# Frequently Asked Questions

## AP (Advanced Placement) Questions

The following questions about Advanced Placement (AP) credit and course choices applies to all incoming students in both Trinity College of Arts & Sciences and the Pratt School of Engineering.

###### I don't know my AP score yet, and it's time for me to select my courses for the fall. What math course should I enroll in?

If you feel good about your calculus course and your performance on the AP test, then go ahead and sign up for the course following the one for which you could get credit.

For example, if you took the AB test, then you can enroll in Math 122L(41L). If it turns out that you don't score high enough for that placement, then you can change your math course after you meet with your advisor in August.

If you took the BC test and are hoping to enroll in Math 202 or Math 212, note that the enforcement of that prerequisite will prevent you from being able to enroll in those courses. Just be sure that your score gets officially reported to Duke when it is available (see the Registrar's webpage for instructions), and if you do earn credit for Math 21 and Math 22 then you will be able to enroll in Math 202 or Math 212 in August.

###### I have credit for Math 21 Introductory Calculus (Earned through AP credit). How can I decide whether to take Math 122L Introductory Calculus II with Applications or Math 112L Laboratory Calculus II? What is the difference?

If you're going to enroll in a calculus II course in your first semester (the fall), then you should take Math 122L Laboratory Calculus II with Applications. In the fall semesters, Math 112L Laboratory Calculus II is reserved for students continuing from Math 111L Laboratory Calculus I or Math 106L Laboratory Calculus and Functions II at Duke. In the spring, however, Math 112L is the only second semester calculus class offered and is open to any student with AP credit for Math 21.

###### I have AP credit for Math 21 Introductory Calculus and would like to take Math 112L Laboratory Calculus II in the spring. I know that this course lists Math 111L as a prerequisite, and that my AB AP curriculum is not exactly the same. What are the differences that I should make sure to prepare for before entering Math 112L?

You should make sure to learn Euler's method and L'Hospital's rule, both of which are covered in Math 111L Laboratory Calculus I. You should be prepared for the fact that Math 111L covers a wider variety of applications of differential equations, and emphasizes a deeper conceptual understanding of Riemann sums, the fundamental theorem of calculus, and differential equations, than many AP AB courses. Finally, note that students who have taken Math 111L will have gained substantial experience with writing lab reports, which will be an important skill in Math 112L.

###### If I am a sophomore (or junior, or senior) at Duke who has never taken a math course at Duke, may I enroll in Math 122L Introductory Calculus II with Applications based on my AP credit?

Yes, the guidelines for your case are the same as for an entering student.

###### I have had a year (or more) of calculus, but I don't have AP credit or precollege credit for any calculus course. Should (or may) I take Math 122L or Math 112L or Math 202 or Math 212, or should I start over with Math 111L?

If your SAT score is at least 730 (700 if taken before Mar. 2016) and your ACT score is at least 32, and if your calculus background was thorough, then it would be a reasonable risk for you to enroll in Math 122L Introductory Calculus II with Applications. But it's your risk! For example, if you did not take the AP test, but you made an A in a demanding calculus course, and your SAT score is about 730 (700 if taken before Mar. 2016) or higher, then if you want to take the risk of enrolling directly in Math 122L (or a higher level course), you may do so. Or perhaps you did take the AB AP test and your score was 4 (so no advance credit) but your SAT score is over 730 (700 if taken before Mar. 2016); then enrolling in Math 122L would be a reasonable risk. Again, it's your risk!

If you have a very strong math background that includes learning Taylor polynomials and infinite series and convergence theorems, and if you want to start with multivariable calculus with no advance or precollege credit, then you should register for the Math 122L Proficiency Exam. Be sure to read all of the discussion on that registration page and prepare appropriately for the exam. If you perform strongly on that exam, then at the discretion of the Supervisor of First-Year Instruction you will be granted permission to enroll in Math 202 or Math 212, depending on your interests.

Or you might also consider taking our Math 221-222 sequence. This is a great choice for students interested in the possibility of a math major or minor. Math 222 covers multivariable calculus at a higher level than either 202 or 212, and makes powerful use of the linear algebra covered in Math 221. This sequence does not enforce its prerequisite of second semester calculus, so to start with Math 221 you should not need to take the Math 122L Proficiency Exam.

If you have had a college course in multivariable calculus and would like to be considered for the possibility of starting in a course above multivariable calculus, you should discuss your case with the Supervisor of First-Year Instruction.

On the other hand, if you took the AB AP test and scored 3 or less, then you should enroll in Math 111L Laboratory Calculus I--assuming your SAT score is at least 710 (680 if taken before Mar. 2016) and your ACT score is at least 30. If your SAT score is much less than 710 (680 if taken before Mar. 2016) or your ACT score is much less than 30, and if your AB AP score is less than 5, then you should enroll in Math 105L Laboratory Calculus and Functions I. Note that completing Math 122L Introductory Calculus II with Applications or a higher level course does NOT entitle you to credit for the "skipped" course(s). But you should be aware that if you do not have AP credit for Math 21 Introductory Calculus I (earned through AP credit), the safer academic route would be for you to enroll in Math 111L (or Math 105L if your SAT score is less than 710 (680 if taken before Mar. 2016) or your ACT score is less than 30).

There is another issue here. If you choose a major that requires Math 111L (and any other "skipped" course), then you will need to ask the Director of Undergraduate Studies in your major department to waive their requirement for the "skipped" course(s). Some departments will do this, as long as you complete the next higher math course with a C or better. Engineering students should also be aware that, in addition to needing permission to skip a required course, the total number of math courses that they are required to take will not be reduced; that is, eventually a higher level math course must be taken to replace the "missing" course(s). Furthermore, if you skip to a higher level and then make less than a C, then the Engineering School will require you to start your math over with the lowest "skipped" course.

###### May I forego my AP credit and enroll in the course for which I could have received AP credit?

Yes. For example, if you have a 5 on the AB AP test or a 4 on the BC AP test, you may choose to forego your AP credit and enroll in Math 111L Laboratory Calculus I. If you have a 5 on the BC AP test, you can forego your AP credit for Math 22 Introductory Calculus II and enroll in Math 122L Introductory Calculus II with Applications.

Your AP scores may indicate that you are sufficiently prepared to move on to the next level, and going backwards might not be worth it. On the other hand, if you are not confident in your knowledge of the material in such a course and feel it will be important to your successful completion of future courses to solidify that knowledge and hone those skills, then you are allowed to do so.

On the other hand, if you are considering taking such a course for which you already have credit "for the easy A", note that this is almost certainly not a good idea. The overwhelming majority of students in Math 111L and Math 122L have already had a full year of calculus in high school, have strong SAT scores, and many of them have waived AP credits to take the course again for the serious purpose of honing their skills further, as per the discussion above. The level of performance and competition in these courses is very high. So, while you might get an "A" (and you might not), it is unlikely that it will be "easy".

###### My AP score has not been reported to Duke, yet I made a score sufficient to earn credit and place in a higher level course. May I go ahead and enroll in the advanced course?

If you are hoping to enroll in Math 122L, then yes. But you should make sure that the score will eventually be reported to the Registrar. It would also be helpful to send an email message to the Supervisor of First-year Instruction and provide him with the information on your AP score and your placement intentions.

If you are hoping to enroll in Math 202 or Math 212, note that the system requires credit for second semester calculus to be on your Duke record, so your AP score must be officially reported, and processed by the Registrar's Office, before you will be able to enroll.

###### Does Duke administer any kind of calculus placement test whereby I can "challenge" a course for credit?

No, that is contrary to Duke's policy on course credits.

###### I did not get a 5 on the BC test, but I would like to go ahead and take Math 212 Multivariable Calculus anyway. May I get permission to do so, or may I take a placement test for Math 212?

Math 212 and Math 202 require credit for second semester calculus on your Duke record. A score of 4 or lower on the BC AP exam results in credit only for Math 21, and does not result in credit for Math 22 that would satisfy this prerequisite.

If you feel you have a much stronger background in second semester calculus than is reflected in your AP score and would like to be considered for eligibility to enroll in Math 202 or Math 212, you might consider taking the Math 122L Proficiency Exam; students who do well on this exam will be granted permission to enroll in multivariable calculus, at the discretion of the Supervisor of First-Year Instruction. This test is administered each semester shortly before the first day of classes. If you would like to take this exam, please submit the Math 122L Proficiency Exam Registration Form.

You should be aware of several issues:

- Completing Math 212 Multivariable Calculus will NOT entitle you to official credit for Math 122L Introductory Calculus II with Applications.
- If your major requires Math 122L, then you'll have to get a waiver for that requirement from the Director of Undergraduate Studies in your major department. Most Directors will grant that waiver if you make a C or better in Math 212 Multivariable Calculus (but that is up to your major department--not the Math Department); however,
*if you do not do well in Math 212*, then you should expect to have to go back and take Math 122L Introductory Calculus II with Applications (or perhaps Math 112L Laboratory Calculus II in the spring). - If you are an engineering student, then you should discuss with your academic dean before you attempt to skip Math 122L. Be aware as well that skipping Math 122L will not reduce the total number of math courses which you must take. Thus, if you "skip" Math 122L and then complete Math 212 Multivariable Calculus successfully, then you won't have to take Math 122L Introductory Calculus II with Applications but you will have to take some other (higher level) math course approved by your dean.

## For Trinity Students

The following are questions frequently asked by students in Trinity College of Arts & Sciences, or engineering students who are double majoring in both engineering and a major from Trinity College.

###### Will my AP credit for calculus satisfy the "Quantitative Studies" curriculum requirement at Duke?

No, advance credits do not satisfy any field of knowledge or mode of inquiry requirements in the curriculum. If you have AP credit for calculus and don't want to pursue higher level math courses, you can satisfy the "QS" requirement by taking a course such as introductory statistics or computer science.

###### I have studied multivariable calculus while I was in high school, but I cannot receive "pre-matriculation" credit because the course appears on my high school transcript. Can I get the requirement for taking Math 212 Multivariable Calculus waived based on my work in high school?

There is no way for you to receive official Duke credit for the multivariable calculus course you took as a high school course. For more information on this policy, you can read the "Pre-Matriculation Credit" paragraph in the "AP,IPC, and PMC" page of Trinity College Requirements.

On the other hand, some departments may let you "skip" Math 212 Multivariable Calculus, provided that you take a specific higher-level math course for which Math 21s is a prerequisite and that you make at least a C in that course, or some other appropriate modification of their standard requirements. As part of this arrangement the department might ask the Math Department to confirm that you have studied the equivalent of Math 212 and that you could place into a math course for which Math 212 is a prerequisite. But, critically, the authority to make such arrangements does not rest with the Math Department; rather, the Director of Undergraduate Studies in the department which requires Math 212 for their major must make such decisions on a case by case basis.

But here's the WARNING: if a department allows you to "skip" Math 212 and take a higher level math course, and if you do not do well in that course, then you will probably be required to start over with Math 212. Above all, you should keep in mind that each department will make its own decision about such cases, and a student considering "skipping" a course required for a major should get written approval from the Director of Undergraduate Studies in that department.

###### How many math courses do I have to take at Duke?

Well, maybe none. Trinity College students must complete two "Quantitative Studies" courses as part of the curriculum's Area of Knowledge requirements. But those two QS courses could be courses in statistics, computer science, or in some other department. (See the following question/answer for directions on how to find courses with the QS designation) Of course, almost any two math courses will satisfy the QS Area of Knowledge requirement. Some excellent discussions of Trinity College's requirements are posted here and here.

###### Are there any courses besides calculus and higher-level math courses which satisfy the "Quantitative Studies" field of knowledge curriculum requirement?

Math 181 gives a significant yet accessible discussion of several interesting topics in mathematics; this course has the QS designation, no calculus prerequisites, and would be an excellent choice for students whose majors do not require calculus. For more information on this course, please see the course webpage.

Math 168S Mathematical Investigations in Genetics and Genomics introduces the basic mathematical methods that are vital to genetics and genomics. In addition to specific techniques and facts, this interdisciplinary course will demonstrate one of the many ways mathematics is important in modern biology. This course has both the QS designation and the seminar (S) designation.

There are also many statistics and computer science courses which carry the QS designation. Note that most statistics courses are taught by the Department of Statistical Science. You can search for all courses with the QS designation by using the Registrar's class search, which can be used to find all QS courses offered in a particular semester.

###### I am interested in a major which has a calculus prerequisite. Will AP credits for calculus satisfy those prerequisites?

Yes. AP credit for Math 21 Introductory Calculus I will satisfy another department's Math 21 (or Math 111L Laboratory Calculus I) prerequisite, and AP credit for Math 22 Introductory Calculus II will satisfy a Math 112L Laboratory Calculus II or Math 122L Introductory Calculus II with Functions prerequisite. But these credits do not satisfy the Quantitative Studies reguirement in the university curriculum.

###### What is Math 202 Mutivariable Calculus for Economics? I'm considering an econ major, and I read something about it in the requirements posted by the Economics Department.

Students who are considering a science major, a math major, or an engineering major should take Math 212 Multivariable Calculus instead of Math 202 Multivariable Calculus for Economics, even if you're considering a double major with economics. The Department of Economics will continue to accept Math 212 as well as Math 202 for those students who want to double major in economics and other majors that do require Math 212.

Math 202 Multivariable Calculus for Economics covers Gaussian elimination, matrix algebra, determinants, linear independence. Calculus of several variables, chain rule, implicit differentiation. Optimization, first order conditions, Lagrange multipliers. Integration of functions of several variables. Prerequisite: Mathematics 112L or 122L. Not open to students who have taken Mathematics 212. Topics from 212 which are not covered in Math 202 include: vector fields, line integrals, surface integrals, integral theorems of Green, Gauss and Stokes. Most of the linear algebra, optimization, and implicit differentiation content of Math 202 is not in Math 212, nor are the examples from economics.

## For Engineering Students

These are common questions from engineering students in the Pratt School of Engineering.

###### I have studied multivariable calculus while I was in high school, but Duke will not grant me official transfer credit because the course appears on my high school transcript. May I "skip" Math 212 Multivariable Calculus based on my work in high school?

Your Pratt School of Engineering academic dean might let you "skip" Math 212 Multivariable under certain circumstances. If you have an 800 on the SAT (or a 36 on the ACT), and a 5 on the BC AP exam, then you should talk to your academic dean about this possibility.

But here's the **WARNING**: if an engineering student "skips" Math 212 Multivariable Calculus and then does not do well in Math 216, then that student might be required to start over with Math 212 in the following semester and then re-take Math 216 only after successful completion of Math 212. Also keep in mind that any waiver of the Engineering School's requirement for a particular math course cannot be granted by the Math Department -- any student considering "skipping" a course should get written approval from your academic dean in the Pratt School of Engineering. Finally, keep in mind that permission from Pratt to skip their requirement for Math 212 does NOT automatically carry over to other second majors you might be considering. If you are considering the possibility of doing a second major in math, be sure to talk to the Math DUS, ADUS, or SFI as soon as possible since there are some related course choice considerations that you should think about.

And be sure you read the next question, because it's about an important implication of this issue.

[For more information on the transfer credit policy, you can read the page on Transfer Credit in the Pratt School of Engineering statement of policies and procedures.]

###### I'm an engineering student, and I plan to "skip" Math 212 Multivariable Calculus as described in the previous question/answer. Assuming I do well in Math 216 Linear Algebra and Differential Equations and all my other math courses, will the number of math courses I am required to take at Duke be reduced by one?

No. In most cases the Engineering school will require you to take the same number of math courses that they require of all students in your particular major. The effect of this policy is to replace Math 212 with a higher level math course (but in a later semester).

###### I am an engineering student, and I have pre-matriculation credit for multivariable calculus. I'm also considering studying mathematics as a double-major. What math course should I take?

Engineering students normally take Math 216 Linear Algebra and Differential Equations and Math 353 Ordinary and Partial Differential Equations after multivariable calculus. These courses cover the parts of three subjects (linear algebra, ordinary differential equations, and partial differential equations) that are most important to engineering students.

However, a student planning to major in math will need a stronger foundation and should instead take full semester courses covering these subjects -- Math 221 (linear algebra), Math 356 (differential equations), and ideally Math 453 (partial differential equations). Note that Math 221 is a prerequisite for the math major, and Math 356 (and Math 453 if you take it) will count toward the required number of courses for the math major. Interested students can confirm with the Pratt School of Engineering that they will accept these courses in place of Math 216 and Math 353.