Softcover ISBN:  9780821819333 
Product Code:  STML/1 
List Price:  $22.00 
Individual Price:  $17.60 
Electronic ISBN:  9781470421229 
Product Code:  STML/1.E 
List Price:  $20.00 
Individual Price:  $16.00 

Book DetailsStudent Mathematical LibraryVolume: 1; 1999; 120 ppMSC: Primary 52; Secondary 58; 47; 82; 20;
“In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics—mathematics unforeseen from the motivating problem …”
—from the Preface
The common thread throughout this book is aperiodic tilings; the bestknown 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 analyze 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 worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.ReadershipAdvanced undergraduates, graduate students, and research mathematicians.

Table of Contents

Chapters

Introduction

Chapter 1. Ergodic theory

Chapter 2. Physics (for mathematicians)

Chapter 3. Order

Chapter 4. Symmetry

Chapter 5. Conclusion

Appendix I. Geometry

Appendix II. Algebra

Appendix III. Analysis


Additional Material

Reviews

The book serves as a solid introduction to the study of aperiodic tilings for anyone with sufficient mathematical background. I would wholeheartedly recommend this book for the library of any mathematics department. It would make a great starting point for the directed study project of a motivated senior.
MAA Online 
In this short book, the author discusses several aspects of the theory of “substitution tilings” and “finite type” aperiodic tilings. The book highlights a number of relations between the longrange order properties of these tilings, properties of the translationinvariant measures on the space of tilings, and the (statistical) symmetries of these measures.
Mathematical Reviews 
Reacted very positively … lovely little book.
Palle Jorgensen


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“In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics—mathematics unforeseen from the motivating problem …”
—from the Preface
The common thread throughout this book is aperiodic tilings; the bestknown 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 analyze 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 worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.
Advanced undergraduates, graduate students, and research mathematicians.

Chapters

Introduction

Chapter 1. Ergodic theory

Chapter 2. Physics (for mathematicians)

Chapter 3. Order

Chapter 4. Symmetry

Chapter 5. Conclusion

Appendix I. Geometry

Appendix II. Algebra

Appendix III. Analysis

The book serves as a solid introduction to the study of aperiodic tilings for anyone with sufficient mathematical background. I would wholeheartedly recommend this book for the library of any mathematics department. It would make a great starting point for the directed study project of a motivated senior.
MAA Online 
In this short book, the author discusses several aspects of the theory of “substitution tilings” and “finite type” aperiodic tilings. The book highlights a number of relations between the longrange order properties of these tilings, properties of the translationinvariant measures on the space of tilings, and the (statistical) symmetries of these measures.
Mathematical Reviews 
Reacted very positively … lovely little book.
Palle Jorgensen