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Ten problems in experimental mathematics

Bailey, David H. and Borwein, Jonathan M. and Kapoor, Vishaal and Weisstein, Eric W. (2006) Ten problems in experimental mathematics. The American Mathematical Monthly, 113 (6). pp. 481-509.

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    Abstract

    This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and in the process present a concise account of how one combines symbolic and numeric computation, which may be termed ''hybrid computation'', in the process of mathematical discovery.

    Item Type: Article
    Uncontrolled Keywords: experimental mathematics, symbolic computation, numeric computation, mathematical discovery
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 12 Jan 2015 13:26
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1237

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