Math 220 at UIUC assumes NO previous experience with calculus. A greater number of incoming students to UIUC have, however, already seen some calculus. It is not uncommon for students who already have Adavanced Placement (AP) credit for the first semester course Math 220 to take it anyhow. The reasons vary, sometimes the students are hoping for 5 credits of an easy good grade, but often the students are self-aware that their grasp of the material is weak despite managing to do well on a placement examination. These students are not always a positive influence for the students who have seen little to none of the material presented in math 220 before.
Another group of students have seen a large portion of Math 220 in highschool but were either not offered an AP calculus course or missed their chance to take the exam. One major problem for these students is boredom. There is a high degree of repetition in the 3 hours of lecture for Math 220 as many of the concepts are very difficult for first time students. Those who have seen much of the material before become bored early in the course and spend little time on it. Later, when the material becomes more difficult or new for these students, they are unprepared to do the additional work the course demands and actually do worse than one would have expected.
Math 221 will cover the SAME syllabus at that of Math 220, but
with 2 lectures per week instead of 3. There will still be
2 recitations a week for doing the exercises. The expected
audience for Math 221 are engineering students with some
calculus experience (as their program will require it)
and students with some confidence in their mathematical
skills but wanting to brush up on their calculus at a college
level. Having no lecture to attend on Friday will appeal
to some students and a faster
paced coverage of the material on Mondays and Wednesdays
may help with boredom. As this audience exists primarily
in the fall, math 221 will not be offered in
the spring or summer.