Student Mathematical Library
Gregory F. Lawler · Vaughn Climenhaga · Ya. B. Pesin · Alex Iosevich · Alex Kasman · Alexander Shen · Bruce M. Landman · Jörg Bewersdorff · Kristopher Tapp · Luis Barreira · M. Ram Murty · Mike Mesterton-Gibbons · Nikolai Konstantinovich Vereshchagin · Wolfgang Kühnel
Latest release: April 24, 2024
Waves & Wave Mechanics · Algebra · Game Theory
Series
75
Books
About this ebook series
The common thread throughout this book is aperiodic tilings; the best-known example is the "kite and dart" tiling. This tiling has been widely discussed, particularly since 1984 when it was adopted to model quasicrystals. The presentation uses many different areas of mathematics and physics to analyse the new features of such tilings. Although many people are aware of the existence of aperiodic tilings, and maybe even their origin in a question in logic, not everyone is familiar with their subtleties and the underlying rich mathematical theory. For the interested reader, this book fills that gap. Understanding this new type of tiling requires an unusual variety of specialties, including ergodic theory, functional analysis, group theory and ring theory from mathematics, and statistical mechanics and wave diffraction from physics. This interdisciplinary approach also leads to new mathematics seemingly unrelated to the tilings. Included are many problems (with solutions) and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.
