Series: Springer Monographs in Mathematics
2017, Approx. 550 p.
Hardcover
ISBN 978-3-662-55419-7
* This Second Edition explores new developments in the field of Inverse
Galois Theory
* Presents the most successful known existence theorems and construction
methods for Galois extensions
* Introduces solutions of embedding problems combined with a collection
of the existing Galois realizations
* Gives an introduction to the results on fundamental groups in positive
characteristic obtained by rigid analytic methods
* Contains tables of example polynomials for transitive respectively primitive
permutation groups up to degree 30
This book is the Second Edition of Inverse Galois Theory. It is concerned with the question
of which finite groups occur as Galois Groups over a given field. In particular, this includes
the question of the structure and the representations of the absolute Galois group of K
and also the question about its finite epimorphic images, the so-called inverse problem
of Galois theory. In all these areas important progress was made in the last few years. The
aim of the book is to give a consistent and reasonably complete survey of these results,
with the main emphasis on the rigidity method and its applications. Among others the
monograph presents the most successful known existence theorems and construction
methods for Galois extensions and solutions of embedding problems combined with a
collection of the existing Galois realizations.
Two important new developments have taken place since the appearance of the first
edition of this book. The first is the algebraization of the Katz algorithm for (linearly) rigid
generating systems of finite groups. The second is the upcoming of a modular Galois
theory. The latter has led to new construction methods for additive polynomials with
given Galois group over fields of positive characteristic. Both methods have their origin in
the Galois theory of differential and difference equations.
Series: Lecture Notes in Mathematics, Vol. 2191
1st ed. 2017, X, 198 p.
Softcover
ISBN 978-1-4471-7343-4
* The first book solely devoted to Leavitt path algebras
* Provides a self-contained and easy-to-read introduction to the subject
* Carefully explains the connection between graph C*-algebras and Leavitt path algebras
* Presents fundamental results and new results alongside open problems
This book offers a comprehensive introduction by three of the leading experts in the field,
collecting fundamental results and open problems in a single volume.
Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown
substantially, with ring theorists as well as researchers working in graph C*-algebras,
group theory and symbolic dynamics attracted to the topic. Providing a historical
perspective on the subject, the authors review existing arguments, establish new results,
and outline the major themes and ring-theoretic concepts, such as the ideal structure,
Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The
book also presents key lines of current research, including the Algebraic Kirchberg Phillips
Question, various additional classification questions, and connections to noncommutative
algebraic geometry.
Leavitt Path Algebras will appeal to graduate students and researchers working in the field
and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing
style, this book is highly accessible.
Series: Universitext
1st ed. 2017, XIV, 547 p. 27 illus., 2 illus. in color.
Softcover
ISBN 978-3-319-62225-5
* Provides a self-contained introduction to stochastic calculus
* Includes applications and numerical methods
* Features more than 200 exercises with detailed solutions
This book provides a comprehensive introduction to the theory of stochastic calculus and
some of its applications. It is the only textbook on the subject to include more than two
hundred exercises with complete solutions.
After explaining the basic elements of probability, the author introduces more advanced
topics such as Brownian motion, martingales and Markov processes. The core of the book
covers stochastic calculus, including stochastic differential equations, the relationship to
partial differential equations, numerical methods and simulation, as well as applications
of stochastic processes to finance. The final chapter provides detailed solutions to all
exercises, in some cases presenting various solution techniques together with a discussion
of advantages and drawbacks of the methods used.
Stochastic Calculus will be particularly useful to advanced undergraduate and graduate
students wishing to acquire a solid understanding of the subject through the theory
and exercises. Including full mathematical statements and rigorous proofs, this book is
completely self-contained and suitable for lecture courses as well as self-study.
Series: Trends in Mathematics
1st ed. 2017, Approx. 250 p.
Hardcover
ISBN 978-3-319-62361-0
* Illustrates recent developments in several directions of
(hyper)complex analysis, operator theory, and infinite dimensional analysis
* Presents new perspectives and current trends for researchers
interested in the aforementioned topics
* Contains contributions written by leading experts
This book gathers contributions written by Daniel Alpay’s friends and collaborators.
Several of the papers were presented at the International Conference on Complex Analysis
and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman
University in November 2016. The main topics covered are complex analysis, operator
theory and other areas of mathematics close to Alpay’s primary research interests. The
book is recommended for mathematicians from the graduate level on, working in various
areas of mathematical analysis, operator theory, infinite dimensional analysis, linear
systems, and stochastic processes.
Series: Springer INdAM Series, Vol. 20
1st ed. 2017, X, 240 p. 21 illus., 1 illus. in color.
Hardcover
ISBN 978-3-319-61942-2
* Provides a comprehensive overview and extensive bibliographic references
* Offers insights into the fields of commutative algebra, algebraic
geometry and homological algebra
* Includes international contributions
This volume collects contributions by leading experts in the area of commutative
algebra related to the INdAM meeting “Homological and Computational Methods
in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The
conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th
birthday. In particular, the topics of this book strongly reflect the variety of Winfried
Bruns’ research interests and his great impact on commutative algebra as well as its
applications to related fields. The authors discuss recent and relevant developments in
algebraic geometry, commutative algebra, computational algebra, discrete geometry
and homological algebra. The book offers a unique resource, both for young and more
experienced researchers seeking comprehensive overviews and extensive bibliographic
references.
Series: Springer Monographs in Mathematics
2017, XVI, 609 p. 38 illus.
Hardcover
ISBN 978-3-319-60230-1
* Provides a comprehensive introduction to the sophisticated
technique of forcing
* Includes Shelah’s astonishing construction of a model in which
exactly 27 Ramsey ultrafilters exist
* Offers topics and open problem for further study
This book, now in a thoroughly revised second edition, provides a comprehensive and
accessible introduction to modern set theory.
Following an overview of basic notions in combinatorics and first-order logic, the author
outlines the main topics of classical set theory in the second part, including Ramsey
theory and the axiom of choice. Here the new edition has been extended to contain a
new Shelah-type permutation model in order to prove the consistency of a surprising
relation between two cardinals in set theory without the axiom of choice. The third part
explains the sophisticated technique of forcing in great detail, now including a separate
chapter on Suslin’s problem. The technique is used to show that certain statements,
such as the continuum hypothesis, are neither provable nor disprovable from the
axioms of set theory. In the final part, some topics of classical set theory are revisited and
further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s
astonishing construction of a model with finitely many Ramsey ultrafilters.
Written for graduate students in axiomatic set theory, Combinatorial Set Theory will
appeal to all researchers interested in the foundations of mathematics. With extensive
reference lists and historical remarks at the end of each chapter, this book is suitable for
self-study.