# Advanced Placement Beyond Calculus

First we address American students who have gone beyond calculus, then international students, since the curricula are different. For work beyond calculus we only give placement, not credit. For our reasons, look under the *Placement and Credit* subsection of our Supplemental Information page.

**American students.**

Those who have gone beyond first-year calculus have typically taken some subset of the four courses linear algebra, multivariate calculus, discrete mathematics, and differential equations.

To place out, bring to campus as much information about the course you took as you can (course description, a syllabus, the name of the textbook's title and author, your homework, your tests) and meet with the Math/Stat Placement Advisor.

Even if you don't plan to take another mathematics course, placement can sometimes be helpful for work in other departments. For instance, you can't major in Physics or Chemistry without taking multivariate calculus – except if we say you have placed out, then you don't need to take it.

However, *if you are considering majoring in mathematics, it may be better to take our honors versions than to place out*. That is, even if you have taken linear algebra, you might want to take our honors linear algebra (Math 28 or 28S). Even if you have taken multivariate calculus, you might want to take our honors multvariate (Math 35).

There are three reasons for this:

- You will be in with the right people, the other first-years who want to do mathematics.
- You will get better prepared for the core major courses Math 63 (Real Analysis) and Abstract Algebra (Math 67).
- These honors courses tend to cover linear algebra and multivariate in quite a different way from standard versions given here or elsewhere.

In the fall, there is also a First-Year Seminar version of Math 28, called 28S. Some version of linear algebra is a prerequisite for M35.

*Can you place out of Math 28 or 35?*

Yes, a few students do. If you place out of M28, you can go right into M35 or M67. If you place out of both M28 and M35, you can go right into M63 or M67. However, there is an extra step to place out of these courses. You must take our Honors Linear Algebra Placement Test [pdf] or our Honors Multivariate Calculus Placement Test [pdf]. These are in addition to any other information you need to send us to place out of first-year calculus.

**International students.**

The curricula you are most likely to have followed (*e.g.*, International Baccalaureate, or the British system) are organized somewhat differently than American curriculum. They emphasize enrichment instead of acceleration. If you have been through such a curriculum, Honors Linear Algebra is quite likely to be the right course. You will have seen some of it, but hardly all. And there probably will be no one Swarthmore course beyond calculus that you have seen all of. However, you are still welcome to take our Honors Linear Algebra Placement Test [pdf] or our Honors Multivariate Calculus Placement Test [pdf] if you wish; see the discussion of these tests under the American students section above. Also, as with American students, you are welcome to show us your texts, syllabi, tests, *etc.* from advanced courses, and we may give you additional placement.

*Caution*: International calculus curricula generally do not include as much about sequences, series, and Taylor series as the American curriculum. In other countries, this material is often done in a later course. But this material is the subject of the second half of our second semester calculus course, Math 25. So even if you have done some linear algebra or multivariate, you may not qualify for any of our post calculus courses because you may not place out of Math 25. For instance, notice that a highest possible score on the IB Higher level mathematics examdoes not place you out of Math 25. You will have to take Math 26. However, this series material is the subject of one of the optional modules for the IB and for the British A-levels, and other international students may have learned it elsewhere. We urge international students who are eager to start in advanced courses to study this series material on their own if they have not learned it in school, and to place out of it with Section 3 of our Calculus Placement Test.