The aim of the book is to study symmetries and tesselation, which have long interested artists and mathematicians. Famous examples are the works created by the Arabs in the Alhambra and the paintings of the Dutch painter Maurits Escher. Mathematicians did not take up the subject intensively until the 19th century. In the process, the visualisation of mathematical relationships leads to very appealing images. Three approaches are described in this book.In Part I, it is shown that there are 17 principally different possibilities of tesselation of the plane, the so-called 'plane crystal...

This textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field.With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization...

Why is the squaring of the circle, why is the division of angles with compass and ruler impossible? Why are there general solution formulas for polynomial equations of degree 2, 3 and 4, but not for degree 5 or higher?This textbook deals with such classical questions in an elementary way in the context of Galois theory. It thus provides a classical introduction and at the same time deals with applications. The point of view of a constructive mathematician is consistently adopted: To prove the existence of a mathematical object, an algorithmic construction of that object is always given. Some...

This book explains compactly, without theoretical superstructure and with as little mathematical formalism as possible, the essential concepts in the encryption of messages and data worthy of protection. The focus is on the description of the historically and practically important cipher, signature and authentication methods. Both symmetric encryption and public-key ciphers are discussed. In each case, the strategies used to attack and attempt to "crack" encryption are also discussed. Special emphasis is placed on the practical use of ciphers, especially in the everyday environment. The book...