* First book project where selected works of Feller are published
* Scholarly comments on Feller’s work and impact, including a
scientific Biography and a complete Bibliography
* About 100 pages of translations of seminal papers (originally written
in German)
This extensive selection of William Feller’s scientific papers shows the breadth of his
oeuvre as well as the historical development of his scientific interests. Six seminal papers
* originally written in German * on the central limit theorem, the law of large numbers,
the foundations of probability theory, stochastic processes and mathematical biology
are now, for the first time, available in English. The material is accompanied by detailed
scholarly comments on Feller’s work and its impact, a complete bibliography, a list of
his PhD students as well as a biographic sketch of his life with a sample of pictures from
Feller’s family album. Volume I covers the early years 1928-1949, featuring the celebrated
Lindeberg-Feller Central Limit Theorem, while Volume II contains papers from 1950-1971
when the theory of Feller processes and boundaries had been developed.
William Feller was one of the leading mathematicians in the development of probability
theory in the 20th century. His work continues to be highly influential, in particular in the
theory of stochastic processes, limit theorems and applications of mathematics to biology.
These volumes will be of value to all those interested in probability theory, analysis,
mathematical biology and the history of mathematics.
2015, L, 1530 p. In 2 volumes, not available separately.
Hardcover
ISBN 978-3-319-17246-0
Series: Universitext
* Can be used as a textbook for courses in dissipative dynamics at
the graduate level
* Contains a large number of exercises
* Presents, develops and uses the quasi-stability method
* Useful not only to mathematicians interested in the general theory of
dynamical systems, but also to physicists and engineers interested in
mathematical background and methods for the asymptotic analysis
of infinite-dimensional dissipative systems that arise in Continuum
Mechanics
This book is devoted to background material and recently developed mathematical
methods in the study of infinite-dimensional dissipative systems.The theory of such
systems is motivated by the long-term goal to establish rigorous mathematical models for
turbulent and chaotic phenomena. The aim here is to offer general methods and abstract
results pertaining to fundamental dynamical systems properties related to dissipative
long-time behavior. The book systematically presents, develops and uses the quasistability
method while substantially extending it by including for consideration new
classes of models and PDE systems arising in Continuum Mechanics. The book can be used
as a textbook in dissipative dynamics at the graduate level.
Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in
Kharkov, Ukraine.
1st ed. 2015, XVII, 390 p. 9 illus.
Softcover
ISBN 978-3-319-22902-7
Series: Sources and Studies in the History of Mathematics and Physical Sciences
* Groups the texts of these twelve tablets from Tell Harmal for the first
time
* Contains translations, philological and mathematical commentaries,
and a general vocabulary
* Contributes to a geography of the Old Babylonian mathematical
practices
This work offers a re-edition of twelve mathematical tablets from the site of Tell Harmal, in
the borders of present-day Baghdad. In ancient times, Tell Harmal was *aduppum, a city
representative of the region of the Diyala river and of the kingdom of E*nunna, to which
it belonged for a time. These twelve tablets were originally published in separate articles
in the beginning of the 1950s and mostly contain solved problem texts. Some of the
problems deal with abstract matters such as triangles and rectangles with no reference to
daily life, while others are stated in explicitly empirical contexts, such as the transportation
of a load of bricks, the size of a vessel, the number of men needed to build a wall and the
acquisition of oil and lard.
This new edition of the texts is the first to group them, and takes into account all the
recent developments of the research in the history of Mesopotamian mathematics.
Its introductory chapters are directed to readers interested in an overview of the
mathematical contents of these tablets and the language issues involved in their
interpretation, while a chapter of synthesis discusses the ways history of mathematics
has typically dealt with the mathematical evidence and inquires how and to what
degree mathematical tablets can be made part of a picture of the larger social context.
Furthermore, the volume contributes to a geography of the Old Babylonian mathematical
practices, by evidencing that scribes at *aduppum made use of cultural material that
was locally available. The edited texts are accompanied by translations, philological, and
mathematical commentaries.
1st ed. 2015, XV, 97 p. 21 illus.
Hardcover
ISBN 978-3-319-22523-4
Series: Universitext
* A concise and as self-contained as possible introduction to the
‘variational approach’ of SPDEs
* Provides a very detailed introduction to stochastic integration on
Hilbert spaces
* Includes a complete proof of the finite-dimensional case using the
Euler approximation
This book provides an introduction to the theory of stochastic partial differential
equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions
in probability theory with several wide ranging applications. Many types of dynamics
with stochastic influence in nature or man-made complex systems can be modelled by
such equations. The theory of SPDEs is based both on the theory of deterministic partial
differential equations, as well as on modern stochastic analysis.
Whilst this volume mainly follows the ‘variational approach’, it also contains a short
account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains
a complete presentation of the main existence and uniqueness results in the case of
locally monotone coefficients. Various types of generalized coercivity conditions are
shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with
explosion in finite time is developed. It is, so far, the only book where the latter and
the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The
extension to this more general framework for SPDEs, for example, in comparison to the
well-known case of globally monotone coefficients, substantially widens the applicability
of the results. In addition, it leads to a unified approach and to simplified proofs in many
classical examples. These include a large number of SPDEs not covered by the ‘globally
monotone case’, such as, for example, stochastic Burgers or stochastic 2D and 3D
Navier-Stokes equations, stochastic
Cahn-Hilliard equations and stochastic surface growth models.
To keep the book self-contained and prerequisites low, necessary results about SDEs in
finite dimensions are also included with complete proofs as well as a chapter on stochastic
integration on Hilbert spaces. Further fundamentals (for example, a detailed account on
the Yamada-Watanabe theorem in infinite dimensions) used in the book have added
proofs in the appendix. The book can be used as a textbook for a one-year graduate
course.
1st ed. 2015, VI, 266 p.
Softcover
ISBN 978-3-319-22353-7
* An updated and expanded edition of a historically important
collection of mathematical problems
* Offers a unique insight into the ideas of a time and place that had an
enormous influence on the development of mathematics
* Contains 193 mathematical problems formulated by leaders in the
field prior to the second World War, some of which remain unsolved
to this day
The second edition of this book updates and expands upon a historically important
collection of mathematical problems first published in the United States by Birkhauser
in 1981. These problems serve as a record of the informal discussions held by a group of
mathematicians at the Scottish Cafe in Lwow, Poland, between the two world wars. Many
of them were leaders in the development of such areas as functional and real analysis,
group theory, measure and set theory, probability, and topology. Finding solutions to the
problems they proposed has been ongoing since World War II, with prizes offered in many
cases to those who are successful.
In the 35 years since the first edition published, several more problems have been fully
or partially solved, but even today many still remain unsolved and several prizes remain
unclaimed. In view of this, the author has gathered new and updated commentaries on
the original 193 problems. Some problems are solved for the first time in this edition.
Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac,
Antoni Zygmund, Paul Erdos, and Andrzej Granas that provide amazing insights into the
mathematical environment of Lwow before World War II and the development of The
Scottish Book. Also new in this edition are a brief history of the University of Wroc*aw’s
New Scottish Book, created to revive the tradition of the original, and some selected
problems from it.
The Scottish Book offers a unique opportunity to communicate with the people and ideas
of a time and place that had an enormous influence on the development of mathematics
and try their hand on the unsolved problems. Anyone in the general mathematical
community with an interest in the history of modern mathematics will find this to be an
insightful and fascinating read.
2nd ed. 2015, XVIII, 310 p.
Hardcover
ISBN 978-3-319-22896-9