I am looking for someone that is proficient in discrete mathematics to
solve six problems.  I would post the questions to this board, but
they require a person to look at examples in Adobe Acrobat format. If
you are interested, then please contact me via email at: 520@cox.net I
will then be able to email you the pertinent information.

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Request for Question Clarification by mathtalk-ga on 19 Jun 2003 21:51 PDT

Researchers are not permitted to share their email addresses with you.
 However if you post the Acrobat documents on a Web site (there are
many free ones; I can post some links if that would help), then
researchers will be able to examine these online and (hopefully!)
answer any questions you may have about them.

regards, mathtalk-ga

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Clarification of Question by activeone-ga on 20 Jun 2003 07:07 PDT

I took your advice and created a web site for my question.  I have
included the problems and the Adobe Acrobat files on the site.  The
URL is as follows:

http://members.cox.net/520/

Thanks :o)

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Request for Question Clarification by mathtalk-ga on 20 Jun 2003 07:21 PDT

Very nice!  I know how to do these problems, but I'm wondering what
kind of help you are looking for.  For $5 I would be willing to give a
"hint" for how to best attack each problem.  From a teaching/learning
perspective I'd feel that I was depriving you if I simply provided
fully worked answers.  You are obviously very bright, and I think you
can burn through these problems, esp. with my suggestions, in about
the time it took you to build that Web page.

regards, mathtalk-ga

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Request for Question Clarification by elmarto-ga on 20 Jun 2003 14:51 PDT

Maybe you would want to consider changing the price you set for this
question? Solving all the problems, especially the project about
Networks, might take some time, which most Researchers won't be
willing to spend for $3.75.

You might also want to check Google Answers' pricing guidelines at
http://answers.google.com/answers/pricing.html

Best regards,
elmarto

Hi, activeone-ga:

Thanks for posting the clarification above.  Let me get you started
with problem 1, which has two parts.

As the problem itself hints, you would want (esp. if this were a timed
written exam) to minimize the amount of matrix arithmetic that needs
to be done by an astute use of the laws of matrix operations.

For example, 1(a) asks you to evaluate AC + BC.  A "naive" approach
would be to multiply AC, multiply BC, and add the respective results. 
Cost:  two matrix multiplications (which are tedious) and one matrix
addition.

The alternative is to use the distributive law for matrix
multiplication, and evaluate instead (A + B)C.  In other words you
would first add A and B, then multiply that sum of matrices by C. 
Cost:  One matrix addition and one matrix multiplication, a clear
savings of time.

The time and effort saved in part 1(b) is even more pronounced.  Here
we are asked to evalute 2A - 3A.  Instead of doing the two scalar
multiplications on A and subtracting the results, you should invoke
the distributive law for scalar multiplication:

2A - 3A = (2 - 3)A = (-1)A

Now the problem can be done "by inspection".  You simply need to write
down the matrix -A obtained by changing the sign of each entry in A.

regards, mathtalk-ga