Synopses & Reviews
Association schemes for graduate mathematicians and statisticians, minimum prerequisites, numerous examples and exercises.
Review
"The author of this impressive monograph is well-known as a world leader who has made fundamental contributions to this field. Now she has come up with this elegantly written volume that provides a unified survey of the developments in and around association schemes...While the presentation has throughout been lucid and well-organized, the book maintains a high level of mathematical rigour and depth. The impressive list of references, including the most up-to-date ones, will make the book particularly valuable. The large number of examples and exercises, all meticulously chosen, will certainly endear the book to its readers. The author has done a tremendous job, and the scientific community will be the beneficiary. This marvelous book should find a place on the bookshelf of any serious researcher in experimental design and combinatorial theory."
Sankhya: The Indian Journal of Statistics"Bailey makes the connections and justifies this book's place in the library. Highly recommended."
D.V. Feldman, University of New Hampshire, CHOICE"Rosemary Bailey's book is a valuable contribution to one of the important aspects of commutative scheme theory: the application of commutative scheme theory to statistics. Scheme theorists will be grateful for this contribution, because it fills one of the many gaps in the global view of schemes and their central role in mathematics."
Bulletin of the AMS"Those interested in experimental design will see this book in the finest tradition of mathematical statistics. It is thorough, precise, and comprehensive within its reach."
Journal of the American Statistical Association"I think the author deserves applause for this book from everybody who is interested in schemes."
Mathematics Reviews"This book will be a welcome addition to researchers in the area of association schemes as it is comprehensive and indicates likely directions for future work."
Journal of the Royal Statistical Society
Synopsis
Based on the author's graduate course on association schemes and the optimal design of scientific experiments, this book is accessible to both pure mathematicians and statisticians alike. It will appeal to researchers as an accessible reference work from which to learn about the statistical/combinatorial aspect of their work.
Synopsis
Association schemes are of interest to both mathematicians and statisticians and this book is written with both audiences in mind. It has arisen from a course successfully taught by the author and as such the material is thoroughly class-tested. There are numerous examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds wishing to bring their understanding of association schemes up to the state of the art.
About the Author
R. A. Bailey has been Professor of Statistics at Queen Mary, University of London since 1994. Currently she is also head of the School of Mathematical Sciences. After doing a DPhil in group theory at Oxford she worked in the Mathematics Faculty of the Open University then took a post-doctoral research fellowship in Statistics at Edinburgh University. Since then her main research interest has been in the design of experiments. She spent 10 years in the Statistics Department of Rothamsted Experimental Station (now the BBSRC Institute of Arable Crops Research) before coming to the University of London as Professor of Mathematical Sciences at Goldsmiths' College. Along the way she was a school teacher for one year and a technician in medical research for another. She has also held short-term appointments at the Universities of Western Australia, Sydney (Australia), and North Carolina at Chapel Hill (USA). She has been a frequent visitor to the Unit\'e de Biom\'etrie in the Institut National de la Recherche Agronomique at Versailles (France), and has given short courses on Statistics in Finland, Buenos Aires (Argentina) and Augsburg (Germany). Her interests span statistics and pure mathematics, and the importance of both to scientists and to ordinary people. She has served the London Mathematical Society as Meetings and Membership Secretary, Vice President and member of the Personnel and Office Committee. She was a member of the British Combinatorial Committee when it established its current successful format for conferences. She was secretary of the UK \TeX\ Users' Group for four years. She is a member of the Council of the International Biometric Society, being president of the British Region 2000-2002. She is a member of the Research Section of the Royal Statistical Society. She is also a member of the Institute of Mathematical Statistics and the International Statistical Institute. She represented the Committee of Professors of Statistics first on the Higher Educatio
Table of Contents
1. Association schemes; 2. The Bose-Mesner algebra; 3. Combining association schemes; 4. Incomplete-block designs; 5. Partial balance; 6. Families of partitions; 7. Designs for structured sets; 8. Groups; 9. Posets; 10. Subschemes, quotients, duals and products; 11. Association schemes on the same set; 12. Where next?; 13. History and references.