Titlebook: On the Shape of Mathematical Arguments; Antonetta J. M. Gasteren Book 1990 Springer-Verlag Berlin Heidelberg 1990 Algorithmenentwurf.Lösen

Anhydrous

On the deisng of an in-situ permutation algorithm, algorithm and the design decisions leading to it. The choice of the notation was guided by constraints of manipulability, constraints that were met primarily by being frugal in the use of nomenclature (of subscripted variables in particular).

陶器

In adherence to symmetry,This chapter is another illustration of the complications engendered by the introduction of nomenclature, here emerging in the form of overspecificity and loss of symmetry. It aaso discusses the choice between recursion and complete unfolding.

废除

占线

A monotonicity argument,The belief that equivalence is always most appropriately proved by showing mutual implication has undoubtedly been strengthened by the way in which proofs in Euclidean geometry are conducted. The purpose of this chapter is to show that some of that “geometrical evidence” is not compelling at all.

寄生虫

Nucleate

,A calculational proof of Helly’s theorem on convex figures,The proof in this chapter is included firstly to show the calculational style in action, this time in a geometrical problem, and, secondly, to illustrate the carefully phased exploitation of data that is enabled by the introduction of nomenclature.

染色体

The formal derivation of a proof of the invariance theorem,The construction of the formal proof in this chapter illustrates to what extent the shape of formulae rather than their interpretation can inspire and assist the design of a proof.

冷淡周边

jet-lag

召集

0302-9743 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 ad