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Applied Math Exams

Preliminary Exams

Each student in the Applied Mathematics graduate group is required to pass a written preliminary examination that tests undergraduate-level understanding and fundamental concepts in the field.


All math students are required to take the preliminary exams in the beginning of the spring semester of their first year of study.


There are four closed-book written exams in

  • differential equations
  • advanced calculus
  • complex variables
  • linear algebra

The examinations are given at the advanced-undergraduate/beginning-graduate level. For each of the four exams, students receive a score of 1, 2, or 3, as determined by the faculty committee in charge of the examination.


All students must obtain a score of at least 2 on all four exams. Any student may retake from one to four of the exams, but exams must be re-taken at the end of the same spring semester.

If you do not obtain a score of at least 2 on all four exams after two attempts, you will be disqualified from further study in Applied Mathematics.

Additionally, Ph.D. students must earn a score of 3 on at least three of the four exams.

  • 3 = Ph.D. pass
  • 2 = Master's pass
  • 1 = fail

Qualifying Exams

All students in the Ph.D. program are required to pass the qualifying exam before advancing to candidacy for their Ph.D. degrees. The dates for the examination are arranged between each student and his or her faculty committee. All members of the faculty committee must be in attendance for Ph.D. qualifying examinations and dissertation defense. The research proposal needs to be submitted to the faculty committee at least 30 days before the oral component. The student must also submit for approval the Application For Qualifying Examination form to the Division of Graduate Studies at least one month before the oral component date.

The Ph.D. qualification exam has several goals:

  1. To motivate students to review and synthesize course work and research material;
  2. To determine the student’s ability to understand and apply fundamental concepts;
  3. To develop and test the student’s ability to communicate orally and to respond to questions and comments;
  4. To evaluate the student’s potential to pursue doctoral research;
  5. To identify areas that need to be strengthened for the student to be successful as a Ph.D. student, independent scholar and teacher;
  6. To provide a mechanism for a range of faculty to come to know the student’s capabilities

Typically, any student who does not pass the qualifying examination will be given one more chance. If a student does not pass on the final attempt, he or she is usually given the opportunity to graduate with a terminal master's degree.

Applying for the Qualifying Exam

  1. Submit the Application for Qualifying Exam one month before your expected exam date.
  2. Attach a copy of your degree audit. Ensure you have completed the required course work established by your graduate group.
  3. If you have a committee member from an institution other than UC Merced, additional requirements apply. Refer to the UC Merced Graduate Advisor's Handbook.

In preparation, clarify expectations with your faculty advisor regarding the following:

  • Your written research proposal (typically five to 10 pages). The proposal needs to be submitted to the faculty committee at least 30 days before the exam.
  • Membership of your faculty committee.
  • Schedule preparatory meetings before exam.

Day of the Exam:

  1. Provide a blank Qualifying Examination Report at the time of your exam. All committee members must sign in original ink.
  2. Provide a copy of the Application for Advancement to Candidacy Form to your committee for their convenience at the time of your exam. All dissertation committee members and the graduate chair must sign the Application for Advancement in original ink.
  3. Submit the Examination Report and Application for Advancement to Candidacy Form to Graduate Division.

Advancement typically takes effect in the term following the one in which the Application for Advancement is submitted. For additional information, see dates and deadlines contact Graduate Division.

Comprehensive Exams

Applied Mathematics Master's Capstone Project (Master's Degree Track II)

The Master's Capstone Project is a written document presenting each student's research accomplished under his or her research advisor's supervision.

The document must be approved by the faculty mentor. The faculty mentor, in consultation with the chair of the graduate program, may also require that the capstone project be approved by additional reviewers. Each reviewer must complete the Capstone Evaluation Rubric.

Each student must submit his or her final project in PDF form to the chair of the graduate program no later than 30 days after the project has been approved, and file the project with the Division of Graduate Studies.