Antonetta J. M. van Gasteren (auth.)9783540528494, 3540528490, 0387528490
This 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. |
Table of contents :
Introduction….Pages 0-6
A termination argument….Pages 8-16
A problem on bichrome 6-graphs….Pages 17-20
Proving the existence of the Euler line….Pages 21-24
In adherence to symmetry….Pages 25-28
On a proof by Arbib, Kfoury, and Moll….Pages 29-33
Not about open and closed sets….Pages 34-40
A monotonicity argument….Pages 41-44
On the inverse of a function….Pages 45-46
A calculational proof of Helly’s theorem on convex figures….Pages 47-56
The formal derivation of a proof of the invariance theorem….Pages 57-63
Proving theorems with Euclid’s algorithm….Pages 64-68
On the deisng of an in-situ permutation algorithm….Pages 69-79
Shiloach’s algorithm….Pages 80-87
Clarity of exposition….Pages 88-120
On naming….Pages 122-135
On the ue of formalism….Pages 136-165
Epilogue….Pages 166-170
Proof rules for guarded-command programs….Pages 171-173
Notational conventions….Pages 174-176 |
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