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Title: Ten Problems in Experimental Mathematics

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.
Authors:
; ; ;
Publication Date:
OSTI Identifier:
878698
Report Number(s):
LBNL--57486
R&D Project: KC6714; BnR: YN0100000; TRN: US200611%%405
DOE Contract Number:
DE-AC02-05CH11231; NSF:DMS-0342255
Resource Type:
Journal Article
Resource Relation:
Journal Name: American Mathematical Monthly; Journal Volume: 113; Related Information: Journal Publication Date: 2006
Research Org:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org:
USDOE Director, Office of Science. Office of AdvancedScientific Computing Research. Mathematical, Information, andComputational Sciences Division; National Science Foundation
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; EVALUATION; MATHEMATICS experimental mathematics