General Information about the preliminary exam
Ph.D. students in the Berkeley mathematics department are required to pass this examination within their first three semesters. It is held every semester on the Monday and Tuesday mornings before instruction begins. The purpose of the prelim exam is to make sure that graduate students have sufficient working knowledge of undergraduate material to complete a PhD, and to give them some early feedback about how well prepared they are. The prelim exam is set and graded by the Preliminary Examination Committee, and questions about the exam can be sent to the current chair of the committee or room 910 Evans Hall.
What will be on the exam
On each day students are expected to do 6 out of 9 questions, which typically consist of one question on calculus, and two questions on each of the topics real analysis, complex analysis, linear algebra, and abstract algebra. The recent prelim exams and solutions and a detailed description of the syllabus and policy are available at the bottom of this page. The questions are intended to be routine applications of undergraduate honors course topics.
Grading of the prelim
There is no quota for the number of students who pass or fail, and the prelim committee will pass all students who have demonstrated that they have the required background, which is roughly the level of an A grade in an honors undergraduate course. The grading is strict, and little or no credit is given for partial answers that do not seem to be heading towards a complete solution. In recent years the passing score has usually been between 70 and 85 out of 120, and typically about two thirds of students pass each time, but these figures are not official policy and may sometimes change.
The Spring 2014 Preliminary Examination
The next prelim will be held Monday January 13 and Tuesday January 14, from 9:00-12:00 in room 939 Evans Hall (or 959 and 961 for students who need special accommodation), and results of the prelim should be available by Friday afternoon the same week from 910 Evans Hall. Please sign up for the exam in 910 Evans Hall to obtain your number (the exam is taken anonymously). There is a workshop for students who wish for help in preparing for the exam; ask in room 910 for details. Students who need special accommodation for the prelim must obtain a letter from the Disabled Student's Program and must contact the chair of the Preliminary Examination Committee by ten days before the exam so that any necessary arrangements can be made.
Options for those who do not pass
Students who score less than about 50% on any of the 4 topics real analysis, complex analysis, linear algebra, and abstract algebra should consider taking the corresponding undergraduate courses to fill the gaps in their background knowledge, after discussing this with their advisor. Students who do not pass may submit a written appeal to room 910 by Friday of the next week after the exam. Appeals are usually only granted for clear mistakes on the part of the grader, such as adding up marks incorrectly or overlooking part of the solution, and are not normally granted for a misprint in a question that the grader was aware of, or because the student feels that the grader was too strict. Students who wish to take the prelim beyond their third semester can appeal to Committee Omega, Students who score less than about 60 on their first attempt or who do not pass by their second attempt often find it hard to complete a PhD, and sometimes choose to do a master's degree instead. The Vice-Chair for Graduate Affairs can give advice about possible options.