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Math Placement


Who should read this?
This document addresses placement questions for incoming students and for undergraduates who have not yet taken a math course at Duke.

Note for potential math majors:
If you are considering a major in mathematics, and if you have advance credit for first and second semester calculus (Math 21 and Math 22), then you should read about  Math 222. Potential math majors should also contact the Director of Undergraduate Studies in Mathematics,  Professor Chad Schoen or the Associate Director of Undergraduate Studies in Mathematics,  Prof. Sarah Schott.  (If you have placement questions, please use the SFI Placement Advice contact page.)

Course codes:
The placement information below refers to math courses by number. If you wish to see a detailed description of a course, then you should refer to the Bulletin of Undergraduate Instruction for descriptions of all math courses.

Still not sure... :
If you have read all of the discussion below, and all of the relevant FAQ's (linked below) and other linked pages, and are still not sure what math class you should start in, you can use the SFI Placement Advice contact page. 

Note, if you cannot decide between two courses, you should also consider attending both courses simultaneously during the first week, to avoid the very serious problem of finding yourself behind schedule if you change your mind.  (Importantly, note that these courses are sufficiently different from each other that "dropping back" is usually not much easier (or more likely to be allowed) than simply adding a course late in the drop/add period.)  See more discussion of this in the Changing Classes section of our Enrollment Policies Page.


Quick Index

For students who have had ... no calculus one year of calculus multivariable calculus

  Frequently Asked Questions  Enrollment Policies



First-year Seminars

Each year the Math Department offers one or more seminars for first-year students. The seminars vary from year to year, and you can check the Registrar's   Course Schedule to see what particular seminars are being offered in the current semester. First-year seminars carry the number 89S(49S) in all departments. The following is a list of topics offered in first-year math seminars in recent years:
  • Applications of Mathematics to Physiology
  • Game Theory and Democracy
  • Introduction to Cryptography
  • Tilings, Symmetry, and Geometry
The prerequisites for math seminars vary, and you can check what these prerequisites are by reading the information linked from the Registrar's Course Schedule.


Information for Students who have had little or no calculus

The entry level for mathematics is Math 105L or Math 111L. The following table provides guidelines for making the choice between these two courses:

Course Minimum Math SAT Minimum Math SAT II
Math 105L 520 500
Math 111L 680 680

If your SAT and SAT-II scores do not indicate consistent placement in this table, or if your scores indicate borderline qualification for Math 111L and you've had no calculus whatsoever, then it would be advisable to start with Math 105L.


Information for Students who have had a year of calculus

Important Note about Math 202 and Math 212:  Starting in Spring 2016, the prerequisites (credit for second semester calculus) for Math 202 and Math 212 will be enforced at registration.  This prerequisite can be satisfied by Math 22 (AP or IPC credit), Math 112L, Math 122L, or Math 122. 

If you have AP or international placement exam scores that you expect to result in AP or IPC credit for Math 22 but have not reported the scores yet, you should do that ASAP to result in the Math 22 credit needed for enrollment in these courses.  If you have taken a second semester calculus course that you hope will result in PMC or transfer credit for Math 122, you should likewise begin that process ASAP.

If you have a very strong background in second semester calculus that you feel is equivalent to the level of our Math 122L, but do not have such credit on your Duke transcript, and if you would like to be considered for an exemption from the second semester calculus prerequisite, you may take our "Math 122L Proficiency Exam"; students who do well on this exam will be granted permission to enroll in Math 212, at the discretion of the Supervisor of First-Year Instruction. This exam is offered every August, on the Saturday morning before the first day of classes.

There will also be a one-time January offering of the "Math 122L Proficiency Exam" this January, due to the Spring start of this restriction.  Click here to REGISTER for this exam.

For students who have taken the AP test: If you have earned credit based upon your Advanced Placement score, then generally you should enroll in the next higher course; however, we have found that students may have difficulty in second-semester calculus unless they also meet certain minimum SAT and Achievement score levels.

  • If you have AP credit for Math 21, an SAT score of at least 680, and an SAT-I or SAT-II score of at least 680, then you should enroll in a calculus II course. In fall semesters Math 122L is reserved for entering students who fit this situation (and Math 112L is reserved for students continuing from Math 111L or Math 106L). In spring semesters Math 122L is not offered but Math 112L is open to all students who qualify for calculus II. The document, Second-semester Calculus , provides more information about these courses.

  • If you have AP credit for Math 21, but you do not meet the minimum SAT and SAT-I/II levels of the last paragraph, and if you need to continue in calculus, then it's ususally best to forgo your AP credit for Math 21 and "start over" with Math 111L so that you gain experience in college-level calculus before you proceed to second-semester calculus. On the other hand, if you're not certain that you need credit for more than one semester of calculus, another strategy in this situation is not to take any math during your first semester; then you could wait to decide what to do after you have been in college for at least a semester and after you have a better idea of what academic direction you will take. After all, it's possible you won't need any more calculus beyond the one AP credit you've already earned.

  • If you have AP credit for Math 22, then you have the necessary credit to enroll in one of our multivariable calculus courses.  However, you are strongly encouraged to consider the option of waiving your Math 22 credit and starting in Math 122L, before going on to multivariable calculus.  For many students, this option will allow for a more successful experience in multivariable calculus, by (1) providing a significantly stronger preparation in single variable calculus, and (2) allowing the adjustment to Duke-level math courses to happen in the context of more familiar material, before the student gets to multivariable calculus. 

    If your Math 22 credit came from the grade of 4 on the BC AP exam, you should give particularly serious consideration to this option.  Likewise if your SAT score is not strong, or if you have any lack of confidence in your mathematical preparation or abilities. 

    There is a myth among students that suggests it is "easier" to get an "A" in Math 212 than in Math 122L, due to that grade being assigned in these courses in different proportions.  This speculation has many serious shortcomings (it assumes exaggerated raw numbers; it ignores the very significantly different sample sets of students in these two courses; it ignores the inherent selection bias coming from how other students make this same choice; ... ).  If you are concerned about being able to get a good grade in Math 212, the best thing you can do is to go in to the course with the best possible preparation, and that would be best accomplished by taking Math 122L at Duke.

    If you received the score of 5 on the BC AP exam, have a strong SAT score, and are confident in your mathematical preparation and abilities, then you might choose to go straight into multivariable calculus.  For many students, Math 212 is the best choice for this subject.  If you are considering majoring in economics or the social sciences, then you should read about Math 202. If you are considering majoring in mathematics or are just interested in getting a more rigorous experience in the subject, then you should read about Math 222.

  • If you have had a year of calculus and took the AP test and did not earn credit, then you should place into Math 105L or Math 111L as indicated by the SAT chart earlier in this document.

  • For Students Who Have Taken an International Entrance Exam: Requests for credit based on an internationally recognized entrance examination, such at the International Baccalaureate, the British A-level, the French Baccalaureate, and the German Arbitur, should be sent to the Registrar. A student can receive up to two credits for one of these tests. In general if Duke grants you credit for a course, then you should enroll in the next higher math course. For example, some international students score high enough on the higher level IB math exam to receive credit for Math 21 and Math 22, and will then be placed into Math 212 (or  Math 202 or   Math 222). Students who receive credit for Math 21 can enroll in Math 122L (in fall semesters) or Math 112L (in spring semesters). If your situation is different from these cases, or if you desire some other placement based upon work out of the country, then you should meet with the Supervisor of First-year Instruction to discuss placement.

    For students who have not taken the Advanced Placement Test or an International Entrance Exam: If your SAT score is at least 700 and your SAT-I or SAT-II score is at least 700, and if you feel you have a strong background in calculus, then you may enroll in a second-semester calculus course (see Second-semester Calculus  for more information) if you are willing to accept the inherent risk--although the safer academic route would be to enroll in Math 111L.

    On the other hand, if you are in this situation but wish to place beyond second-semester calculus, then you should write to the Supervisor of First-year Instruction, and describe the contents of the math courses you have had (e.g., textbook and chapters covered), how well you did in those courses, your SAT and Achievement scores, and a statement of the placement you desire. It is especially helpful if you can email a copy of the syllabus, including the title of the textbook you used and the sections you studied.

    If your SAT score is below 700, you should enroll in either Math 105L or Math 111L, according to the table above.


    Information for students who have completed a course in multivariable calculus or higher level mathematics

    First, you should be aware that our multivariable calculus course, Math 212, includes an important chapter on vector calculus, including line integrals, Green's Theorem, surface integrals, and Stokes' Theorem. This material accounts for approximately a fourth of our course; thus, if your multivariable calculus course did not include these topics and if you plan to continue taking math, then you should enroll in Math 212 (You may also want to consider Math 221, to be followed by Math 222, if you're interested in being a math major.)

    If you have been granted "pre-matriculation" credit for Math 212, and if you want to proceed to a higher level math course in your first semester, then you can simply enroll in the appropriate course when your registration window opens in the summer. For example, if you are an engineering student, then you would normally take Math 216 next. (Unless you plan on getting a double major with math. Please see FAQ #14 below.)

    If you do not have credit for Math 212, but you have studied all of the topics in Math 212 and you feel you should take a course numbered above Math 212, then write to the Supervisor of First-year Instruction. In your email message you should describe the contents of the courses you have had (e.g., textbooks and chapters covered), the name of the school where you took the courses, how well you did in the courses, your SAT and Achievement scores, and a statement of the placement you desire. It is especially helpful if you can email copies of the syllabi, including the titles of the textbooks you used and the sections you studied.  Note, Math 212 covers multivariable calculus at a level that is more rigorous and substantial than high school courses; so, even if have studied all of the topics in Math 212, you should still expect to find Math 212 to be a challenging course.  And Math 222 (taken after Math 221) would be even more challenging and rewarding.

    Students who hope to skip multivariable calculus (or any math course) should be sure to consider carefully the math requirements of their likely majors, minors, and certificate plans.  Those math requirements are overseen and enforced by those departments -- not the Department of Mathematics.  Enrollment in and successful completion of a higher level course CANNOT be assumed to satisfy a requirement of a lower level course, and very often it will not.  You must get written permission from the Director of Undergraduate Studies of the appropriate department before you skip any such required course.



    Many questions are in this list of   Frequently Asked Questions.

    If you have a question about enrollment, wait lists, or permission numbers, see the Enrollment Policies Page for first- and second-year courses in the Mathematics Department.

    If you have placement questions not covered in the FAQs above, you can send an email message to the Supervisor of First-Year Instruction.

    Additional web pages:
    Information for First-Year Students

    ph:  919.660.2800
    fax: 919.660.2821

    Mathematics Department
    Duke University, Box 90320
    Durham, NC 27708-0320