Department of Mathematics  
Address: Mathematics
25337

Caltech
 Pasadena, CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728 
Project MATHEMATICS!  Caltech Home Physics, Mathematics, and Astronomy @ Caltech 

The major requirement for the Ph.D. in Mathematics at Caltech is the presentation and acceptance by the faculty of a thesis containing results of original research. For admission to candidacy for the Ph.D., students are required to: (a) Demonstrate a good working knowledge in the three core areas: Algebra, Analysis, and Topology/Geometry by
(b) Complete at
least 9 quartercourses in advanced mathematics in addition to the core
courses. At least two of these must be in discrete mathematics
(combinatorics, logic, complexity and computability).
(c) Pass a candidacy examination consisting of an oral presentation to a committee of mathematics faculty describing the proposed thesis research and the area of research it belongs to. At least a week prior to the examination, candidates submit a written summary of their presentation. Qualifying examinations are usually taken in June. Some entering students take a qualifying examination in October in order to demonstrate knowledge of one of the core areas and be excused from taking the corresponding course. It is expected that the core courses will be completed in the first year, unless the student needs to take a preparatory course, such as Ma 109 (Introduction to Geometry and Topology). The candidacy examination is expected to be completed before the end of the student's third year. In addition to the core courses, students are required to complete nine quarters of other advanced mathematics courses, of which at least two quarters must be in the area of discrete mathematics: combinatorics, logic, complexity, and computability. Under special circumstances (e.g., finishing the degree in three years), exceptions to these requirements may be granted by the graduate option representative. 
