Preliminary Examination

General Information about the preliminary exam

Ph.D. students in the Berkeley mathematics department are required to pass a preliminary examination within their first three semesters of study. It is held every semester on the Monday and Tuesday mornings before instruction begins. The purpose of the prelim exam is to identify gaps in undergraduate education, and to provide early feedback on core areas that could benefit from further study. The prelim exam is set and graded by the Preliminary Examination Committee. Questions about the exam can be directed to the current chair of the committee or the graduate office. 

What Will be on the Exam?

On each day students are expected to attempt 6 out of 9 questions, which usually consist of one question on calculus, and two questions on each of the topics: real analysis, complex analysis, linear algebra, and abstract algebra. Questions are intended to cover applications of undergraduate honors course topics. Documents detailing exam policy, the syllabus and recent exams and solutions are available at the bottom of this page.

To help students prepare, a workshop is held several weeks prior to the exam. You can find additional resources in the PRELIM RESOURCE FOLDER. You need to be logged in to your bmail account to access the folder. 

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. Each question is graded out of 10. 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 - 85 out of 120, and typically about two thirds of students pass each time, but these figures are not official policy and sometimes change.

The Fall 2023 Preliminary Examination

The prelim exam will be held from 9:00 am to 12:00 (Pacific Time) on the Monday and Tuesday before instruction begins (August 21 and 22).  The prelim will be held in person. Results of the prelim are usually sent by email Friday afternoon the same week of the exam. You will be prompted to sign up for the exam via an online form sent out by the graduate office. After signing up, you will be assigned a 1 or 2 digit exam number (by email) that you will use on the exam as questions are graded anonymously.

Academic Accommodations for the Prelim

The Graduate Office encourages students needing accommodations or extra support to seek guidance from the Vice Chair for Graduate Studies or the Graduate Advisor as the prelim exam is not meant to be a barrier to program completion. The exam is purely intended to identify gaps in undergraduate education and facilitate the learning of new (or old) material.  

Students who need exam accommodations must register with and obtain a letter of accommodation (LOA) from the Disabled Students' Program. The letter should be given to the chair of the Prelim Exam Committee in advance of the exam in order for the necessary arrangements to be made. Early notice is appreciated to allow time to coordinate the accommodations - we are happy to provide accommodations stipulated in the LOA.

Options for those who do not pass

Students who do not pass and believe errors in grading were made may submit a written appeal to the Graduate Office by Friday of the 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 the question, or because the student feels that the grader was too strict. While it is required that students pass the prelim before the start of their second year/third semester in the program, students who wish to take the prelim beyond their third semester can appeal to Committee Omega for an additional attempt. The Vice-Chair for Graduate Studies can give advice about possible options.

Resources (past exams, syllabus, and policy)