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ºtÁ¿¥DÃD¡GSums, Products, and the Zeta Function: Visualizing a $1,000,000 Problem

¥DÁ¿¤H¡GProf. Paul Abbott (School of Physics and School of Mathematics and Statistics, The University of Western Australia, AUSTRALIA)

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In 1865 Lewis Carroll, the Oxford mathematician (1855-81), wrote Alice¡¦s Adventures in Wonderland. A colleague took the liberty of updating possibly the most famous opening lines in English literature as follows: What is the use of a book without pictures, conversations, or experiments? This question is the focus here. A concrete example of interactive experimentation applied to sums, products, and the Riemann zeta function, will be used to provide the answer.

The application and use of technology in mathematics research and teaching is of fundamental importance. However, most conference proceedings and research papers are¡Xlike most texts, papers, websites, and ebooks¡Xstatic PDF documents, sometimes with bookmarks or hyperlinks. Some ebooks include video content, but true interactivity is rare. iPads are becoming pervasive in higher education and interactivity is the norm. Textbook publishers are converting books to ePub format, which only has limited functionality (e.g. it does not support MathML). Using Flash or Java one can add limited interactivity to ebooks and web pages, but Flash will not run on iPads, and extensive programming is required.

However, there is a way to make mathematics truly interactive¡Xand available on a wide range of portable devices¡Xusing the Computable Document Format (CDF). CDF builds upon, and greatly extends, previous work using computer algebra systems (CAS) and computer aided learning (CAL). This talk was authored in Mathematica and then saved as a CDF interactive document, which can be explored using the free CDF player, also available as a web plugin. This technology can be used to make lecture notes, websites, textbooks, and scientific papers truly interactive¡Xwhich, after all, is what Alice would have wanted.¬ÛÃöÀÉ®×¡Gattachment1021015-1.doc