This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermo…
Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn't require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleig…
This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbe…
This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modellin…
Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniqu
Volume 2 of this revised and updated edition provides an accessible and practical introduction to the two non-Abelian quantum gauge field theories of the Standard Model of particle physics: quantum chromodynamics (QCD) and the Glashow-Salam-Weinberg (GSW) electroweak theory.This volume covers much of the experimental progress made in the last ten y
Based on the author’s well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries. After linking symmetries with conservation laws, the book works thr…
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE s…
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows …
Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical inves…