When Randy McCarthy met with the Engineering-Mathematics Liaison Committee, it was stressed that the naming and numbering of the newly reorganized calculus sequence would be important for students, advisors and faculty.
Since there would be two variants of math 220 in the new system, a lot of discussion focused upon how to properly number and name these. In addition, some members of the UAC felt that the standard math sequence should appear more sequential (for example, to have 220, 230, 240 instead of 220, 230 and 242 or 243). Since math 220 is required or recommended by many divisions on campus it was felt that changing its number would cause unnecessary confusion.
A solution which seemed to resolve these problems was to simply renumber the new sequence 221, 231 and 241. Of course, this would become the recommended sequence in Engineering, while 220/221 and 231 would most likely be the recommended one year calculus sequence for non-engineers. The only artificial change is the renumbering of math 230 to math 231. Some short term trouble will occur by this change, but it was felt that it would not be serious.
Some debate focussed upon the numbering of the primary sequence. There were two logical choices, either (220, 230, 240) or (221, 231, 241). There was a desire to have the sequence reflect that freshmen at UIUC often have some previous exposure to calculus. In addition, it was felt that if one used the sequence (220, 230, 240), Math 221 would appear as an accelerated or advanced course. If one uses the sequence (221, 231, 241) then Math 220 appears as a slightly less intense start to the standard sequence, which is indeed what Math 220 is supposed to be.
The new course, Calculus with Applications, was suggested to be numbered 236 for a couple reasons. It was felt that its number should be greater than 231 and less than 241. Math 240 was suggested, but since 240 is not a gentler version of Math 241 (as Math 220 is to Math 221) it was felt some confusion might arrise if 240 were used. In recent history, Math 235 existed as a different accelerated calculus course and so one did not want the new course confused with this. Thus, Math 236 was chosen, as simply the average of 231 and 241 and having no obvious historical counterpart to cause confusion.
Naming the new courses was cause for much spirited discussions
both in the Engineering Liason Committee and by members of
the Mathematics UAC. It was generally agreed that calling the
new Math 221 some sort of "accelerated'' name would discourage
enrollment. At the same time, one wanted it made clear that
the content of both Math 220 and 221 was the same, and only
the expect level of the enrolled students differed. Thus, the
title ``Calculus I for Beginners'' for Math 220 and ``Calculus I''
for the new Math 221 was suggested.