An Incomplete Guide to Happiness (Yours and Mine)

A specific format is required for the term paper.
Not surprisingly, this format follows the same form as a scientific
paper, whose purpose is to inform the reader about the results of a scientific
investigation.

Why so picky? Two reasons, really, which both follow from the same fact:
Computers are great ways to spew out tons of unorgainized (as opposed to
organized) gibberish in rather short periods of time. By requiring students
to organize their results in a report, they must synthesize their output.
In the process, they will be required to think about the results. This
will lead to greater understanding of the material and, hopefully, catch
errors. Nothing is worse than simply turning in a bunch of wrong answers
without noticing that they are wrong. It is much easier to turn in incorrect
computer results than incorrect analytical homework problems typically
done in other classes, and the hope is that by following this ritual, turning
in incorrect solutions will be avoided. The second reason is more practical:
I don't want to have to read piles of computer generated gibberish.

The format is:

**I. Statement of Problem**

A short synopsis of the problem. Example: "Use a fourth order Taylor polynomial to approximate exp(x) on the interval [-1,1] and estimate the error. Show the error estimate is valid."

**II. Description of The Mathematics**

Briefly describe the mathematics used. For example, for the Taylor polynomial, describe the general form and the form of the remainder. Derive the approximation for exp(x) and derive a bound for the error.

**III. Description of the Algorithm**

Write down and explain the numerical method and how you implemented it. For the example you would show how the polynomial evaluation is factored and explain why this is the most efficient way to evaluate the polynomial. You might also copy (by hand) the relevant piece of code.

**IV. Results**

Present the results of the computations. __Use Tables and Graphs!__
A concise, easy to read format is very important!

**V. Conclusions** (*The Most Important Part!*)

Discuss your results. **Show me** that you understand the meaning
of the results you get. If you predicted in Section II that the error is
less than some bound and this is reflected in your table, say so. Like,
"as predicted, the results show that the actual error is less than the
estimate". If your predictions don't come true, try to explain why. You
could have a mistake in your code or there are assumptions made in Sec.
II that aren't valid. A good explanation could salvage an otherwise incorrect
set of numbers. **You** must convince** me** in this section that
you know what the answers should be and that you did indeed get them. Not
only are correct answers important, but the fact that you can show me the
answers are correct is important. (Think about it, if you can't convince
someone that the results are correct, how will you know when they are incorrect?)
This view is very different than that of most other classes where the student
turns in the solutions and the professor gives determines the grade based
on the correctness of the solution. The reason for the difference is that
the computer is doing the work! I don't trust the computer, and the student
shouldn't either. This section is very important.

**VI. Program Listing**

Include this for completeness. I do not grade specifically on programming style, but I might want to comment on more efficient ways of coding something.

Finally,

**(1) All work must be organized on standard 8.5**
x **11** **Paper!**
This means that you must **either** copy your results onto a sheet
of notebook paper **or** carefully format them so that they can be cut
out and pasted onto such paper, or include them in your word processor
document. I will not grade it otherwise. If I have to hunt for your answer(s)
through a pile of computer output I will assume that **you** don't know
what the answers are and hence you will not get credit for the work!

**(2)** All graphs must be computer generated
or hand plotted on **graph paper** according to the standard conventions.
Standard conventions include labels, titles, etc. Ask if you are not sure.
Notebook paper is not graph paper.