Aperiodic Order

'Mathematicians add hypotheses to theorems either to bar known monsters or provisionally to enable proof, pending better ideas that lead to more general results ... Monsters no more, aperiodic filings have joined mainstream mathematics, and undergraduates drawn here by beautiful graphics will find themselves initiated into algebraic number theory, Lie theory, ergodic theory, dynamical systems, finite-state automata, Fourier analysis, and more.' D. V. Feldman, University of New Hampshire
'Aperiodic Order is a comprehensive introduction to this relatively new and multidisciplinary field. Sparked by Dan Shechtman's discovery of quasicrystals in 1982, which earned him the 2011 Nobel Prize in Chemistry, the field incorporates crystallography, discrete geometry, dynamical systems, harmonic analysis, mathematical diffraction theory, and more. Because the field spans such disparate fields, advances by one group often go unnoticed by the other. An important goal of this book is to remedy this by unifying and contextualizing results and providing a common language for researchers. ... Readers who want to follow up on any details can certainly find a reference in the nearly 30 pages of bibliographic entries. Full of examples, construction techniques, and an array of analytic tools, this book is an outstanding resource for those hoping to enter the field, yet also contains plenty of useful information for seasoned experts.' Natalie Priebe Frank, Mathematical Association of America