M 311                                           Spring 2004
                                                                                
                HOMEWORK SUMMARY REPORT
                                                                                
                                                                                
Chapter number: 5
                                                                                
Section number: 1
                                                                                
Exercise number: 8
                                                                                
Number of papers received: 7
                                                                                
Reviewing committee: Theta
                                                                                
List all participating committee members:
    Xujia Zhang,Jason Madsen
                                                                                
                                                                                
Author(s) of paper(s) chosen for publication:
                                                                                
Kathryn Turner [and Amanda Coots and Brian Young]
                                                                                
Comments:
                                                                                
Seven papers were received for problem 5.1.8. All of them are correct.
Three different methods were used by the authors to solve this problem.
Among them, Kathryn Turner did a very good job with explaning how to solve
this problem step-by-step, and that's why her paper was chosen for
publication.
                                                                                
GRADER'S COMMENT:  Many papers checked the expression for linearity 
without even mentioning the solution set.  I think this doesn't really 
answer the question.

INSTRUCTOR'S COMMENT:  Since there are three different methods, I'll 
publish all three.  The methods are:
1.  Check the expression for linearity and draw the correct conclusion 
about the solution set.
2.  Show an explicit counterexample to closedness under the algebraic 
operations.
3.  Find a parametric representation of the solution set.