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Algebra and Tiling: Homorphisms in the Service of Geometry
 
Algebra and Tiling
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-5111-0
Product Code:  CAR/25
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-61444-024-6
Product Code:  CAR/25.E
List Price: $55.00
MAA Member Price: $41.25
AMS Member Price: $41.25
Softcover ISBN:  978-1-4704-5111-0
eBook: ISBN:  978-1-61444-024-6
Product Code:  CAR/25.B
List Price: $120.00 $92.50
MAA Member Price: $90.00 $69.38
AMS Member Price: $90.00 $69.38
Algebra and Tiling
Click above image for expanded view
Algebra and Tiling: Homorphisms in the Service of Geometry
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-5111-0
Product Code:  CAR/25
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-61444-024-6
Product Code:  CAR/25.E
List Price: $55.00
MAA Member Price: $41.25
AMS Member Price: $41.25
Softcover ISBN:  978-1-4704-5111-0
eBook ISBN:  978-1-61444-024-6
Product Code:  CAR/25.B
List Price: $120.00 $92.50
MAA Member Price: $90.00 $69.38
AMS Member Price: $90.00 $69.38
  • Book Details
     
     
    The Carus Mathematical Monographs
    Volume: 251994; 207 pp
    Recipient of the Mathematical Association of America's Beckenbach Book Prize in 1998!

    Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts.

    The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Minkowski’s Conjecture
    • Chapter 2. Cubical Clusters
    • Chapter 3. Tiling by the Semicross and Cross
    • Chapter 4. Packing and Covering by the Semicross and Cross
    • Chapter 5. Tiling by Triangles of Equal Areas
    • Chapter 6. Tiling by Similar Triangles
    • Chapter 7. Rédei’s Theorem
    • Epilog
    • Appendix A. Lattices
    • Appendix B. The Character Group and Exact Sequences
    • Appendix C. Formal Sums
    • Appendix D. Cyclotomic Polynomials
  • Reviews
     
     
    • The prerequisites for this book are an acquaintance with the very basics of group and field theory. The appendices, on lattices, exact sequences, formal sums, and cyclotomic polynomials make this book quite self-contained and accessible to non-experts. There are plenty of historical remarks, making the exposition lively, and there are dozens of illustrations. The exercises and problems are abundant and stimulating.

      Fabio Mainardi, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 251994; 207 pp
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 1998!

Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts.

The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.

  • Chapters
  • Chapter 1. Minkowski’s Conjecture
  • Chapter 2. Cubical Clusters
  • Chapter 3. Tiling by the Semicross and Cross
  • Chapter 4. Packing and Covering by the Semicross and Cross
  • Chapter 5. Tiling by Triangles of Equal Areas
  • Chapter 6. Tiling by Similar Triangles
  • Chapter 7. Rédei’s Theorem
  • Epilog
  • Appendix A. Lattices
  • Appendix B. The Character Group and Exact Sequences
  • Appendix C. Formal Sums
  • Appendix D. Cyclotomic Polynomials
  • The prerequisites for this book are an acquaintance with the very basics of group and field theory. The appendices, on lattices, exact sequences, formal sums, and cyclotomic polynomials make this book quite self-contained and accessible to non-experts. There are plenty of historical remarks, making the exposition lively, and there are dozens of illustrations. The exercises and problems are abundant and stimulating.

    Fabio Mainardi, MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.