Math 251, sections 19 & 20, fall semester, 1996

Math 251 is third semester calculus, calculus in more than one variable. Almost all the students who take the course have majors which require it: engineering, various "hard" sciences (such as physics and chemistry), and some of the mathematical sciences (such as statistics and mathematics). The course isn't required for a computer science major, but many CS majors interested in advanced study take it. The course is required for biochemistry majors, whose backgrounds and ambitions are rather non-traditional, since the subject of multivariable calculus is still structured and taught as it was at the end of the nineteenth century, aimed towards solving the problems of classical mathematical physics.

We made large changes in calculus instruction last year in Math 151-2 and wanted to continue these changes in Math 251. Our ambitious revisions in Math 251 included a new textbook, incorporation of Maple labs in the curriculum, smaller class size, increase in recitatation time from 55 to 80 minutes, and the use of part of recitation time for workshops where students would be encouraged to work in small groups discussing non-routine problems. Written solutions of some workshop problems would be required, and these solutions would be graded both for mathematical content (is the answer responsive and correct?) and presentation (exposition of the question and the method used to solve it). Each Maple lab would also require students to hand in material. The course covered the same topics as in the past. Student workload, especially preparation of material to be read and graded, increased substantially.

Here is material related to the course, including (in addition to what's described above) the syllabus, exams and review problems, and some notes.

The students in sections of the course which met on Busch were almost all engineering majors. The relevance of the subject matter to their studies is immediate: it's a language used in many of their upper-level courses. Most of the students in sections 19 and 20 were majoring in biochemistry. These students typically were quite busy with other courses (chemistry, biology) with less mathematical content. The rapid development of technology, however, has made the ideas of calculus more important to biochemists while mastery of the computational complexities, due to such tools as Maple, has become less important. I showed a two-dimensional NMR plot of a protein (a complex collection of contour lines) to convince students that Math 251 was indeed useful and relevant. I assured students that our addition of Maple to the course was an effort to help them in their future endeavors. We may have tried to do too much. I analyzed the course in several memos.

Please send mail to Stephen Greenfield if you have questions or comments about this material or if you use some of it in a course. An acknowledgment that the source of the material is the Rutgers Mathematics Department would be appreciated.

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