Softcover ISBN:  9781470451110 
Product Code:  CAR/25 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614440246 
Product Code:  CAR/25.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470451110 
eBook: ISBN:  9781614440246 
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 
Softcover ISBN:  9781470451110 
Product Code:  CAR/25 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614440246 
Product Code:  CAR/25.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470451110 
eBook ISBN:  9781614440246 
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 DetailsThe Carus Mathematical MonographsVolume: 25; 1994; 207 ppRecipient 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 selfcontained and accessible to nonexperts. 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


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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 selfcontained and accessible to nonexperts. 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