Volume: 25; 1994; 207 pp; Softcover
Print ISBN: 978-1-4704-5111-0
Product Code: CAR/25
List Price: $46.00
AMS Member Price: $34.50
MAA Member Price: $34.50
Electronic ISBN: 978-1-61444-024-6
Product Code: CAR/25.E
List Price: $46.00
AMS Member Price: $34.50
MAA Member Price: $34.50
Algebra and Tiling: Homorphisms in the Service of Geometry
Share this pageSherman K. Stein; Sándor Szabó
MAA Press: An Imprint of the American Mathematical Society
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.
Reviews & Endorsements
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
Table of Contents
Algebra and Tiling: Homorphisms in the Service of Geometry
- Cover 11
- Title 44
- Preface 88
- Contents 1212
- Chapter 1. Minkowski's Conjecture 1414
- Chapter 2. Cubical Clusters 4848
- Chapter 3. Tiling by the Semicross and Cross 7070
- Chapter 4. Packing and Covering by the Semicross and Cross 9898
- Chapter 5. Tiling by Triangles of Equal Areas 120120
- Chapter 6. Tiling by Similar Triangles 148148
- Chapter 7. Redei's Theorem 168168
- Epilog 200200
- Appendix A. Lattices 202202
- Appendix B. The Character Group and Exact Sequences 206206
- Appendix C. Formal Sums 210210
- Appendix D. Cyclotomic Polynomials 212212
- Bibliography for Preface 214214
- Supplement to the Bibliography 216216
- Name Index 218218
- Subject Index 220220
- Symbol Index 222222
- Back Cover 223223