**Brief history and current use**

Workshops have been used in the Math 151-2 calculus courses since the
1995 academic year. At that time, S. Greenfield, building on much
previous work done by M. Beals, A. Cohen, and S. Greenfield in the
Intensive Calculus "Excel" courses, wrote a collection of workshop
problems. Some of these problems originated in that collection, but
many other people have contributed to what's presented
here. V. Scheffer contributed much to the preservation and expansion
of the second semester problems.

The current set of problems is intended to assist instructors in
selecting problems appropriate for their students. Instructors
certainly will not use every problem listed here, and many instructors
may create problems of their own. Please note that the textbook has
many problems which could be used for workshops, and including a
textbook problem occasionally is almost surely a very good idea. The
problems vary in difficulty from the totally routine to the more
intricate. Note that phrases such as "Explain why ..." or "Justify
..." have been systematically omitted, since the writeups of the
problems will *always* be graded for exposition as well as
content (see below).

Here is the background
material which we have asked (June, 2007) to be inserted into the
Rogawski calculus text. Information about workshops begins on page 4
of this 9 page insert.

**An update: July 2010**

**Additional problems**Additional workshop problems have been added. Almost two dozen problems written by M. O'Nan have been installed, and, a novelty for this collection, more than 60 problems for multivariable calculus (Math 251 and 291 at Rutgers-New Brunswick) have been added, most contributed by S. Greenfield and E. Speer with additional material from E. Carrington.**Multivariable Calculus and workshops**During the 1990's both S. Greenfield and E. Speer were course coordinators for Math 251. At that time, both of these individuals strongly recommended the use of weekly workshops (a total of 8 to 10 in the semester) in Math 251. Since then few 251 instructors have used workshops. But many honors sections of 251 and also sections of 291 have had workshop-like activity. S. Greenfield and E. Speer would like to recommend strongly that all lecturers in Math 251 use workshops some of the time. The`Maple`labs in Math 251 need more effort than similar assignments during the 1990's. Recognizing this, Greenfield and Speer recommend that 3 to 4 workshops be assigned during a typical 251 semester. Small honors sections and sections of 291 may choose to assign more of them.**Using what's here creatively ...**Certainly some of these problems are difficult. A number of problems were created for honors courses (especially the multivariable problems). But many problems also originated as exam problems in standard courses (151/152/251). They can be used. Please*feel free*to change the problems to suit your own classes and purposes. The problems can be made easier or harder. They can be given as workshop problems, and may used as a source of exam problems or as seeds for lecture presentations. Any instructional use is legitimate.

G. Cherlin has suggested that problems from the textbook be occasionally used as workshop problems (with indications as to the source). This may help students recognize that the workshops are linked to other aspects of the course such as the textbook.**They can't do this!**Some instructors have believed or asserted that "Our students can't cope with open-ended problems. For example, they lack the algebraic skills to manipulate formulas including parameters rather than constants. And the students can't create adequate technical exposition." Certainly many of our students find these problems difficult. But what's needed to cope with these problems are skills also needed in applications, in future courses, and vocationally.

A considerable number of our students never learn accurate versions of Taylor's Theorem and the Chain Rule in several variables. Should we then drop these topics from our courses, or try to help these students as well as we can? We don't, and we try to help students learn. Similar effort can lead to better workshop solutions, and such accomplishments are directly applicable later in most students' lives.

Successful solution of workshop problems (including good exposition!) may be a low-percentage outcome. But that doesn't mean it should be a goal which is less important.

**The index links**

The Rogawski section number and title, when "moused", will give a very
brief outline of the problem. "Clicking" will give a pdf link with a
view of the single problem, including any pictures. The plain
T_{E}X file is a text file. Strange or
intricate typography will be avoided. The epsf package is invoked with
`\input epsf` and is used to insert
pictures, diagrams, or graphs as needed. Each such illustration should
have a link in the last column, in eps format. Usually the pictures
will be created using `Maple` or using the
free program, `Xfig`. If the picture is
created with `Xfig`, a corresponding
`Xfig` file is included in the `picstuff` directory (thus the companion to
`wA.eps` is `wA.fig`).

**Grading workshops**

Please grade both for content and presentation. One instructor
has written the following for students:

Each workshop report will be graded on a scale of 0-10. Half the points are for "mathematical content" and half for "exposition". If the mathematics is illegible then you cannot get either the content points or the exposition points. "Exposition" includes the format described above, the layout of your computations, and the explanatory sentences. More words are not necessarily better! "Content" includes the mathematical appropriateness of the work you do, and the correctness of the computations (numerical and symbolic) and any diagrams and graphs you use to motivate, carry out, and report your work and your results.What's handed in should be

Late workshops will generally not be accepted!

Roughly speaking scores are given as follows: 0 means nothing legible is there. 2 means there is some relevant work in proper format, but it makes almost no progress. 4 means the format is okay and there is some mathematical progress. 6 means format and exposition is okay and there is reasonable mathematical progress. 8 means format and exposition is okay and the mathematics is almost complete. 10 means there are no important errors in math or exposition. Intermediate score are intermediate: e.g. 7 is between 6 and 8.

**How to use this collection of workshops**

**Method 1**

Download the T_{E}X files you would like to use. Also download the corresponding picture files. Place these files in the same directory. Reassemble the T_{E}X files, adding titles, dates, and any other material needed. If the reassembled file is called`workshop1.tex`, the following sequence of commands should create an appropriate postscript or pdf file, which can be posted on the web or printed for copying and distribution:tex workshop1.tex dvips workshop1.dvi -o workshop1.ps ps2pdf workshop1.ps

Those who use other "dialects" of T_{E}X should make appropriate modifications.**Method 2**

Just print out the problems you like from the prepared pdf files, use scissors and tape, make copies and distribute. This is low-tech, but it will work and is simple.

The workshop problems also can be a useful

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/15/2008;
additions made 7/5/2010.
**