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The Tiling Book: An Introduction to the Mathematical Theory of Tilings
 
Colin Adams Williams College, Williamstown, MA
Softcover ISBN:  978-1-4704-7461-4
Product Code:  MBK/142.S
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-7101-9
Product Code:  MBK/142.E
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-7461-4
eBook: ISBN:  978-1-4704-7101-9
Product Code:  MBK/142.S.B
List Price: $118.00 $88.50
MAA Member Price: $106.20 $79.65
AMS Member Price: $94.40 $70.80
Click above image for expanded view
The Tiling Book: An Introduction to the Mathematical Theory of Tilings
Colin Adams Williams College, Williamstown, MA
Softcover ISBN:  978-1-4704-7461-4
Product Code:  MBK/142.S
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-7101-9
Product Code:  MBK/142.E
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-7461-4
eBook ISBN:  978-1-4704-7101-9
Product Code:  MBK/142.S.B
List Price: $118.00 $88.50
MAA Member Price: $106.20 $79.65
AMS Member Price: $94.40 $70.80
  • Book Details
     
     
    2022; 298 pp
    MSC: Primary 05; 52

    Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications.

    Furthermore, tiling theory happens to be an area where many of the subfields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject.

    This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

    Preview some of these beautiful and intricate patterns here.

    Readership

    Undergraduate and graduate students and researchers interested in tilings and tessellations.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Introdction to tiling
    • Types of tilings
    • Aperiodic tilings
    • Tilings in other geometries and other dimensions
    • Appendix
  • Reviews
     
     
    • In his book, Adams provides many fantastic hiking paths suitable for a wide range of readers. The paths are all walkable, and there is no need to bring ropes or carabiners. The hiking paths contain many scenic points where we can take rest and see interesting tilings. Occasionally along the path, the dimension leaps from 2 to 3. A hiker might notice that the metric system changes from Euclidean to hyperbolic. The paths are open-ended with the possibility that a hiker constructs a brand new path to a new scenic point.

      Keiko Kawamuro (University of Iowa), AMS Notices
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2022; 298 pp
MSC: Primary 05; 52

Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications.

Furthermore, tiling theory happens to be an area where many of the subfields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject.

This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

Preview some of these beautiful and intricate patterns here.

Readership

Undergraduate and graduate students and researchers interested in tilings and tessellations.

  • Chapters
  • Introduction
  • Introdction to tiling
  • Types of tilings
  • Aperiodic tilings
  • Tilings in other geometries and other dimensions
  • Appendix
  • In his book, Adams provides many fantastic hiking paths suitable for a wide range of readers. The paths are all walkable, and there is no need to bring ropes or carabiners. The hiking paths contain many scenic points where we can take rest and see interesting tilings. Occasionally along the path, the dimension leaps from 2 to 3. A hiker might notice that the metric system changes from Euclidean to hyperbolic. The paths are open-ended with the possibility that a hiker constructs a brand new path to a new scenic point.

    Keiko Kawamuro (University of Iowa), AMS Notices
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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