First let me speak to American students who have gone beyond calculus, then foreign students, since the curricula are different.
American students 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. Regardless of your combination (or even if you have done something else), the right course to take at Swarthmore in most cases turns out to be Honors linear algebra (one of Math 28/28S/28P), since
Most of those students go on to take Honors Multivariate Calculus (Math 35) in the spring.
Can you place out of Math 28 or 35?
Yes, a few students do. To do so, you need to take our Honors Linear Algebra Placement Problems or our Honors Multivariate Calculus Placement Problems. These are in addition to any other information you need to send us to place out of first-year calculus. If you do well enough on the linear algebra problems, you may take Abstract Algebra, one of our core junior level courses. If you do well enough on the multivariate calculus problems, you may take Real Analysis, our other core junior course.
Will everyone who has done a year of calculus be placed into Honors Linear Algebra?
No. First, it is not the right course unless you are contemplating taking a lot of upper-level mathematics at Swarthmore. Second, your preparation may not be strong enough. Alternatives are to take something outside the calculus/linear algebra sequence. Some good choices are Discrete Math (Math 29), Number Theory (Math 37, offered every other Fall), Statistical Methods (Stat 11), and Data Analysis and Visualization (Stat 31). If, based on our Calculus Placement exam, you don't know sequences and series very well, then yet another alternative is Math 26.
What if your preparation isn't strong enough for the Honors courses but you want to take them?
Do one of the options in the previous paragraph, and then do the honors sequence the following year.
Foreign 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. In short,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 or our Honors Multivariate Calculus tests if you wish; see the discussion of these tests under the American students section above.
First, let's make the distinction between placement and credit clear. Placement is what math/stat course we think you should take next. Credit is a listing of a course on your Swarthmore transcript, so that it counts as one of the 32 course credits you need forgraduation.
Your first year of college should not be a repetition of what you know, nor should it overwhelm you. As with Goldilocks, placement should be just right. Through our own placement exams, and individual consultation in many cases, we try to see that it is.
So why don't we give any credit beyond first-year courses? Because what's the point of coming to Swarthmore if you are going to fill up your transcript with courses you took before you got here? Your transcript should be a record of what you did during your college years, here or in programs elsewhere approved once you are here. Your Swarthmore credit should be a record of what we stand behind.
Math is almost unique in that it is possible to have studied before entrance many courses for which you would get credit if you studied them here. The closest parallel is with foreign language. You may well have studied as much German or Chinese before entrance as would get you 6 credits here at Swat. If so, the college will exempt you from the language requirement, but it won't give you any credits toward graduation.
There are members of the Math/Stat Dept who feel we should not give any credits on entrance towards graduation either. However, as a compromise, and partly to fit in with what many other departments and colleges do, we will give you up to 2 credits for calculus (as explained elsewhere) and 1 for statistics.
Please note that if you enter as a first-year student, the same rules apply whether you took your advanced math in secondary school or through a college or university. However, if you took it at a college or university, and have a transcript from that institution, there is a difference. Suppose you were hoping Swat would also give you credit for that course because some outside organization requires college credits (e.g., medical schools require two college credits in math). Then keep that transcript. It probably won't matter to that outside organization that the credit it not a Swarthmore credit. Of course, you should double check with such outside organizations, or their representatives at Swat (e.g., the pre-med advisor).
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