1st ed. 2017, XVII, 311 p.
Hardcover
ISBN 978-3-319-66211-4
* Collects both classical and recent results into a single, comprehensive
source
* Provides all necessary proofs in full detail
* Can be used as a standard reference on the topic by both graduate students
and researchers
This monograph presents both classical and recent results in the theory of nilpotent
groups and provides a self-contained, comprehensive reference on the topic. While
the theorems and proofs included can be found throughout the existing literature, this
is the first book to collect them in a single volume. Details omitted from the original
sources, along with additional computations and explanations, have been added to foster
a stronger understanding of the theory of nilpotent groups and the techniques commonly
used to study them. Topics discussed include collection processes, normal forms and
embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie
algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a
strong undergraduate or beginning graduate background in algebra, graduate students
and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable
resource.
1st ed. 2017, V, 365 p. 5 illus.
Hardcover
ISBN 978-3-319-65872-8
* Contributions cover areas in commutative algebra and related noncommutative
generalizations that have flourished in the last few decades and are not yet well
represented in book form
* In addition to research articles, the volume provides comprehensive
survey articles on recent advances and new trends in the field
* The volume includes open problems that point to future directions of research
This volume presents a collection of articles highlighting recent developments in
commutative algebra and related non-commutative generalizations. It also includes an
extensive bibliography and lists a substantial number of open problems that point to
future directions of research in the represented subfields. The contributions cover areas
in commutative algebra that have flourished in the last few decades and are not yet well
represented in book form. Highlighted topics and research methods include Noetherian
and non-Noetherian ring theory, module theory and integer-valued polynomials
along with connections to algebraic number theory, algebraic geometry, topology and
homological algebra.
Most of the eighteen contributions are authored by attendees of the two conferences
in commutative algebra that were held in the summer of 2016: “Recent Advances in
Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and
Polynomials” Graz, Austria. There is also a small collection of invited articles authored by
experts in the area who could not attend either of the conferences. Following the model
of the talks given at these conferences, the volume contains a number of comprehensive
survey papers along with related research articles featuring recent results that have not
yet been published elsewhere.
Series: Springer Texts in Statistics
2017, XXIX, 648 p. 40 illus.
Softcover
ISBN 978-3-319-64866-8
* A hugely important work for statisticians, the book’s emphasis is
on the areas of matrix analysis that are key sectors for this group of
people
* Practical use: includes a large number of exercises with some
solutions provided in an appendix
* Relevant in all the right areas, this book addresses computational
issues as well as placing more emphasis on applications than existing
texts
* Written in an informal style that makes the book’s complex material
accessible
This textbook for graduate and advanced undergraduate students presents the theory of
matrix algebra for statistical applications, explores various types of matrices encountered
in statistics, and covers numerical linear algebra. Matrix algebra is one of the most
important areas of mathematics in data science and in statistical theory, and the second
edition of this very popular textbook provides essential updates and comprehensive
coverage on critical topics in mathematics in data science and in statistical theory.
Part I offers a self-contained description of relevant aspects of the theory of matrix algebra
for applications in statistics. It begins with fundamental concepts of vectors and vector
spaces; covers basic algebraic properties of matrices and analytic properties of vectors
and matrices in multivariate calculus; and concludes with a discussion on operations
on matrices in solutions of linear systems and in eigenanalysis.
Part II considers various
types of matrices encountered in statistics, such as projection matrices and positive
definite matrices, and describes special properties of those matrices; and describes
various applications of matrix theory in statistics, including linear models, multivariate
analysis, and stochastic processes.
Part III covers numerical linear algebra*one of the
most important subjects in the field of statistical computing. It begins with a discussion
of the basics of numerical computations and goes on to describe accurate and efficient
algorithms for factoring matrices, how to solve linear systems of equations, and the
extraction of eigenvalues and eigenvectors.
Although the book is not tied to any particular software system, it describes and gives
examples of the use of modern computer software for numerical linear algebra. This part
is essentially self-contained, although it assumes some ability to program in Fortran or C
and/or the ability to use R or Matlab.
1st ed. 2018, XXXI, 910 p. 39 illus.
Hardcover
ISBN 978-3-319-64294-9
This is a two-volume collection presenting the collected works of Herbert Busemann,
one of the leading geometers of the twentieth century and one of the main founders of
metric geometry, convexity theory and convexity in metric spaces. Busemann also did
substantial work (probably the most important) on Hilbert’s Problem IV. These collected
works include Busemann’s most important published articles on these topics.
Volume I of the collection features Busemann’s papers on the foundations of geodesic
spaces and on the metric geometry of Finsler spaces.
Volume II includes Busemann’s papers on convexity and integral geometry, on Hilbert’s
Problem IV, and other papers on miscellaneous subjects.
Each volume offers biographical documents and introductory essays on Busemann’s
work, documents from his correspondence and introductory essays written by leading
specialists on Busemann’s work. They are a valuable resource for researchers in synthetic
and metric geometry, convexity theory and the foundations of geometry.
Series: Developments in Mathematics, Vol. 52
1st ed. 2017, VIII, 194 p.
Hardcover
ISBN 978-981-10-6348-0
* Discuss the open problems relevant to each particular topic
* Investigates the algebraic properties of the Drazin inverse
* Covers the latest references on the generalized inverses
This book addresses selected topics in the theory of generalized inverses. Following a
discussion of the “reverse order law” problem and certain problems involving completions
of operator matrices, it subsequently presents a specific approach to solving the problem
of the reverse order law for {1} -generalized inverses.
Particular emphasis is placed on the existence of Drazin invertible completions of an
upper triangular operator matrix; on the invertibility and different types of generalized
invertibility of a linear combination of operators on Hilbert spaces and Banach algebra
elements; on the problem of finding representations of the Drazin inverse of a 2x2 block
matrix; and on selected additive results and algebraic properties for the Drazin inverse.
In addition to the clarity of its content, the book discusses the relevant open problems
for each topic discussed. Comments on the latest references on generalized inverses are
also included. Accordingly, the book will be useful for graduate students, PhD students
and researchers, but also for a broader readership interested in these topics.