Guidelines for writing up Professional Problems
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For the most part, everybody is starting to get a good understanding of 
what we're looking for in professional problems.  If you're still not 
sure, go back and look over the example problem we gave you at the 
beginning of the semester, and read the guidlines here.

* DON'T REINVENT THE WHEEL

You can assume knowledge within the section; for example, if you're 
converting an integral to spherical coordinates, you can use the 
appropriate fudge factor without writing down and computing the Jacobian.  
You certainly shouldn't go back and redevelop the entire theory of fudge 
factors from scratch.

Having said that, you should specifically cite any theorems or big results 
that you use.

* USE SENTANCES

You should write in sentances.  Many sentances.  More than one.  Really.  
Your sentances should be grammatically correct.  Don't use sentance 
fragments unless you're trying to make a point, as I was at the beginning 
of this paragraph.  There is no minimum number of sentances required for a 
professional problem writeup, but if you have fewer than five, for 
example, you're probably skating on thin ice.

Incidentally, this also means you shouldn't do your entire writeup using 
bullet points.  If you're attached to them, you could use bullet points to 
mark different sections of your solution.

* USE YOUR THINKING CAP

You should always try to justify your answer.  You might be able to 
confirm it exactly by using some completely different method.  Sometimes 
you might only be able to show that it's a reasonable answer by using some 
kind of estimate.

As announced in class, we do not consider it appropriate to confirm your
work by simply feeding the problem to Mathematica, Maple, or your graphing
calculator and getting the same answer.  If this seems to be the only way 
to confirm your answer, you should look for some other way which will at 
least show that it's reasonable, if not proven correct.

For an example of this, read the solution for 12.4 #14.  Another example
that comes to mind is 10.5 #21.  Rather than confirming your
parametrization by graphing it with a computer, you could make sure that
your x, y, and z components satisfy the equation of the sphere.  While
this doesn't prove your paramtrization is correct, it at least shows the
points of your surface lie on the sphere.  (This is an example of trying 
to show that your answer isn't _obviously_ wrong, which is what the 
confirmation step is really all about!)

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As always, talk to your workshop instructor if you have questions.

Jonathan Rogness
rogness@math.umn.edu