Administrative Responsibilities
At the beginning of each academic year the chair of the department will appoint at least one member of the department as the Mathematics Honors and Comprehensives advisor(s). Any questions related to the administration of the honors qualifying and comprehensive exams should be directed to the Mathematics Honors and Comprehensives Advisor(s) through the MathComps@amherst.edu email address.
For the academic year 2023-2024 the Mathematics Honors and Comprehensives advisors are David Zureick-Brown and Yongheng Zhang.
Exam Schedule and Signup
For the 2023-24 academic year, the first round of the comprehensive exam is administered on the Friday of the first week of the Spring semester (Friday, February 2, 2024), and the second round of the comprehensive exam is the Friday of the seventh week of classes (Friday, March 15, 2024). These dates coincide with the first and second rounds of the honors qualifying exam.
At the beginning of each academic year, the Mathematics Honors and Comprehensives Advisor(s) will send out an email informing all declared math majors about the procedure to signup for that year's exam. The signup form for seniors will ask for basic information about the student signing up. The signup period generally closes in mid-November so that the department can make the necessary arrangements to accommodate all the students who are taking the exams.
Students with commitments that might prevent them from taking the exam during the regularly scheduled time should communicate these conflicts with the Mathematics Honors and Comprehensives Advisor(s) as soon as possible. This increases the likelihood that we can provide equitable accommodations to all students. The department makes no guarantee that a student with a conflict will be able to take the exam at an alternative time.
Any E student (i.e. a student with graduation year 20XXE) who wishes to take the exam in their final semester should contact the department before the start of that semester in order to discuss a schedule for taking the exam.
Who Takes the Exam
All Mathematics majors, except those who simultaneously earned a pass or above on both parts of the Honors Qualifying Examination as juniors, will be required to take and pass the Comprehensive Examination by the end of their senior year. NB: In order to graduate on schedule this requirement must be satisfied in time for the results to be processed by the registrar.
Only students who have declared the Mathematics major and are second-semester seniors (possibly first semester seniors for E students) are eligible to take the comprehensive exam. Students must have passed at least one of Math 350 or Math 355 (or equivalent) prior to taking the exam (except by petition to the department). Juniors are not permitted to take the Comprehensive Exam; however, any Junior who earns a Pass or above on both sections of the Honors Qualifying Exam in a single sitting will be deemed to have completed the comprehensive requirement for the Mathematics major. See the departmental policy on the Honors Qualifying Exam page for more details.
Content and Format
The Comps exam covers material from Multivariable Calculus (Math 211) and Linear Algebra (Math 271 or 272). It is a closed-book, written exam, generally with eight problems (four from each of the two courses), and the time limit is two hours. The exam does not cover the full syllabi of these courses, but instead the more abbreviated comprehensive syllabi linked on this website.
Grading: Pass, Conditional Pass, and Fail
Before the exam, each student who has registered for the exam will be assigned an identification number. This number is to be written on the exam rather than the student's name. This allows each part of the exam to be graded blindly by at least two members of the department. After the graders are finished, they will confer and assign the exam an overall score of either Pass, Conditional Pass, or Fail.
A rough rule-of-thumb is that for the first round, a Pass means 60% or better, and a Fail means lower than 60%; and for the second round, a Pass means 60% or better, a Conditional Pass means between 50% and 60%, and a Fail means 50% or lower. (Conditional Pass is assigned only in the second round.) These percentages are NOT fixed and may vary depending on many factors.
Conditional Pass, and Oral Exam
When a senior major gets a Conditional Pass on a part of the comprehensive examination, they will be given a set of problems that deal with those topics that gave the student the most difficulty on that part of the exam. The student will work on these problems in consultation with any faculty or staff in the department or QCenter. Within five weeks of taking the written exam, the student will present the solutions orally to two faculty members chosen by the comprehensives advisor. The oral exam will also involve problems the student has not seen before but which are similar to those the student has prepared. Upon successful completion of the oral exam, the student's grade on this part of the Comprehensive Examination will be changed to Pass. However, the grade will be changed to Fail if the oral exam is deemed unsuccessful by the faculty conducting the oral exam.
Fail, and Retaking the Exam
When a senior math major takes the Comprehensive Examination and gets a grade of Fail, they will need to retake the exam in the second round. As described above, this is generally the Friday of the first full week after Spring Break, or for E students taking the exam in their final semester, around the corresponding time in the Fall semester.
Number of Attempts
The number of times a senior can take the Comprehensive Examination is governed by College policy (see the last paragraph of the section "The Major Requirement" in the Catalog). The current policy specifies at most two attempts during the senior's last semester at the College. Missing the first scheduled administration of the exam counts as an attempt, with exceptions only by petition to the department. The policy does allow a third attempt, though this usually involves a delay in graduation. In this situation, the senior must return to campus to take the examination and must get a grade of Pass on the exam.
Resources for Students to Prepare
For each topic on the exam, the department has made syllabi and study guides available through the departmental website. On the same website, students can find copies of old comprehensive exams and solutions to some of those exams. Students are strongly encouraged to start their studying early and use the departmental study guides.