Format: Hardback, 401 pages, height x width: 235x155 mm, X, 401 p
Pub. Date: 24-Mar-2024
ISBN-13: 9783031435010
William Thurstons ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The purpose of the present volume and of the other volumes in the same series is to provide a collection of articles that allows the reader to learn the important aspects of Thurstons heritage. The topics covered in this volume include Kleinian groups, holomorphic motions, earthquakes from the Anti-de Sitter point of view, the Thurston and WeilPetersson metrics on Teichmuller space, 3-manifolds, geometric structures, dynamics on surfaces, homeomorphism groups of 2-manifolds and the theory of orbifolds.
1 Kenichi Ohshika and Athanase Papadopoulos: Introduction.- 2 Huiping
Pan and Weixu Su: The geometry of the Thurston metric: a survey.- 3 Binbin
Xu: Thurston's metric on the Teichmuller space of flat tori.- 4 Farid Diaf
and Andrea Seppi: The Anti-de Sitter proof of Thurston's earthquake
theorem.- 5 Nicholas Vlamis: Homeomorphism groups of self-similar
2-manifolds.- 6 Eric Schippers and Wolfgang Staubach: Weil-Petersson
Teichmuller theory of surfaces of infinite conformal type.- 7 Hiroshige Shiga
and Toshiyuki Sugawa: Kleinian groups and geometric function theory.- 8
Ken'ichi Ohshika: Thurston's broken windows only theorem revisited.- 9
Christoforos Neofytidis: Geometric structures in Topology, Geometry, Global
Analysis and Dynamics.- 10 Jayadev Athreya: Counting problems for invariant
point processes.- 11 Juan Martin Perez and Florent Schaffhauser: Orbifolds
and the modular curve.- 12 Athanase Papadopoulos: On Thurston's notes on the
Geometry and Topology of 3-manifolds.
Format: Hardback, height x width: 240x168 mm, 35 Illustrations, color; Approx. 200 p. 35 illus. in color.,
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 28-May-2024
ISBN-13: 9783031488245
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Pol?ks theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Pol?ks theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
General Sublattices of L(CR).- Neutrality and Intervals.- Free Objects.-
Constructions.- Canonical Varieties.
Pages: 224
ISBN: 978-981-12-8044-3 (hardcover)
ISBN: 978-981-128-149-5 (softcover)
This book offers a short and accessible account of the history of mathematics, written for the intelligent layman to gain a better appreciation of its beauty, relevance, and place in history. It traces the development of the subject throughout the centuries, starting with the so-called Lebombo bone, the oldest known mathematical object that was estimated to be at least 43,000 years old, and ending with the 21st century.
The presentation is informal, and no prior knowledge of mathematics is needed to enjoy the systematic chronological insights. A collection of appendices is included for more technical material ? though still at the level of secondary school mathematics ? and is concerned with the historically important proofs and concepts that can be explained in a simple way.
Preface
From the Beginnings to 6th Century BCE
The Greeks (From 6th Century BCE to 5th Century CE)
Ancient Chinese and Indian Mathematics (From 5th Century BCE to 5th Century CE)
The Romans and the Middle Ages (From 1st Century BCE to the 15th Century)
The Early Modern World (From the 15th to 17th Century)
The 18th Century
The 19th Century
The 20th and 21st Centuries
Final Remarks
Further Reading
Appendices
Bibliography
Name Index
Non-specialist readers interested in general literature about mathematics at an informal level. The book could also be used for an undergraduate course on history of mathematics at mathematics, computer science, physics and/or engineering studies. It should be also of interest to graduate students of engineering studies and first-year students of mathematics, as well as undergraduate or graduate students of technical studies.