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001 978-3-540-47166-0
003 DE-He213
005 20160624102020.0
007 cr nn 008mamaa
008 121227s1990 gw | s |||| 0|eng d
020 _a9783540471660
_9978-3-540-47166-0
024 7 _a10.1007/BFb0020908
_2doi
050 4 _aQA76.9.L63
050 4 _aQA76.5913
050 4 _aQA76.63
072 7 _aUM
_2bicssc
072 7 _aUYF
_2bicssc
072 7 _aCOM051000
_2bisacsh
072 7 _aCOM036000
_2bisacsh
082 0 4 _a005.1015113
_223
100 1 _aGasteren, Antonetta J. M.
_eauthor.
245 1 0 _aOn the Shape of Mathematical Arguments
_h[electronic resource] /
_cby Antonetta J. M. Gasteren.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1990.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1990.
300 _aXII, 184 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Computer Science,
_x0302-9743 ;
_v445
505 0 _aA termination argument -- A problem on bichrome 6-graphs -- Proving the existence of the Euler line -- In adherence to symmetry -- On a proof by Arbib, Kfoury, and Moll -- Not about open and closed sets -- A monotonicity argument -- On the inverse of a function -- A calculational proof of Helly's theorem on convex figures -- The formal derivation of a proof of the invariance theorem -- Proving theorems with Euclid's algorithm -- On the deisng of an in-situ permutation algorithm -- Shiloach's algorithm -- Clarity of exposition -- On naming -- On the ue of formalism -- Epilogue -- Proof rules for guarded-command programs -- Notational conventions.
520 _aThis book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.
650 0 _aComputer science.
650 0 _aSoftware engineering.
650 0 _aLogic design.
650 1 4 _aComputer Science.
650 2 4 _aLogics and Meanings of Programs.
650 2 4 _aSoftware Engineering.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540528494
786 _dSpringer
830 0 _aLecture Notes in Computer Science,
_x0302-9743 ;
_v445
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0020908
942 _2EBK5993
_cEBK
999 _c35287
_d35287