a refresher course for students who intend to take Calculus but do not have adequate background for it.
Advanced Placement: Students who have passed the advanced placement test for Calculus AB with a grade of 4 or 5 or BC with a grade of 4 receive 3 points of credit. Those who passed Calculus BC with a grade of 5 will receive 4 points of credit or 6 points on placing into Calculus III or Honors Math III and completing with a grade of C or better.
Calculus I, II, III: Students who have not previously studied calculus should begin with Calculus I. Students with 4 or higher on the Calculus AB or BC advanced placement test may start with Calculus II. Students with 5 on the Calculus BC test should start with Calculus III.
Honors Mathematics A: Students who have passed the Calculus BC advanced placement test with a grade of 5, and who have strong mathematical talent and motivation, should start with Honors Mathematics III. This is the most attractive course available to well-prepared, mathematically talented first-year students, whether or not they intend to be mathematics majors. Students who contemplate taking this course should consult with the instructor. If this is not possible ahead of time, they should register and attend the first class.
The majors program in both mathematics and applied mathematics are appropriate for students who plan to continue their training in graduate school. Students who begin with Honors Mathematics III–IV will need to plan their succeeding course carefully with the help of an adviser.
For a major in Mathematics: 14 courses as follows:
Four courses in calculus or Honors Mathematics III–IV, including Advanced Placement Credit. Six courses in mathematics numbered at or above 2000, and four courses in any combination of mathematics and cognate courses. The courses in mathematics must include:
| V 2010 | Linear Algebra (or Honors Mathematics A-B) |
| W 4041–2 | Introduction to Modern Algebra* |
| W 4061–2 | Introduction to Modern Analysis* |
| V 3951x, 3952y | Undergraduate Seminar in Mathematics (at least one term) |
However, students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH W 4061-W 4062 by one or two of the following courses: MATH V 2500, V 3007, or W 4032. In exceptional cases, the chair will approve the substitution of certain more advanced courses for those mentioned above.
*Note: It is strongly recommended that the sequences Math W 4041-2 and W 4061-2 be taken in separate years.
For a major in Applied Mathematics: 14 courses plus Junior Seminar in Applied Mathematics:
Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit.
| V 2010 | Linear Algebra |
| W 4061 | Introduction to Modern Analysis |
| APMA E 4901 | Seminar in Applied Mathematics: Fall, Junior year |
| APMA E 4903 | Seminar in Applied Mathematics: Fall, Senior year |
| APMA E 3900 | Undergraduate Research in Applied Mathematics |
(APMA E 3900 may be replaced by the combination APMA E 4902/4904, second semester of the junior and senior applied mathematics seminar, when these are offered or, with approval, another technical elective for seniors that involves an undergraduate thesis or creative research report.)
Additional electives, to be approved by the Applied Math Committee, e.g.:
| V 2500 | Analysis and Optimization |
| V 3007 | Complex Variables |
| V 3027 | Ordinary Differential Equations |
| V 3028 | Partial Differential Equations |
| V 3030 | Dynamical Systems |
| W 4032 | Fourier Analysis |
| SIEO W 3658 | Probability |
| APMA E 4300 | Numerical Methods |
For a major in Mathematics-Statistics: 14 courses:
Five courses in mathematics:
| V 1101, V 1102 and V 1201 | Calculus I, II and III or equivalent |
| MATH V 2010 | Linear Algebra |
| MATH V 2500 | Analysis and Optimization |
Five courses in statistics:
| STAT W 1211 | Introduction to Statistics B |
| STAT W 3000 | Introduction to Statistics: Probability Models or |
| SIEO W 4105 | Probability |
STAT W 3659
or |
Statistical Inference |
| STAT W 4315 | Linear Regression Models |
| IEOR E 4106 | Introduction to Operations Research: Stochastic processes or |
| SIEO W 4606 | Elementary Stochastic Processes |
One course in computer science that requires substantial work in programming.
Three courses of electives: An approved selection of advanced courses in mathematics, statistics, applied mathematics, computer science, or mathematical methods courses in physical or social sciences, including biology, economics, and physics.
Students should plan to include a senior thesis or the Undergraduate Seminar in Mathematics in their program, in consultation with their advisors.
Note: Students must obtain approval from an adviser in each of the two departments before selecting electives. Students should take MATH V 2010 Linear Algebra in the second semester of the second year. With the approval of their adviser, students may replace the two requirements STAT W 3000 or SIEO W 4105 and STAT W 3659/4107 with the 6-point course STAT W 4109.
For a major in Mathematics-Computer Science:
15 courses as follows:
Courses in mathematics:
| V 1101, V 1102, V 1201, V 1202 | Calculus I, II, III, IV (including AP Credit) |
| or V 1207, V 1208 | Honors Math A-B (Note A) |
| V 2010 | Linear Algebra |
| V 3020* | Number Theory and Cryptography (Note B) |
| W 4041 | Introduction to Modern Algebra |
| W 4061* | Introduction to Modern Analysis (Note C) |
| V 3951 or V 3952 | Undergraduate Seminars in Mathematics |
Courses in computer science:
| W 1004 | Computer Science I (or AP credit) |
| W1007 | Computer Science II |
| W 3137 | Data Structures and Algorithms |
| W 3157 | Computer Science III (Advanced Programming) |
| W 3203 | Discrete Mathematics |
| W 3261 | Computability and Models of Computation |
| W 3827 | Fundamentals of Computer Systems |
| W 4231* | Analysis of Algorithms I |
| W 4241* | Numerical Algorithms and Complexity I |
*Electives--take two of four; in exceptional cases, other courses may be substituted with the approval of departmental representatives of both departments.
Note A: The Honors sequence also fulfills the MATH V 2010 Linear Algebra requirement.
Note B: May substitute MATH V 3021 or BC 2006 or MATH V 1103.
Note C: May substitute MATH V 2500, V 3007, V 4032, V 3386, or W 4051.
Students seeking to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.
For a major in Economics and Mathematics, see the catalogue.
For a minor in Mathematics or Applied Mathematics: Six courses from any of the courses offered by the department except Math W 1003 College Algebra and Analytic Geometry, Math V 1101/2 Calculus I/II.