Series: Trends in Mathematics
1st ed. 2017, XVI, 346 p. 30 illus., 15 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-57803-3
* Provides an overview of recent developments in mathematical fields
related to fractals
* Includes original research contributions as well as surveys written by
experts in their respective fields
* Readers will find interesting and motivating results as well as new
avenues for further research
This contributed volume provides readers with an overview of the most recent
developments in the mathematical fields related to fractals, including both original
research contributions, as well as surveys from many of the leading experts on modern
fractal theory and applications. It is an outgrowth of the Conference of Fractals and
Related Fields III, that was held on September 19-25, 2015 in ile de Porquerolles, France.
Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis,
geometric measure theory, ergodic theory and dynamical systems, probability theory,
number theory, wavelets, potential theory, partial differential equations, fractal tilings,
combinatorics, and signal and image processing. The book is aimed at pure and applied
mathematicians in these areas, as well as other researchers interested in discovering the
fractal domain.
Series: SpringerBriefs in Mathematics
1st ed. 2017, X, 90 p. 44 illus., 25 illus. in color.
Printed book
Softcover
ISBN 978-3-319-59622-8
* Brings together results in wavelet functional data analysis that to
date were only available in papers
* The only book to present functional data analysis from a wavelet
point of view in a general framework
* Offers numerous sample coded applications for use with MATLAB
* Includes chapters in state-of-the-art topics like visualization of
functional analysis via wavelets, optimal estimation and testing methods
Wavelet-based procedures are key in many areas of statistics, applied mathematics,
engineering, and science. This book presents wavelets in functional data analysis, offering
a glimpse of problems in which they can be applied, including tumor analysis, functional
magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors
explore myriad families of wavelets and how they can be used. High-dimensional data
visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure
for nonparametric models) and a selection of estimation and testing techniques (including
a discussion on Steinfs Paradox) make this a highly valuable resource for graduate
students and experienced researchers alike.
Series: Lecture Notes in Mathematics, Vol. 2184
1st ed. 2017, X, 391 p. 79 illus., 35 illus. in color.
Printed book
Softcover
ISBN 978-3-319-58001-2
* A unique coherent glimpse of the state-of-the-art in Discrete
CurvatureOf interest to both mathematicians and computer
scientistsA vertiginous collection of ideas and tools
In the recent years, a very active field of research has appeared, blending discrete
mathematics, differential geometry, probabilities and computer graphics, as much
as a theoretical development as in response to unforeseen challenges coming from
applications. Discrete and continuous geometries have turned out to be intimately
connected, and the bridges between the two are manifold, and involve numerous
fields: metric spaces, Riemannian and Euclidean geometries, geometric measure
theory, topology, partial differential equations, calculus of variations, gradient flows,
asymptotic analysis, probabilities, harmonic analysis, graph theory, etc. In spite of the
crucial importance both in theoretical mathematics and in applications, there are, up
to now, almost no books providing a coherent outlook on this emerging field.
This work offers a fantastic glimpse into this rich new world and its recent developments. It
shows a vertiginous collection of ideas and tools, and every reader interested in discrete
curvature will learn something new. This book aims to be a meeting point not only for
mathematicians and computer scientists, but also between various fields of mathematics
that are usually separated. It will be profitable both for graduate students and experts
wishing to broaden their knowledge.
1st ed. 2017, VIII, 329 p. 47 illus., 18 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-58183-5
* First book to outline the history of both differential and complex geometry in parallel
* Includes quotes and scans from original documents
* Considers mathematical knowledge known at the time of the key geometers
Differential and complex geometry are two central areas of mathematics with a long and
intertwined history. This book, the first to provide a unified historical perspective of both
subjects, explores their origins and developments from the sixteenth to the twentieth
century.
Providing a detailed examination of the seminal contributions to differential and complex
geometry up to the twentieth century embedding theorems, this monograph includes
valuable excerpts from the original documents, including works of Descartes, Fermat,
Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash.
Suitable for beginning graduate students interested in differential, algebraic or complex
geometry, this book will also appeal to more experienced readers.
Series: Progress in Mathematics, Vol. 323
1st ed. 2017, X, 544 p. 23 illus., 2 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-59727-0
* Details recent advances in fields influenced by the work of Roger Howe
* Based on talks given at the eponymous conference held at Yale University in 2015
* Speakers include Roger Howe himself and other world renowned mathematicians
This book contains selected papers based on talks given at the "Representation Theory,
Number Theory, and Invariant Theory" conference held at Yale University from June 1
to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger
Howe, on the occasion of his 70th birthday, whose work and insights have been deeply
influential in the development of these fields. The speakers who contributed to this
work include Roger Howe's doctoral students, Roger Howe himself, and other world
renowned mathematicians. Topics covered include automorphic forms, invariant theory,
representation theory of reductive groups over local fields, and related subjects.