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Neural Net Mathematics
David Wallace Croft
2005-12-28
These are the answers to a midterm and a final that I took in "Neural Net
Mathematics", a course taught by
Dr. Richard M. Golden at the
University of Texas at Dallas.
In working through these take-home
exams, I came to a point where I felt that I had "cracked the code" in that
I had identified a step-by-step algorithm or process that I could apply
manually for solving problems
of this type. Although some might disagree with me, I feel that these
matrix calculus problems could be solved by a computer program with the
right stuff. While I was taking the course, I started looking into
automated theorem proving
and proof verification software.
When I wrote my computer programming
book, I took pride in ensuring that all of the code samples had been
compiled and tested. When I did VLSI chip design, I used a "silicon
compiler" to check the layout prior to fabrication. I was pleased to
discover that a number of decades
ago, mathematicians started inventing languages that were readable to both
humans and computers so that the mathematics in textbooks could
be verified by a computer prior to publication. I wish this were in
widespread use today as I find that nothing is more discouraging to a math
student
than an incorrect proof or example in introductory educational material.
I am now convinced that in the future all
proofs should be should be expressed in a language such as
MathML,
OpenMath, or
OMDoc
so that they can be checked by proof verification software,
a "math compiler".
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You will need a MathML-enabled browser such as
Mozilla Firefox to view this tutorial.
You might also need to install the
math fonts.
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