The first Challenge Problem set .

**Background**

The Math Department has required writeups of multistep, nonstandard problems (here referred to as "challenge problems") as part of the general calculus curriculum since 1995. This requirement is a consequence of our recognition that:

**Written and oral communication of scientific and technical work is important and can be difficult.**

Professor Stephen Greenfield has led the implementation of this policy at least for multivariable calculus, and the material on this page, apart form the assigment itself, is based on material on his web pages.

**What is a writeup?**

A writeup is a small essay. It should progress logically and be easy to read. It will be graded both on mathematical content and on presentation.

- Explanations should be given in complete sentences.
- Include any information (such as pictures and computations) that you think is useful.
- Label any pictures.
- You should not include straightforward computational details. For example, you may just state that if
*f(x)=3x*^{7}*+25x*^{4}*-19x*^{2}*+5*, then*f(-2)=-87*. The details of substitution and evaluation should not be shown. - Neatness counts: your workshop report must be written legibly on standard size paper. Observe margins on all four sides. Please write on
*one side only*. You must put your name, your section number, the workshop number, and the page number on each sheet. You must*staple*the pages together in the proper order.

One *very* good reference on writing is *The Elements of Style* by Strunk and White. It is quite brief. The fourth edition is a thin, reasonably priced paperback ($8). An early edition is available online.

**Exposition is a skill which can be learned. The comments on your work are intended to help this process.**

**The rules**

While you are encouraged to discuss the problem with other students, and will work together in groups, and are also encouraged to discuss the problems with the peer mentors and me, the written work you hand in must be your own writing. That is, if you are working in a group and another student in your group figures out a key idea for the solution, by all means, do include this idea in your write-up. However, make sure the **explanation** of this idea is your own. In short, work together on the solutions of the problems, but work by yourself in explaining the solution, once it is worked out. Please acknowledge any quotes and reference any sources, but as far as attributing insights to group members, simply say at the outset of your write-up the names of the people in your group: Give your write-up a title, under that write "by My Name" and in a line below that, write "Joint work with ...", listing the names.

**(1)** The first challenge problem set

**(2)** The second challenge problem set

**(3)** The third challenge problem set