mathematics

It is easy to imagine that a future populated with an ever-increasing number of mobile and pervasive devices that record our minute goings and doings will significantly expand the amount of information that will be collected, stored, processed, and shared about us by both corporations and governments. The vast majority of this data is likely to benefit us greatly—making our lives more convenient, efficient, and safer through custom-tailored and context-aware services that anticipate what we need, where we need it, and when we need it. But beneath all this convenience, efficiency, and safety lurks the risk of losing control and awareness of what is known about us in the many different contexts of our lives. Eventually, we may find ourselves in a situation where something we said or did will be misinterpreted and held against us, even if the activities were perfectly innocuous at the time. Even more concerning, privacy implications rarely manifest as an explicit, tangible harm. Instead, most privacy harms manifest as an absence of opportunity, which may go unnoticed even though it may substantially impact our lives. In this Synthesis Lecture, we dissect and discuss the privacy implications of mobile and pervasive computing technology. For this purpose, we not only look at how mobile and pervasive computing technology affects our expectations of—and ability to enjoy—privacy, but also look at what constitutes ''privacy'' in the first place, and why we should care about maintaining it. We describe key characteristics of mobile and pervasive computing technology and how those characteristics lead to privacy implications. We discuss seven approaches that can help support end-user privacy in the design of mobile and pervasive computing technologies, and set forward six challenges that will need to be addressed by future research. The prime target audience of this lecture are researchers and practitioners working in mobile and pervasive computing who want to better understand and account for the nuanced privacy implications of the technologies they are creating. Those new to either mobile and pervasive computing or privacy may also benefit from reading this book to gain an overview and deeper understanding of this highly interdisciplinary and dynamic field.

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 groups'. Complementary to this, ideas of Harald Heesch are described, who showed how these theoretical results can be put into practice: He gave a catalogue of 28 procedures that one can use creatively oneself – following in the footsteps of Escher, so to speak – to create artistically sophisticated tesselation.In the corresponding investigations for the complex plane in Part II, movements are replaced by bijective holomorphic mappings. This leads into the theory of groups of Möbius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.Finally, in Part III, a third aspect of the subject is treated, the Penrose tesselation. This concerns results from the seventies, when easily describable and provably non-periodic parquetisations of the plane were given for the first time.