The Cambridge area is one of the most active centers of mathematics in the world. Harvard, Brandeis, MIT, and Northeastern have an especially close association in mathematics, sharing several seminars and a weekly colloquium. The degree of doctor of philosophy is awarded to students who have demonstrated their mastery of the basic techniques of mathematics and their ability to do independent research. The thesis, however, is the more important of the two. The qualifying examination is given twice annually, and students are encouraged to take it as soon as possible so that they may begin work towards their theses.
Most students pass the exam during their first year.
For those who do not pass it on their first attempt, it may be retaken any number of times. The PhD thesis is an original treatment of a suitable subject leading to new results, usually written under the guidance of a faculty member. The final manuscript must conform to the requirements described in The Form of the Doctoral Thesis , a booklet which is available in the Registrar's Office. Many of the more advanced courses and seminars are designed to lead the student to areas of current research. On the other hand, the PhD usually takes four to five years.