Series: Springer Monographs in Mathematics
1st ed. 2016, XXXIV, 436 p.
Hardcover
ISBN 978-3-319-49845-4
* Provides an introduction to the ergodic theory and topological dynamics of actions of general countable groups
* Covers several topics of current research interest, including Popa's cocycle superrigidity, sofic entropy, and algebraic actions
* Contains a consolidated account of amenability and its ramifications for dynamics, including a systematic exposition of the entropy theory
for actions of amenable groups
This book provides an introduction to the ergodic theory and topological dynamics
of actions of countable groups. It is organized around the theme of probabilistic and
combinatorial independence, and highlights the complementary roles of the asymptotic
and the perturbative in its comprehensive treatment of the core concepts of weak mixing,
compactness, entropy, and amenability. The more advanced material includes Popa's
cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.
The structure of the book is designed to be flexible enough to serve a variety of
readers. The discussion of dynamics is developed from scratch assuming some
rudimentary functional analysis, measure theory, and topology, and parts of the text can
be used as an introductory course. Researchers in ergodic theory and related areas will
also find the book valuable as a reference.
Series: Undergraduate Texts in Mathematics
XI, 539 p. 122 illus.
Hardcover
ISBN 978-1-4939-6793-3
* Contains enthusiastic prose and exciting and imaginative exercises that will motivate the reader
* Covers the fundamental ideas, axioms, definitions, and theorems upon which real analysis is built and flourishes
* Motivates the material with historical remarks and well-chosen quotes
Lively prose and imaginative exercises draw the reader into this unique introductory real
analysis textbook. Motivating the fundamental ideas and theorems that underpin real
analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm
for the subject throughout. A student reading this book is invited not only to acquire
proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction
and the language of its expression.
In studying this book, students will encounter:
* the interconnections between set theory and mathematical statements and proofs;
* the fundamental axioms of the natural, integer, and real numbers;
* rigorous Ã-N and Ã-Â definitions;
* convergence and properties of an infinite series, product, or continued fraction;
* series, product, and continued fraction formula for the various elementary functions and constants.
Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.
Series: Trends in Mathematics
1st ed. 2016, VIII, 229 p. 34 illus., 31 illus. in
color.
Hardcover
ISBN 978-3-319-48816-5
* Present four different (nevertheless related) topics in Diophantine Analysis
* Each part serves as a self-contained introduction to the topic
* Each part present central results, relevant applications and open problems
This collection of course notes from a number theory summer school focus on aspects
of Diophantine Analysis, addressed to Master and doctoral students as well as everyone
who wants to learn the subject.
The topics range from Bakerfs method of bounding linear forms in logarithms
(authored by Sanda Buja?i? and Alan Filipin), metric diophantine
approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon
Kristensen), Minkowskifs geometry of numbers and modern variations by Bombieri and
Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists)
at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an
essentially self-contained introduction to the topic. The reader gets a thorough impression
of Diophantine Analysis by its central results, relevant applications and open problems.
The notes are complemented with many references and an extensive register which
makes it easy to navigate through the book.
Series: Trends in Mathematics
1st ed. 2016, X, 201 p.
Hardcover
ISBN 978-3-319-47511-0
* Features real-life applications
* Visualizes an important variant of the wavelet transform, i.e., by presenting the Stockwell transform
* Includes applications to fields other than mathematics
This volume consists of papers inspired by the special session on pseudo-differential
operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015
and the mini-symposium on pseudo-differential operators in industries and technologies
at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015.
The twelve papers included present cutting-edge trends in pseudo-differential operators
and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters
3-5) and applications (Chapters 6-12). Many contributions cover applications in
probability, differential equations and time-frequency analysis. A focus on the synergies of
pseudo-differential operators with applications, especially real-life applications, enhances
understanding of the analysis and the usefulness of these operators.
Series: Research Perspectives
1st ed. 2017, XXII, 524 p.
Softcover
ISBN 978-3-319-48810-3
* Provides a representative sample of the international current
research in the large field of Analysis and its Applications
* First systematic collection in book format of chapters devoted to special areas in Analysis
* Gives insight into outstanding research activities in Asian countries
This book presents a collection of papers from the 10th ISAAC Congress 2015, held in
Macau, China. The papers, prepared by respected international experts, address recent
results in Mathematics, with a special focus on Analysis. By structuring the content
according to the various mathematical topics, the volume offers specialists and nonspecialists
alike an excellent source of information on the state-of-the-art in Mathematical
Analysis and its interdisciplinary applications.