Mathematics for Computation (M4c)

The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation. This volume also investigates the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not. Recently, abstract mathematics has proved to have more computational content than ever expected. In fact, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only to clarity but also to efficiency. Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally is all mathematics, including abstract concepts such as functions. The purpose of M4C is actually strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software. While M4C is officially situated within mathematical logic and the related areas of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory. The volume aims to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.