Bøger af Ralph-Johan Back

Mathematics is based on proofs. The proof shows the logical reasoning behind a theorem, allows us to understand the meaning of it, its limitations and its consequences. Without a proof, a theorem is like magic; with a proof it is (sometimes more, sometimes less) self evident. But proofs are considered difficult in mathematics education of today, in particular at secondary level, and are therefore often avoided in teaching. When proofs are given, they are often informal and the underlying logic is not explicated. The purpose of this book is to put forward an alternative method for teaching mathematics at secondary and tertiary level that reintroduces proofs and careful argumentation as the solid basis for mathematics education. The method, structured derivations, is essentially a format for presenting mathematical arguments (calculations, derivations, proofs, problem solutions, etc). The format is designed to show the overall structure of the argument, while at the same time allowing a detailed inspection of each step in the argument. The method does not put any restrictions on the mathematical domain where the argumentation is carried out, nor on the level of detail or mathematical rigor of the argumentation. Hence, structured derivations can be used in any area of mathematics, and at any level of education. The focus in this book is on how to use structured derivations in teaching mathematics at high school level.

The LNCS journal Transactions on Computational Systems Biology is devoted to inter- and multidisciplinary research in the fields of computer science and life sciences and supports a paradigmatic shift in the techniques from computer and information science to cope with the new challenges arising from the systems oriented point of view of biological phenomena.This, the 13th Transactions on Computational Systems Biology volume, guest edited by Ralph-Johan Back, Ion Petre, and Erik de Vink, focuses on Computational Models for Cell Processes and features a number of carefully selected and enhanced contributions initially presented at the CompMod workshop, which took place in Eindhoven, The Netherlands, in November 2009. From different points of view and following various approaches, the papers cover a wide range of topics in systems biology, addressing the dynamics and the computational principles of this emerging field.

Much current research in computer science is concerned with two questions: is a program correct? And how can we improve a correct program preserving correctness? This latter question is known as the refinement of programs and the purpose of this book is to consider these questions in a formal setting. In fact, correctness turns out to be a special case of refinement and so the focus is on refinement. Although a reasonable background knowledge is assumed from mathematics and CS, the book is a self-contained introduction suitable for graduate students and researchers coming to this subject for the first time. There are numerous exercises provided of varying degrees of challenge.