This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoret…
This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical…
This open access book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem solving with the treatment of the curricul…
Recalling the century which preceded the founding of all the big international scientific unions which are still going strong today is more than a chore that one has to get out of the way before moving on to the real story; it is the only way to understand what these international unions could be in the first place, at the time of their creation, and how they could develop thereafter. The n…
In diesem Open-Access-Buch untersucht Nele Abels geometrische Beweise und Beweisprozesse von Studierenden des Grundschullehramts in ihrem letzten Studienjahr. Mathematisches Argumentieren und Beweisen sind wesentliche fachliche Kompetenzen, die für ein mathematisches Verständnis von zentraler Bedeutung sind. Insbesondere Lehrkräfte im Primarbereich, welche die Grundlagen für ein fachspezifi…
This open access book introduces the modern tontine and its applications in retirement and decumulation. Personal financial management in the later stages of life presents unique challenges, and renowned retirement planning expert Dr. Milevsky proposes the modern tontine as a solution. With the goal of guiding professionals and retirees in more efficient decumulation, the book demonstrates how …
This open access book investigates current issues related to the evolution of research on teaching mathematics and examines up to thirty years of presage-process-product research (PPPR) in mathematics with respect to conceptualization, instrumentation, and design. The book discusses the theoretical and methodological challenges associated with PPPR, critically reviews current research, and expl…
This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in appl…
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, …
This Open Access book is an excellent synthesis of the initial and continuing preparation for Mathematics Teaching in Bolivia, Ecuador, Paraguay and Peru, from which comparative analyses can be made that show similarities and differences, and highlight various perspectives. In February 2016, the 5th Capacity and Networking Project (CANP) workshop of the International Commission on Mathematic…