Departmental Information
Director of Undergraduate Studies
Prof. Patrick X. Gallagher
411 Math
(212) 854-4346
pxg@math.columbia.edu
Departmental Adviser
Prof. Robert Friedman
605 Mathematics
(212)
854-4355
rf@math.columbia.edu
Calculus Director
Prof. Julius Ross
423 Mathematics
(212)
854-4306
jaross@math.columbia.edu
Directors of Instruction
Mikhail Smirnov
425 Mathematics
(212)
854-4303
Peter Woit
421 Mathematics
(212)
854-2642
Departmental Office
410 Mathematics
(212) 854-2432
Departmental Web Site
http://www.math.columbia.edu/
| Professors
David A. Bayer (Barnard)
Panagiota Daskalopoulos
Aise Johan de Jong
Robert Friedman
Patrick X. Gallagher
Dorian Goldfeld
Brian Greene
Richard Hamilton
Troels Jørgensen
Ioannis Karatzas
Igor Krichever
Dusa McDuff (Barnard)
John W. Morgan (chair)
Walter Neumann (Barnard)
Peter S. Ozsváth
D. H. Phong
Henry Pinkham
Shou-Wu Zhang
Associate Professors
Mikhail Khovanov
Chiu-Chiu Melissa Liu
Ovidiu Savin
Michael Thaddeus
Eric Urban
Mu-Tao Wang
Assistant Professors
Ciprian Manolescu
Catherine H. O’Neil (Barnard)
Dylan Thurston (Barnard)
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J. F. Ritt Assistant Professors
Refik Inanc Baykur
Jason Behrstock
Joël Bellaïche
Mirela Ciperiani
Daniela De Silva (Barnard)
G. Michael Guy
Zholiang Hou
Aaron Lauda
Xiaobo Liu
Robert W. Neel
Timothy Perutz
Julius Ross
Natasa Sesum
Ye Tian
Kenneth Tignor
Christian Virdol
Adjunct Assistant Professor
Tat Sang Fung
Yi Ni
Elliott V. Stein
Visiting Professors
Christophe Breuil
Yakov Eliashberg
Charles Fefferman
Michael Harris
Visiting Associate Professor
András I. Stipsicz
On Leave
Profs. Khovanov, C.C. Liu, and O'Neil for the academic year
Prof. Bellaiche for the spring semester
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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 B normally take 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 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 approved by the director of undergraduate
studies. In general, a course not taught by the mathematics department is
cognate for the mathematics major if either (a) it has calculus as a stated prerequisite,
or (b) the subject matter in the course is mathematics, such as the set theory
and logic courses in the Philosophy Department, and the graph theory and combinatorics
courses 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.
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