Background
Falconer, Kenneth John was born on January 25, 1952 in Hampton, United Kingdom. Son of Angus Duncan and Ivy Magdalene (King) Falconer.
(Since its original publication in 1990, Kenneth Falconera...)
Since its original publication in 1990, Kenneth Falconera s Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. aeo Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. aeo Each topic is carefully explained and illustrated by examples and figures. aeo Includes all necessary mathematical background material. aeo Includes notes and references to enable the reader to pursue individual topics. aeo Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. aeo Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0--471--95724--0 Please click here to download solutions to exercises found within this title: http://www.wileyeurope.com/fractal
http://www.amazon.com/gp/product/0470848626/?tag=prabook0b-20
(Mathematicians and non-mathematicians alike have long bee...)
Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
http://www.amazon.com/gp/product/1461269628/?tag=prabook0b-20
(Mathematicians and non-mathematicians alike have long bee...)
Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
http://www.amazon.com/gp/product/0387975063/?tag=prabook0b-20
(The seminal text on fractal geometry for students and res...)
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals * Carefully explains each topic using illustrative examples and diagrams * Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics * Features a wide range of exercises, enabling readers to consolidate their understanding * Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)
http://www.amazon.com/gp/product/111994239X/?tag=prabook0b-20
(This book contains a rigorous mathematical treatment of t...)
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
http://www.amazon.com/gp/product/0521337054/?tag=prabook0b-20
(Following on from the success of Fractal Geometry: Mathem...)
Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals. Much of the material presented in this book has come to the fore in recent years. This includes methods for studying dimensions and other parameters of fractal sets and measures, as well as more sophisticated techniques such as thermodynamic formalism and tangent measures. In addition to general theory, many examples and applications are described, in areas such as differential equations and harmonic analysis. This book is mathematically precise, but aims to give an intuitive feel for the subject, with underlying concepts described in a clear and accessible manner. The reader is assumed to be familiar with material from Fractal Geometry, but the main ideas and notation are reviewed in the first two chapters. Each chapter ends with brief notes on the development and current state of the subject. Exercises are included to reinforce the concepts. The author's clear style and up-to-date coverage of the subject make this book essential reading for all those who with to develop their understanding of fractal geometry.
http://www.amazon.com/gp/product/0471957240/?tag=prabook0b-20
educator mathematician researcher
Falconer, Kenneth John was born on January 25, 1952 in Hampton, United Kingdom. Son of Angus Duncan and Ivy Magdalene (King) Falconer.
Bachelor, University Cambridge, England, 1974. Master of Arts, University Cambridge, England, 1978. Doctor of Philosophy, University Cambridge, England, 1978.
He is Professor of Pure Mathematics in the School of Mathematics and Statistics at the University of Street Andrews. He is known for his work on the mathematics of fractals and in particular sets and measures arising from iterated function systems, especially self-similar and self-affine sets. Closely related is his research on Hausdorff and other fractal dimensions.
He formulated Falconer"s conjecture on the dimension of distance sets and conceived the notion of a digital sundial.
In combinatorial geometry he established a lower bound of 5 for the chromatic number of the plane in the Lebesgue measurable case. Falconer was educated at Kingston Grammar School, Kingston upon Thames and Corpus Christi College, Cambridge.
He graduated in 1974 and completed his Doctor of Philosophy in 1979 under the supervision of Hallard Croft. He was a Research Fellow at Corpus Christi College, Cambridge from 1977–1980 before moving to Bristol University.
He was appointed Professor of Pure Mathematics at the University of Street Andrews in 1993 and was Head of the School of Mathematics and Statistics from 2001-2004.
He was elected a Fellow of the Royal Society of Edinburgh in 1998. He served on the Council of the London Mathematical Society from 2000-2009 including as Publications Secretary from 2006-2009. His recreational interests include long distance walking and hill walking.
He was Chair of the Long Distance Walkers Association from 2000-2003 and Editor of their journal Strider from 1987-1992 and 2007-2012.
He has twice climbed all the Munros as well as all the Corbetts.
(Mathematicians and non-mathematicians alike have long bee...)
(Mathematicians and non-mathematicians alike have long bee...)
(Following on from the success of Fractal Geometry: Mathem...)
(Since its original publication in 1990, Kenneth Falconera...)
(The seminal text on fractal geometry for students and res...)
(This book contains a rigorous mathematical treatment of t...)
(This book contains a rigorous mathematical treatment of t...)
Fellow Royal Society Edinburgh. Member Edinburgh Mathematics Society (member committee 1996-1999), London Mathematics Society (member council since 2000), Long Distance Walkers Association (chair 2000-2003).
Married Isobel Jessie Nye, July 15, 1978. Children: Benedict, Jennifer.