Columbia Home
Searching for "advanced"
What PhD Graduate Students are Assumed to Know

Below are listed basic topics from various areas of mathematics. The first-year graduate courses in the Department are predicated on the assumption that all entering Ph.D. students are familiar with all these topics. As a practical matter, the Department knows that this will not be the case – every student will have gaps in his […]

Summer Undergraduate Research

Columbia Math Undergraduate Summer Research (CMUSR) The Mathematics Department offers a ten week summer research program for undergraduate students with a strong interest in pure mathematics. The program is designed primarily for rising juniors and seniors majoring in mathematics or closely related fields. Participants work in small groups and collaborate closely with faculty members and […]

Information for Math Majors

Why should I major in this subject? Many students are attracted to the discipline of mathematics for the same reason as the faculty, because of its great intrinsic beauty, its abstract and logical nature, and the insights that it gives into the physical world, as well as because of its many applications, such as to […]

Undergraduate Program

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 […]