Distance Education and Multimedia

Here are some of the formats I have used for publishing mathematics on the Web. Since the technology is still evolving, they are not exactly perfect, but can show the trend.
1. Shannon's Communication Channels and Word Spaces. Communication channels are represented by labelled graphs and analyzed using the concept of word spaces. A slight generalization of the notion of regular expressions is used to represent channel signals.
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2. Theory of Search Engines. Using Perron-Frobenius theorem, four stochastic matrices are defined, that can be used to rank the pages and hyperlinks in the Web.
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3. White Hole, Black Whole, and The Book. Physical and intellectual spaces are visualized making use of concepts from Intuitive Set Theory. A book containing all the proofs of mathematics is called The Book.
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4. The Mathematical Universe in a Nutshell. The mathematical universe discussed here gives models of possible structures our physical universe can have.
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5. Geometrical Equivalents of Goldbach Conjecture and Fermat Like Theorem. Five geometrical eqivalents of Goldbach conjecture are given, calling one of them Fermat Like Theorem.
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6. Information-Theoretic Equivalent of Riemann Hypothesis. Riemann Hypothesis is viewed as a statement about the capacity of a communication channel as defined by Shannon.
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7. The Ecstacy of HyperLaTeX. A technology that allows TeX typesetting to be put on the Web is the recent innovation HyperTeX. If you feel that you should learn how to use HyperTeX, follow the three steps given here. Note that the hyperref program on which HyperTex depends has changed considerably since this article was written, and hence carrying out the steps mentioned here may not be smooth sail.
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8. Twenty Problems of Information Technology. Out of the many significant and pressing problems of information technology, twenty are listed.
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9. Foundations of Computer Science. NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation rules to Elementary Arithmetic of Godel and calling it Sentient Arithmetic (SA), the incompleteness theorems are proved within SA, without using any metalanguage. Intuitive Set Theory (IST), a theory in which we do not have to deal with cardinals higher than aleph-null, is described. In IST, there is no Skolem Paradox and there are no nonLebesgue measurable sets.
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The reader is forewarned that many of the concepts discussed in these articles are new, and hence they should be accepted only after careful consideration.