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 2022-2023 the Mathematics Honors and Comprehensives advisors are Rob Benedetto and Yongheng Zhang.

Exam Schedule and Signup

For the 2022-23 academic year, the first round of the honors qualifying exam is administered on the Friday of the first week of the Spring semester (Friday, February 3, 2023), and the second round of the comprehensive exam is the Friday of the seventh week of classes (Friday, March 24, 2023). These dates coincide with the first and second rounds of the comprehensive 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 juniors will ask for basic information about the student signing up including which subject portion they would like to take (for more information see the section on Content and Format below). 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 a graduation year 20XXE) who wishes to take the honors qualifying exam while a second semester junior should contact the Mathematics Honors and Comprehensives Advisor(s) before the start of that semester in order to discuss a schedule for taking the exam.

Who Takes the Exam

Students who have declared the Mathematics major and are second semester juniors (possibly first semester juniors for E students) are eligible to take the honors qualifying 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). Any student wishing to apply to write a thesis in Mathematics must take and high pass the exam (for more information about this, see the section below on Grading: High Pass, Pass, and Fail.)

Content and Format

The exam consists of two parts, the Core and the Subject part, covering material from three courses.

The Core part of the exam covers material from Multivariable Calculus (Math 211) and Linear Algebra (Math 271 or 272). For the Subject part of the exam, students choose between either Algebra (Math 350) or Analysis (Math 355). It is a closed-book, written exam, generally with twelve problems (four from each of the three courses), and the time limit is three hours. The exam does not cover the full syllabi of these courses, but instead the more abbreviated comprehensive syllabi linked on this website.

Note that the Exam syllabi for Multivariable Calculus and Linear Algebra are the same as for the Comprehensive Exam, but the Core portion of the Honors Qualifying exam is slightly harder than the Comprehensive Exam.

We strongly encourage that students have a conversation with their mathematics advisor about which subject to choose for their exam. A student who wishes to take a different subject portion on the second round of the exam must petition the department to do so.

Grading: High Pass, 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 each section of the exam an overall score of either High Pass, Pass, or Fail.

In order to High Pass the honors qualifying exam as a whole and start the process towards entering the honors program in mathematics, a student must get a High Pass on both the Core and Subject part of the exam.

A student 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 Comprehensive Exam for more details.

A rough rule-of-thumb is that a High Pass means 80% or better, a Pass means between 60% and 80%, and a Fail means 60% or lower. These percentages are NOT fixed and may vary depending on many factors.

Retaking the Exam

A student who receives a Fail on either section of the first round of the honors qualifying exam would need to retake both sections in order to apply for the honors program or to satisfy the comprehensive requirement as a junior.

A student earning a Pass or above on both sections of the honors qualifying exam does not need to retake any part of the exam in order to satisfy the comprehensive requirement, but would need to retake any section that was not High Passed in order to apply for the honors program.

If a student decides to retake any section of the exam, they need to sign up to take the second round of the exam. As described above, this is generally the Friday of the first full week after Spring Break, or for E students taking the exam in the second semester of their junior year, around the corresponding time in the Fall semester.

If the retake only involves one part of the exam, the amount of time the student is given is determined by what part is being taken. The time limit is two hours when retaking just the Core portion of the exam and one hour when retaking just the Subject portion of the exam.

Number of Attempts

A student may only attempt the honors qualifying exam twice. These attempts occur during the second semester of the junior year (possibly first semester of the junior year for an E student) and happen at the regularly scheduled times. Missing a scheduled administration of the exam counts as an attempt, with exceptions only by petition to the department.

Taking the Exam Away

Students studying away as second-semester juniors can still take the honors qualifying exam. In order to take the exam, students will need to find a proctor at their visiting institution. For more information about how to take the honors qualifying exam while away, please speak with your Mathematics advisor or the Mathematics Honors and Comprehensives advisor(s).

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 previous comprehensive exams and solutions to some of those exams. Students are strongly encouraged to start their studying early and use the departmental study guides.

A full list of all the materials available to students.