Deciding which math course is the best fit may feel like a real challenge when you arrive to Princeton. Keep in mind that this process often involves a bit of trial and error, and as the first few days of the semester provide additional important information, it will be easy to make adjustments in your schedule if necessary. This process is very flexible and gives excellent results, but the add/drop adjustment step is crucial and the process relies on students to take an active role in gathering information and (re)assessing the situation in the early weeks of the semester. All the general information needed to get started can be found here on these web pages, and various advisors, formal and informal, are available to help with your questions.
The University makes an initial placement recommendation for all incoming students based on the limited information available through standardized test scores. Students refine this initial placement recommendation based on potential majors and other information. Representatives from the math department will be available to answer questions at freshman registration, but this will go more smoothly (and many routine questions can be cleared up ahead of time) if you have done some preliminary research using the placement tools and course information collected here.
Quick Placement Summary: Students with little or no background in calculus, but with strong pre-calculus skills, may opt to take 103. Alternatively, 100 offers intensive pre-calculus review, along with an introduction to the main ideas of calculus, as preparation for 103. Students with a strong background in differential calculus (at the level of a 5 on the BC Advanced Placement Examination) may opt to enter the calculus sequence with 104 or 175, with the choice depending on their prospective choice of concentration. Students with a strong calculus preparation in differential and integral calculus as well as infinite series may opt to start in 201. Such students who also possess a strong interest in physics or mathematics might consider 203 or 215 instead. Students with a particularly strong interest in mathematics (or other strongly theoretical disciplines) as a concentration may opt for 215 or 216 instead.
The math placement workshops at registration in the Fall are designed to help you think about which course is right for you, regardless of standardized test scores.