Series: Universitext
2008, XII, 212 p. 26 illus., Softcover
ISBN: 978-0-387-74655-5
Due: December 2007
About this textbook
Includes a new section on isoparametric hypersurfaces in spheres
Offers revised sections on taut submanifolds, Lie frames, compact proper dupin submanifolds and reducible Dupin submanifolds with up-to-date results
Provides new material on Dupin hypersurfaces with three and four principal curvatures
Includes a more systematic treatment of frame reductions
This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres.
This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
Further key features of Lie Sphere Geometry 2/e:
- Provides the reader with all the necessary background to reach the frontiers of research in this area
- Fills a gap in the literature; no other thorough examination of Lie sphere geometry and its applications to submanifold theory
- Complete treatment of the cyclides of Dupin, including 11 computer-generated illustrations
- Rigorous exposition driven by motivation and ample examples.
Table of contents
Preface.- Introduction.- Lie Sphere Geometry.- Lie Sphere Transformations.- Legendre Submanifolds.- Dupin Submanifolds.- Bibliography.- Index.
Series: Undergraduate Texts in Mathematics
2008, Approx. 290 p., Hardcover
ISBN: 978-0-387-74748-4
Due: December 2007
About this textbook
Bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry
Contains plenty of examples, exercises, and illustrations
Ideal for classroom use with a self-contained and careful presentation
For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so that now it is often treated on a par with the Hausdorff measure. The topological dimensions were rearranged for Chapter 3, so that the covering dimension is the major one, and the inductive dimensions are the variants. A "reduced cover class" notion was introduced to help in proofs for Method I or Method II measures. Research results since 1990 that affect these elementary topics have been taken into account. Some examples have been added, including Barnsley leaf and Julia set, and most of the figures have been re-drawn.
Table of contents
Preface.- Fractal Examples.- Metric Topology.- Topological Dimension.- Self-similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.- Appendix.- Index.
Series: Springer Series in Statistics
2008, Approx. 694 p., Hardcover
ISBN: 978-0-387-73193-3
Due: December 2007
About this book
A superb and comprehensive introduction to statistical decision theory, this book presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner
Throughout, the work maintains statistical relevance
A book that is one of a kind as it fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory
This monograph is written for advanced graduate students, Ph.D. students, and researchers in mathematical statistics and decision theory. All major topics are introduced on a fairly elementary level and then developed gradually to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. It can be used as a basis for graduate courses, seminars, Ph.D. programs, self-studies, and as a reference book.
The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. Highlights are systematic applications to the fields of parameter estimation, testing hypotheses, and selection of populations. With its broad coverage of decision theory that includes results from other more specialized books as well as new material, this book is one of a kind and fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.
One goal is to present a bridge from the classical results of mathematical statistics and decision theory to the modern asymptotic decision theory founded by LeCam. The striking clearness and powerful applicability of LeCamfs theory is demonstrated with its applications to estimation, testing, and selection on an intermediate level that is accessible to graduate students. Another goal is to present a broad coverage of both the frequentist and the Bayes approach in decision theory. Relations between the Bayes and minimax concepts are studied, and fundamental asymptotic results of modern Bayes statistical theory are included. The third goal is to present, for the first time in a book, a well-rounded theory of optimal selections for parametric families.
Friedrich Liese, University of Rostock, and Klaus-J. Miescke, University of Illinois at Chicago, are professors of mathematical statistics who have published numerous research papers in mathematical statistics and decision theory over the past three decades.
Table of contents
Statistical models.- Tests in models with monotonicity properties.- Statistical decision theory.- Comparison of models, reduction by sufficiency.- Invariant statistical decision models.- Large sample approximations of models and decisions.- Estimation.- Testing.- Selection.
Series: Lecture Notes in Mathematics , Vol. 1920
Subseries: Ecole d'Ete Probabilit.Saint-Flour
2008, XII, 200 p. 43 illus. With Saint-Flour Probability Summer Schools List on (virtual) p. 195 and Series ad on (virtual) p. 197, 198, 199, 200.., Softcover
ISBN: 978-3-540-74797-0
Due: October 9, 2007
About this book
Random trees and tree-valued stochastic processes are of particular importance in combinatorics, computer science, phylogenetics, and mathematical population genetics. Using the framework of abstract "tree-like" metric spaces (so-called real trees) and ideas from metric geometry such as the Gromov-Hausdorff distance, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behaviour of such objects when the number of vertices goes to infinity. These notes survey the relevant mathematical background and present some selected applications of the theory.
Keywords:
60B99, 05C05, 51F99, 60J25
Dirichlet form
Gromov-Hausdorff distance
Markov process
coalescent
continuum random tree
Table of contents
2008, Approx. 276 p., Hardcover
ISBN: 978-0-387-75480-2
Due: January 2008
About this textbook
Includes an annotated bibliography of books on the history of mathematics
Emphasizes the importance of using primary sources by looking at the distortion of historical facts over time
Author provides exercises and research projects for students
This book attempts to fill two gaps which exist in the standard textbooks on the History of Mathematics. One is to provide students with material that could encourage more critical thinking. General textbooks, attempting to cover three thousand years of mathematical history, must necessarily oversimplify almost everything, the practice of which can scarcely promote a critical approach to the subject. For this reason, Craig Smorynski chooses a more narrow but deeper coverage of a few select topics.
The second aim of this book is to include the proofs of important results which are typically neglected in the modern history of mathematics curriculum. The most obvious of these is the oft-cited necessity of introducing complex numbers in applying the algebraic solution of cubic equations. This solution, though it is now relegated to courses in the History of Mathematics, was a major occurrence in the history of mathematics. It was the first substantial piece of mathematics in Europe that was not a mere extension of what the Greeks had done and thus signified the coming of age of European mathematics. The fact that the solution, in the case of three distinct real roots to a cubic, necessarily involved complex numbers both made inevitable the acceptance and study of these numbers and provided a stimulus for the development of numerical approximation methods.
Table of contents
Introduction.- Annotated Bibliography.- Foundations of Geometry.- The Construction Problems of Antiquity.- A Chinese Problem.- The Cubic Equation.- Hornerfs Method.- Some Lighter Material.- Appendix A: Small Projects.- Index.