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Neural Net Mathematics

David Wallace Croft


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".

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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