Mathematics and Statistics

Introductory Courses

Some first-year students entering Swarthmore have had calculus while in high school and place out of at least one semester of Swarthmore’s calculus courses. However, some entering students have not had the opportunity to take calculus or would like to begin again. Therefore, Swarthmore offers a beginning calculus course (MATH 015) and several courses that do not require calculus or other advanced mathematics coursework. These courses are STAT 001 (Statistical Thinking, alternate Fall semesters) MATH 003 (Introduction to Mathematical Thinking, alternate Spring semesters), and STAT 011 (Statistical Methods I, both semesters).  Once one has taken or placed out of one or more classes, many other courses are available, such as linear algebra and discrete mathematics.

• STAT 071. Topics in Probability

Placement Procedure

All entering students, regardless of whether they plan to take math/stat courses, are required to take Swarthmore’s Math/Stat readiness exam.  Students can place into courses above the introductory level via a combination of Advanced Placement (AP) exams, higher-level International Baccalaureate (lB) exams, and the department’s placement exams.

Advanced Placement/International Baccalaureate Credit

Placement and credit mean different things. Placement allows students to skip material they have already learned well by starting at Swarthmore in more advanced courses. Credit confers placement as well but also is recorded on the student’s Swarthmore transcript and counts toward the 32 credits needed for graduation.

The Swarthmore Calculus Placement Exam is used for placement only, not credit. The credit awarded on the basis of the AP and IB exams was updated during the 2018-2019 year and resulted in the following rules:

• 1 credit (for STAT 011) for a score of 4 or 5 on the Statistics AP Exam.
• 1 credit (for MATH 015) for a score of 4 or 5 on the AB Calculus AP Exam (or for an AB subscore of 4 or 5 on the BC Test) or for a score of 6 or 7 on the Higher Level Mathematics Test of the IB.
• 2 credits (for MATH 015 and 025) for a main score of 4 or 5 on the BC Calculus AP Exam.

Students who receive placement but not credit for a course may attempt to earn credit without regular attendance by taking the final exam to demonstrate mastery of the material.  See section 8.1 of the course catalog for details. 

Students who are eligible on entrance for credit for a course, but who take the course anyway, will lose the entrance credit.  For instance, if a student scores 5 on the AB Calculus AP Exam but then takes Math 15, credit for AP Calculus will be lost.  

First-year students seeking advanced placement and/or credit for calculus taken at another college or university must normally validate their work by taking the appropriate external or Swarthmore placement examination, as described earlier. The department does not grant credit directly for college courses taken while a student is in high school. For work beyond calculus completed before entering Swarthmore, students should consult the departmental placement coordinator to determine the Swarthmore courses into which they may be placed and additional materials they may need to present for this placement. The department will not award credit for work above the first-year calculus level completed before entering Swarthmore.

Major and Minor Application Process

Students apply for a major (or minor) in the middle of the second semester of the sophomore year.  Upon applying for a major (or minor) in the department, students will be assigned a departmental sophomore plan advisor who will help them decide on a reasoned plan of study for their last two years.  This plan is then submitted to the department via their online Sophomore Plan.  After the Sophomore Plan process is over, students may apply to add or change a major (or minor) at any time, but applications will normally be held until the next time that sophomore applications are considered (around March 1).

Acceptance into the Major

The Department offers three different pathways to a course major: a course major without special emphasis, a course major with an emphasis in statistics, and a course major with an emphasis in applied mathematics. The normal preparation for all majors in mathematics is to have obtained credit for, or placement out of, at least four of the following five course groups by the end of the sophomore year: Calculus I (MATH 015), Calculus II (MATH 025), Discrete Mathematics (MATH 039 - previously called Math 029), Linear Algebra (MATH 027 or 028), and Several Variable Calculus (MATH 033, 034, or 035). In any event, all majors must complete the Linear Algebra and Several Variable Calculus requirement by the end of the first semester of the junior year.

To be accepted as a major or a minor, a candidate normally should have a grade point average of at least C+ in courses taken in the department to date, including courses in the fall term of the first year, for which we have shadow grades.  A candidate should have at least one grade at the B level. Students should be aware that upper-level courses in mathematics are typically more demanding and more theoretical than the first-  and second-year courses, which is an important consideration in borderline cases. In some cases, applicants may be deferred pending successful work in courses to be designated by the department.

Requirements for the Course Major

Graduation Requirements for all Course Majors (see additional requirements below):

• At least 10 credits in mathematics and statistics courses. (Certain courses - mostly numbered under 010 - do not count toward the major. These are indicated under the individual course listings.)
• Credit for, or placement out of, the following courses: MATH 015; MATH 025; MATH 027 or 028; and MATH 033, 034, or 035.  
• Credit for, or placement out of, Introduction to Real Analysis (MATH 063).
• Credit for Senior Conference (MATH 097), the department’s comprehensive requirement.  Students take this zero-credit course in both the fall and spring of their senior year. This comprehensive will have students engage with mathematicians and statisticians who present lectures on various topics, and will have students participate in a range of departmental activities. Any student who will not be on campus during one of those semesters must replace that semester’s MATH 097 course with a department-approved substitution. The substitution should be approved during the sophomore planning stage, or, if that is not possible, by speaking with their department advisor as soon as possible.

In the multivariate group (MATH 033, 034, or 035), it is strongly preferred that candidates for the major take MATH 034 or 035, which are the versions that assume a background in linear algebra.

Note that placement out of a course does not add to a student’s credit total; students need to earn 10 credits of coursework in the department. If you believe you are eligible for credit for courses taken before Swarthmore (because of AP or IB scores) but these credits are not showing on your transcript, please address this matter immediately with the registrar. Your application to our department may be held up otherwise.

Each of the three pathways to the course major (without special emphasis, emphasis in Statistics, emphasis in Applied Mathematics) has its own additional requirements, which are detailed below.   

Course Majors without special emphasis must also:

• Earn credit for, or placement out of, Introduction to Modern Algebra (MATH 067)
• Earn at least 5 credits in mathematics and statistics courses for courses numbered over 038.  At most one of these courses may be graded CR/NC.  No course numbered over 100 may be taken CR/NC.
• Take at least one of MATH 063 or MATH 067 at Swarthmore.

The departmental schedule offers the two required core courses, Introduction to Real Analysis (MATH 063) and Introduction to Modern Algebra (MATH 067), in alternate semesters (MATH 063 in the fall and MATH 067 in the spring).  Because MATH 063 is guaranteed to be offered only in the fall, students should plan to take it before the spring semester of their senior year. 
 

Course Majors with an emphasis in Statistics must also:

• Earn credit for, or placement out of:
  • Statistical Methods II (STAT 021)
  • Probability (STAT 051)
  • Mathematical Statistics I (STAT 061)
  • Mathematical Statistics II (STAT 111)
  • Computer Science 021. Students are advised to take CPSC 021 as early as possible, as it can be difficult to add this course in the junior or senior year. 

• Earn at least 5 credits in mathematics and statistics courses numbered over 038 OR earn credit (not placement) for STAT 021 and at least 4 credits in math/stat courses numbered over 038. At most one of these five credits may be graded CR/NC. No course numbered over 100 may be taken CR/NC.
• STAT 111 and at least one of STAT 051 or STAT 061 must be taken at Swarthmore.
   

Course majors with an emphasis in Applied Mathematics must also:

• Earn credit for, or placement out of:
  • Stochastic and Numerical Methods (MATH 066)
  • Differential Equations (MATH 043 or MATH 044)
  • At least one of
    • Partial Differential Equations (MATH 054)
    • Modeling (MATH 056)
  • At least one additional course from the following:
    • Partial Differential Equations (MATH 054)
    • Modeling (MATH 056)
    • Probability (STAT 051)
    • Complex Analysis (MATH 083¹)     
  • Computer Science 021. Students are advised to take CPSC 021 as early as possible, as it can be difficult to add this course in the junior or senior year. 
• Earn at least 5 credits in math/stat courses numbered over 038.  At most one of these 5 credits may be graded CR/NC.  No course numbered over 100 may be taken CR/NC.
• Take Math 066 at Swarthmore.

All majors are encouraged to study in some depth an additional discipline that makes use of mathematics or statistics.  We also recommend that they acquire some facility with computer programming.

_{¹Previously called Math 103, this will now be a course and not a seminar.}

Credit/No Credit Policy

At most one upper-level course counted towards the major can be graded credit/no credit. This does not include courses which are only offered credit/no credit.  No seminars can be taken credit/no credit.

Acceptance into the minors

The department offers two types of course minors: a course minor in mathematics and a course minor in statistics.  There are two pathways to the course minor in mathematics: a minor without special emphasis and a minor with an emphasis in applied mathematics.  Students may not have more than one minor in the department. The requirements for acceptance into any course minor, such as prerequisite courses and grade average, are the same as for acceptance into the major.

Requirements for the Course Minor

Graduation Requirements for all Course Minors (see additional requirements below)

• At least 6 credits in mathematics and statistics courses.  Those courses offered by the Department that do not count towards the course major also do not count towards the course minor.
• Credit for, or placement out of, the following courses: MATH 015 or MATH 025; MATH 027 or 028; and MATH 033, 034, or 035.  

Course Minors in Mathematics without special emphasis must also:

• Earn at least 3 credits in mathematics and statistics courses for courses numbered over 043. (Note the difference from the course major requirement, which is 5 courses over 038.)
  • At least 2 of these 3 credits must be taken at Swarthmore.
  • One of these 3 credits must be either Introduction to Real Analysis (MATH 063) or Introduction to Modern Algebra (MATH 067)
  • At most one of these 3 credits may be graded CR/NC.  No course numbered over 100 may be taken CR/NC.

Course Minors in Mathematics with an emphasis in Applied Mathematics must also:

• Earn credit for, or placement out of, each of the following: CPSC 021, MATH 043 or 044, MATH 066, and at least one additional course from MATH 054, MATH 056, or STAT 051.
• Take MATH 066 at Swarthmore.
• Earn at least 3 credits in mathematics and statistics courses numbered over 040 (Note the difference from the course major requirement, which is 5 courses over 038).
  • At most one of these 3 credits may be graded CR/NC. No course numbered over 100 may be taken CR/NC.

 Course Minors in Statistics must also:

• Earn credit for, or placement out of, each of the following courses: CPSC 021, Stat 021, Stat 051, Stat 061
• Take at least one of Stat 051 or Stat 061 at Swarthmore College.

• Earn at least 3 credits in mathematics and statistics courses numbered over 040 OR earn credit (not placement) for Stat 021 and at least 2 credits in math/stat courses numbered over 040 (Note the difference from the course major requirement, which is 5 courses over 038).
  • At most one of these 3 credits may be graded CR/NC.  No course numbered over 100 may be taken CR/NC.

Acceptance into the Honors Major

The requirements to be accepted as an honors major are the same as those to be accepted as a course major except that such students should have a grade point average in mathematics and statistics courses to date of at least B+.

Requirements for the Honors Major

• At least 10 credits in mathematics and statistics courses
• Credit for, or placement out of, the following courses: MATH 015 or MATH 025; MATH 027 or 028; and MATH 033, 034, or 035  
• Three preparations of two credits each, for a total of six distinct credits, in the following areas:
  • Real Analysis (MATH 063, and either 101 or 103*).  
    *starting the academic year 2025-26, this preparation must be in Math 063 and Math 101.
  • Modern Algebra (MATH 067 and 102)
  • One of:
    • Geometry (MATH 065 and MATH 105)
    • Statistics (STAT 061 and 111)
    • Topology (MATH 104 (2 credits) or Math 064 and MATH 104 (1 credit)).
       
• At most one of the courses in the three preparations may be graded CR/NC. No course numbered over 100 may be taken CR/NC.

Students who are doing an Honors math major with the Statistics preparation are required to take a data-driven statistics course as well (e.g. Stat 011 or 021).

Each of the three preparations is subject to External Examination, which consists of a 3-hour written examination and a 45-minute oral examination. The External Examination component of the program is meant to prompt students to learn their core subjects well and to show the examiners that they have done so.  However, no three fields cover everything a student would ideally learn as an undergraduate.  Honors majors should consider including in their studies a number of advanced courses and seminars beyond what they present for Honors should their schedules allow it.

Especially strong students who take many advanced courses may petition to substitute an advanced preparation for either Algebra or Analysis.  For instance, a student who has taken essentially all our seminars might petition to be examined in Algebra, Topology, and Geometry, omitting an analysis examination.  However, all honors students must take the algebra sequence and one of the analysis sequences, even if they are given permission to be examined in something else.

Note that to be an Honors math major, a student is required to also have an Honors minor in another subject. Senior Honors Study or Portfolio is not required or offered, and Honors majors do not need to take Senior Conference (MATH 097).

Acceptance into the Honors Minor

The requirements to be accepted as an honors minor are the same as those to be accepted as a course major except that such students should have a grade point average in mathematics and statistics courses to date of at least B.

Requirements for the Honors Minor

• Credit for, or placement out of, the following courses: MATH 015 or MATH 025; MATH 027 or 028; and MATH 033, 034, or 035 
• Satisfy the requirements for a course math minor (either with no emphasis or with an emphasis in applied math) or the stat minor. 
• One preparation consisting of two credits in one of the following areas:
  • Real Analysis (MATH 063 and 101)
  • Complex Analysis (MATH 063 and 103*)
    *Starting with the academic year 2025-26, this honors preparation will no longer be offered. 
  • Modern Algebra (MATH 067 and 102)
  • Geometry (MATH 065 and 105)
  • Statistics* (STAT 061 and 111)
  • Topology (MATH 104 (2 credits) or MATH 064 and MATH 104 (1 credit)).
     

All prospective minors who are majoring in a subject related to mathematics or statistics are encouraged to consult with a member of the Department to see which preparation is most appropriate to their interests.  Honors minors are encouraged to take at least one of MATH 063 and 067 even if it is not part of their Honors preparation. As mentioned before, no seminar may be taken credit/no credit.

* Students who are doing an Honors math minor with the Statistics preparation are required to take a data-driven statistics course as well (e.g., STAT 011 or 021).

Note that to be an Honors math minor, a student is required to also have an Honors major in another subject.

Seminars

• MATH 101. Real Analysis II
• MATH 102. Modern Algebra II
• MATH 103. Complex Analysis
• MATH 104. Topology
• MATH 105. Geometry II
• STAT 111. Mathematical Statistics II