The undergraduate 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 […]
This course is taken in sequence, part 1 in the fall, and part 2 in the spring. Prerequisites: Basic notions of differentiable manifolds (see Chapter 0 and 1 of do Carmo’s Riemannian Geometry). Fundamental group, van Kampen’s theorem, covering spaces. Commutative algebra of PIDs (free modules, classification of finitely generated modules). Algebraic Topology I FALL […]
Students select Analysis and Probability I in the fall semester, and then pick a specialization in the spring; either Analysis II or Probability II. Analysis and Probability I I Measure Theory Construction of the integral, limits and integration Lp spaces of functions Construction of measures, Lebesgue-Stieltjes product measures Examples: ergodicity, Liouville measure, Hausdorff measure II […]
The core mathematics graduate courses are offered in six different areas, and Ph. D. students in mathematics are required to complete three full year courses in three of these six areas. Note that in some of these areas (Analysis and Probability, Algebraic Geometry and Number Theory) there are two different choices offered for the second […]
The Columbia University Mathematics Department offers courses in mathematics at all levels through various degree programs at Columbia University and Barnard College. Course listings for some of these programs are available here: Directory of Classes Columbia College Bulletin School of General Studies Bulletin
The Mathematics department organizes two help rooms as places for students to seek assistance with material that comes up in their mathematics courses. These rooms are staffed by graduate students and undergraduate teaching assistants. Help Room hours for Spring 2026 will begin on Tuesday, January 27 Barnard Help Room The Salmasi Computational Science/Math Collaboration Space is […]
The Louis Harry Cantor Lounge on the fifth floor of the Mathematics Building (room 508) plays a crucial role in bringing together graduate students, postdocs, and faculty. Tea and refreshments are served there each afternoon, on the following schedule*: Monday-Thursday: 4pm Friday: 3pm This daily event provides a wonderful opportunity for members of the department […]
General Questions How do I get an account on the main university computer system? How do I change my password on the math department computer system? How do I SSH into the math department server? I’m at another institution and need Eduroam for network access. How do I set that up? How do I access […]
All available full-time faculty positions are advertised on the Columbia University Academic Search & Recruiting (ASR) website. In addition, positions are generally also posted on the American Mathematical Society’s Mathjobs.Org site. Applicants are required to follow all instructions to be considered for a position, including applying to both locations if directed. The review process typically […]
The Columbia Mathematics Department is located in the Mathematics Hall on the Morningside campus of Columbia University, at 117th Street and Broadway. The main departmental administrative offices are in Room 509 on the fifth floor. Faculty offices can be found throughout floors 3, 4, 5, 6, and 7. Graduate student offices are located on floors […]