Mathematics and Statistics

Introductory Courses

Many 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, whether they continue with calculus or decide, as is often best, to try other sorts of mathematics. See the discussion of placement later. However, some entering students have not had the opportunity to take calculus or need to begin again. Therefore, Swarthmore offers a beginning calculus course (MATH 015) and several courses that do not require calculus or other sophisticated mathematics experiences. These courses are STAT 001 (Statistical Thinking, Fall semester), MATH 003 (Introduction to Mathematical Thinking, Spring semester), and STAT 011 (Statistical Methods I, both semesters). MATH 003 is a writing course. MATH 039 (Discrete Mathematics, both semesters) also does not require any calculus but is a more sophisticated course; thus, some calculus is a useful background for it in an indirect way. Once one has had or placed out of two semesters of calculus, many other courses are available, such as linear algebra and several-variable calculus.

Placement Procedure

To gain entrance to mathematics or statistics courses at any time during one’s Swarthmore years, students are expected to take at least one of the following exams: the Advanced Placement (AP) or higher-level International Baccalaureate (IB) exams, Swarthmore’s Calculus Placement Exam, or Swarthmore’s Math/Stat Readiness Exam. Students who take AP or IB exams may be required to take the departmental exams as well, or parts thereof. In particular, students intending to take MATH 015 must take Swarthmore’s Calculus Readiness Exam.

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 Test of the College Board.
• 1 credit (for MATH 015) for a score of 4 or 5 on the AB Calculus AP Test of the College Board (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 Test.

Students who receive placement but not credit for a course occasionally make use of section 8.1 of the course catalog to arrange to take a course without regular attendance.  See section 8.1 for details.  Students who are eligible on entrance for credit for a course, but who take the course anyway, will lose the entrance credit.

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 normally award credit for work above the first-year calculus level completed before entering Swarthmore.

Major and Minor Application Process

Students apply for a major in the middle of the second semester of the sophomore year.  Upon indication of intent to 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 electronic 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 or 026), 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. (We do not have shadow grades from Spring 2020, so those courses will not be included in the grade point average.) 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. This is an important factor in considering 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 10 - 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 or 026; MATH 027 or 028; and MATH 033, 034, or 035.  
• Credit for, or placement out of, Introduction to Real Analysis (MATH 63).
• Credit for Senior Conference (MATH 97), the department’s comprehensive requirement, which has a new format as of the 2021-22 academic year. Students must now 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 97 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 33, 34, or 35), it is strongly preferred that candidates for the major take 34 or 35, 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 67)
• Earn at least 5 credits in mathematics and statistics courses for courses numbered over 38.  At most one of these courses may be taken CR/NC.  No course numbered over 100 may be taken CR/NC.
• Take at least one of MATH 63 or MATH 67 at Swarthmore.

The departmental schedule offers the two required core courses, Introduction to Real Analysis (MATH 63) and Introduction to Modern Algebra (MATH 67), in alternate semesters (MATH 63 in the fall and MATH 67 in the spring). Because MATH  63 is only guaranteed to be offered in the fall, students should plan to take it before the spring semester of senior year. 
 

Course Majors with an emphasis in Statistics must also:

• Earn credit for, or placement out of:
  • Statistical Methods II (STAT 21)
  • Probability (STAT 51)
  • Mathematical Statistics I (STAT 61)
  • Mathematical Statistics II (STAT 111)
  • Computer Science 21. Students are advised to take CPSC 21 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 38 OR earn credit (not placement) for STAT 21 and at least 4 credits in math/stat courses numbered over 38. At most one of these five credits may be taken CR/NC. No course numbered over 100 may be taken CR/NC.
• STAT 111 and at least one of STAT 51 or STAT 61 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 66)
  • Differential Equations (MATH 43 or MATH 44)
  • At least one of
    • Partial Differential Equations (MATH 54)
    • Modeling (MATH 56)
  • At least one additional course from the following:
    • Partial Differential Equations (MATH 54)
    • Modeling (MATH 56)
    • Probability (STAT 51)
    • Complex Analysis (MATH 103)     
  • Computer Science 21. Students are advised to take CPSC 21 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 38.  At most one of these 5 credits may be taken CR/NC.  No course numbered over 100 may be taken CR/NC.
• Take Math 66 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.

Credit/No Credit Policy

At most one upper level course counted towards the major can be taken credit/no credit. This does not include courses which are only offered credit/no credit, but does include courses for which the grade is uncovered after completion of the course. In any case, 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; MATH 025 or 026; 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 43. (Note the difference from the course major requirement, which is 5 courses over 38.)
  • 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 63) or Introduction to Modern Algebra (MATH 67)
  • At most one of these 3 credits may be taken 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 21, MATH 43 or 44, MATH 66, and at least one additional course from MATH 54, MATH 56, or STAT 51.
• Take MATH 66 at Swarthmore.
• Earn at least 3 credits in mathematics and statistics courses numbered over 40 (Note the difference from the course major requirement, which is 5 courses over 38).
  • At most one of these 3 credits may be taken 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 21, Stat 21, Stat 51, Stat 61
• Take at least one of Stat 51 or Stat 61 at Swarthmore College.

• Earn at least 3 credits in mathematics and statistics courses numbered over 40 OR earn credit (not placement) for Stat 21 and at least 2 credits in math/stat courses numbered over 40 (Note the difference from the course major requirement, which is 5 courses over 38).
  • At most one of these 3 credits may be taken CR/NC.  No course numbered over 100 may be taken CR/NC.

Credit/No Credit Policy

For the math minor, at most one of the required upper level courses counted towards the minor can be taken credit/no credit. For the statistics minor, only one of Stat 21, Stat 51, and Stat 61 may be taken credit/no credit.  For the applied math minor, at most one of the 4 required courses listed previously may be taken credit/no credit. This does not include courses which are only offered credit/no credit, but does include courses for which the grade is uncovered after completion of the course. In any case, no seminar can be taken credit/no credit.

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; MATH 025 or 026; 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 63 and 101) or Complex Analysis (MATH 63 and 103)
  • Modern Algebra (MATH 67 and 102)
  • One of:
    • Geometry (MATH 65 and MATH 105)
    • Statistics (STAT 61 and 111)
    • Topology (MATH 104, a 2-credit seminar)
• At most one of the courses in the three preparations may be taken 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 11 or 21).

Each of the three preparations is subject to External Examination, including 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 - that is, show that they deserve Honors.  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.

No course is allowed to count in two honors preparations, so it is not possible for a student to do honors preparations in both Real Analysis and Complex Analysis.

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 97).

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; MATH 025 or 026; MATH 027 or 028; and MATH 033, 034, or 035  
• One preparation consisting of two credits in one of the following areas:
  • Real Analysis (MATH 63 and 101)
  • Complex Analysis (MATH 63 and 103)
  • Modern Algebra (MATH 67 and 102)
  • Geometry (MATH 65 and 105)
  • Statistics* (STAT 61 and 111)
  • Topology (MATH 104, a 2-credit seminar)

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 63 and 67 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 11 or 21).

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