About the Mathematics Major

The mathematics major is fun and rewarding and can lead to great jobs!

If you are thinking about majoring in math, you should go to Seeley Mudd and talk to a math professor. In the meantime, this page provides an outline of the requirements for a major. (The catalog is the official word on these matters, so read it, too.)

Once you have decided to declare the major, begin the process by filling out and submitting the departmental declaration form here.  After submitting that form, you will be contacted by the Department Chair (Prof. Amanda Folsom).  The last step in the process of declaring the Mathematics major is submitting a Declaration of Major form to the Registrar's office, as outlined here.  

As you proceed through the major or are trying to decide if you can complete it, check out our checklist for the Math Major: 

 You might also want to check out our example pathways through the mathematics major.

Clarification on Intro Stats for Math Majors

Stat 111 does NOT count towards the mathematics major, but Stat 135 does count as a mathematics elective. Either introductory course (Stat 111 or Stat 135) counts towards the statistics major, though Stat 135 is strongly recommended. We strongly encourage students with questions about majors in mathematics and statistics to talk to a faculty member in the Department.

Required Courses

  • Introduction to the Calculus (Mathematics 111)
  • Intermediate Calculus (Mathematics 121)
  • Multivariable Calculus (Mathematics 211)
  • Linear Algebra (Mathematics 271 or 272)
  • Groups, Rings and Fields (Mathematics 350)
  • Introduction to Analysis (Mathematics 355)

Depending on background, mathematics majors may place out of several of these core courses. Students who place out of Math 271/272 must replace the course with an additional mathematics course numbered 225 or higher. Students who place out of Math 350 or 355 must replace that course with an additional mathematics course numbered 300 or higher. (See details of this policy below.) Mathematics majors may not apply* a Pass grade from an FGO or pass/fail option to any of the core courses required for the mathematics major: MATH 111, 121, 211, 271/2, 350, or 355 (exceptions by petition to the department).

*For the 2020-21 academic year only, Mathematics and Statistics students may apply a Pass grade from an FGO or pass/fail option to any course taken in 2020-21 required for the Math or Stat majors (including core courses) with the following restrictions:  no more than one Pass grade may be applied to the Math or Stat major per term (Fall 20, January 21, Spring 21), and at most two total Pass grades from Fall 20, January 21, or Spring 21, can be applied to the Math or Stat major.  

*For the Spring 2020 semester only, Mathematics and Statistics students may apply a Pass grade from an FGO or pass/fail option to any course taken in Spring 2020 required for the Math or Stat majors (including core courses).  ​

Elective Mathematics Courses

Along with the required courses, a major must complete three elective courses in Mathematics numbered 135 or higher.  For majors declared after May 12, 2017, two of these electives must be numbered 200 or higher, and the remaining elective must be numbered 135 or higher**. In addition, a major must complete two other courses, each of which is either an elective course in Mathematics numbered between 135 and 490 or a course from outside Mathematics, but in a related field, chosen from among COSC 201 or 211, 301 or 311, and 401; ECON 300, 301, 361, and 420; PHIL 350; any Physics course numbered 116 or higher (excluding PHYS 227); any Astronomy course numbered 226 or higher; and any Statistics course numbered 200 or higher. Statistics courses cross-listed with Mathematics count as Mathematics electives.  This two-course requirement can be satisfied by taking two math electives, one math elective and one related-fields course, or two related-fields courses. Requests for alternative courses must be approved in writing by the chair of the department in consultation with the Mathematics faculty via a petition from the student. To submit a petition, email the chair of the department with relevant information about the course to be considered, for example, a syllabus from a recent semester of the course or a link to the course description. For study abroad petitions, approvals are contingent on submission of a transcript showing the grade earned in the course, in order to aid in student advising. Honors students may petition the department to count one math thesis course as an elective toward the major**.

**For Mathematics majors in class of 2021 or 2021E, instead of requiring that at least two of the three required Math electives towards the Mathematics major are numbered 200 or higher, it is required that at least one of the three required Math electives is numbered 200 or higher.  Additionally, honors Mathematics thesis students in class of 2021 or 2021E may count either Math 498 or Math 499 as a Math elective towards the Math major.  No petition is required to do so. 

Double majors in mathematics and statistics must complete a total of 20 courses (or 19, if statistics was declared prior to May 3, 2019). Math 111, Math 121, Math 271-or-272 (if required for their statistics major), and at most one other course (usually Math/Stat 360) can be counted towards both majors. Aside from this permitted overlap, statistics courses or computer science courses counted towards the statistics major may not also be counted towards the mathematics major. Double majors should fill out both major checklists and are encouraged to consult with faculty in the Department to verify that they have satisfied all requirements.

Amherst math group at JMM 2020

Comprehensive Examination

A comprehensive examination for majors who are not participating in the Honors Program will be given near the beginning of the spring semester of the senior year. (Those who will complete their studies in the fall semester may elect instead to take the comprehensive examination at the beginning of that semester.) The examination covers MATH 211, 271 or 272, and a choice of MATH 350 or 355. Information describing the comprehensive examination can be obtained here.

Honors Program

Students are admitted to the Honors Program on the basis of a qualifying examination given at the beginning of the spring semester of their junior year and the acceptance of a thesis proposal. (Those for whom the second semester of the junior year occurs in the fall may elect instead to take the qualifying examination at the beginning of that semester.) The examination is described here. A thesis proposal will typically be due in early April of the junior year. If a student is accepted to the Honors Program, they will finalize a topic in consultation with Mathematics faculty. After intensive study of this topic, the candidate will write a report in the form of a thesis which should be original in its presentation of material, if not in content. In addition, the candidate will report to the departmental colloquium on their thesis work during the senior year. Honors candidates are also required to complete MATH 345 and at least one Mathematics course numbered 400 to 489.  See Recent Theses for a list of recent theses and Thesis Regulations for thesis regulations.

The department will work to accommodate as many suitable thesis proposals as possible, but it may be the case that not all proposals will be accepted if we have a very large group of students seeking to write theses. Note that submission of a proposal after passing the Honors Qualifying Exam does not guarantee getting to write a thesis in Mathematics.

Juniors who passed the Honors Qualifying Exam, but either did not submit a thesis proposal or submitted an unsuccessful thesis proposal, will still have passed the Mathematics Comprehensive Exam and will not need to take the exam in their senior year.

Other Aspects of the Mathematics Major

  • Departmental Colloquium:  All students majoring in Mathematics are expected to attend Mathematics colloquia during their junior and senior years.
  • For a student considering graduate study, the Departmental Honors program is strongly recommended.  Such a student is advised to take the Graduate Record Examination early in the senior year.  It is also desirable to have a reading knowledge of a foreign language, usually French, German, or Russian, as this is a requirement of many graduate programs in mathematics.
  • Study Away:  It is easy to combine the mathematics major with a semester or year spent away.  See our math study away page for more information, or talk with a faculty member.

Policy on Competency Exams for MATH 211, 271/272, 350 and 355

Mathematics majors who wish to place out of MATH 211, 271/272, 350 or 355 must provide a transcript from a college or university for an equivalent course approved by the Department; courses offered by a high school will be considered on a case-by-case basis. Alternately, if the Department determines the outside course to be mostly but not completely sufficient, then the student may opt to take a competency exam, administered by the Department, on the material of the course. This competency exam is intended only for students who have actually taken a roughly similar course. Students are strongly discouraged from self-studying courses to avoid or skip them. 

In the latter case, it is important that the competency exam is taken in a timely fashion. In particular:

1) If a math major wishes to place out of one of these four courses via a competency exam and wants to take a subsequent course requiring that course, then the appropriate competency exam must be taken before the subsequent course begins.

2) It could happen that a student declares the math major as a junior or senior and has taken a course such as MATH 350 without having taken MATH 271 or 272.  For example, the student could be a Physics major who was given consent to take MATH 350 on the basis of having taken Physics 227.  In this situation, the student must take the competency exam for the skipped course by the end of the semester in which they declared the math major.

A student has only one chance to pass the competency exam, so careful preparation is strongly recommended.  Advisors are responsible for reminding their advisees of this policy (approved May 6, 2015).

Note: The College does not offer course credit for competency exams or for courses taken while in high school. Students who place out of Math 271/272 must replace the course with an additional mathematics course numbered 225 or higher. Students who place out of Math 350 or 355 must replace that course with an additional mathematics course numbered 300 or higher. 

Learning Goals

Upon completion of the Mathematics major, we expect our graduates:

  1. To have acquired both proficiency at calculation and a theoretical understanding of single-variable calculus, multivariable calculus, and linear algebra.

  2. To have developed an ability to read and understand mathematical proofs, as well as to construct and communicate their own mathematical proofs.
  3. To have demonstrated in a variety of courses the ability to learn and apply new mathematical concepts, definitions, theorems, reasoning skills, and proof skills.

  4. For honors students, to have delved deeply into an advanced topic and written a clear and detailed exposition in the form of a senior thesis.

Nathan, Amalia, Ryan, and Kara

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