Series: Springer Monographs in Mathematics
1st ed. 2017, X, 456 p.
Hardcover
ISBN 978-3-319-57116-4
* Offers a concise course on topological vector spaces oriented towards
readers interested in infinite-dimensional analysis
* Introduces a systematic and accessible presentation for beginners of
measure theory on infinite-dimensional spaces in its interplay with
the theory of topological vector spaces
* Explores differential calculus on general locally convex spaces
This book gives a compact exposition of the fundamentals of the theory of locally convex
topological vector spaces. Furthermore it contains a survey of the most important
results of a more subtle nature, which cannot be regarded as basic, but knowledge
which is useful for understanding applications. Finally, the book explores some of
such applications connected with differential calculus and measure theory in infinitedimensional
spaces. These applications are a central aspect of the book, which is why it is
different from the wide range of existing texts on topological vector spaces. In addition,
this book develops differential and integral calculus on infinite-dimensional locally convex
spaces by using methods and techniques of the theory of locally convex spaces.
The target readership includes mathematicians and physicists whose research is related to
infinite-dimensional analysis.
Series: Compact Textbooks in Mathematics
1st ed. 2017, XII, 106 p.
Printed book
Softcover
ISBN 978-3-319-57218-5
* Entirely self-contained non-technical introduction to protomodular
categories*and to Malftsev categories
* Hardly any previous knowledge is assumed
* Examples and exercises isllustrate basic definitions and results
This book gives a thorough and entirely self-contained, in-depth introduction to a
specific approach to group theory, in a large sense of that word. The focus lie on the
relationships which a group may have with other groups, via guniversal propertiesh, a
view on that group gfrom the outsideh. This method of categorical algebra, is actually not
limited to the study of groups alone, but applies equally well to other similar categories of
algebraic objects.
By introducing protomodular categories and Malftsev categories, which form a larger
class, the structural properties of the category Gp of groups, show how they emerge from
four very basic observations about the algebraic litteral calculus and how, studied for
themselves at the conceptual categorical level, they lead to the main striking features of
the category Gp of groups.
Hardly any previous knowledge of category theory is assumed, and just a little experience
with standard algebraic structures such as groups and monoids. Examples and exercises
help understanding the basic definitions and results throughout the text.
1st ed. 2017, XVIII, 687 p. 1 illus.
Printed book
Hardcover
ISBN 978-3-319-56171-4
* Contains a detailed and systematic analysis of theta functions, by level and by weight
* Serves as a useful, encyclopedic reference, designed to be a full and comprehensive
study of select levels of Theta functions and modular forms
* Features topics that have been the subject of much recent research,
with the material organized into a systematic setting
* Marks the first time many of the topics within will have appeared in book form
Theta functions were studied extensively by Ramanujan. This book provides a systematic
development of Ramanujanfs results and extends them to a general theory. The authorfs
treatment of the subject is comprehensive, providing a detailed study of theta functions
and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate
students, and researchers, the organization, user-friendly presentation, and rich source
of examples, lends this book to serve as a useful reference, a pedagogical tool, and a
stimulus for further research.
Topics, especially those discussed in the second half of the book, have been the subject of
much recent research; many of which are appearing in book form for the first time. Further
results are summarized in the numerous exercises at the end of each chapter.
Series: SpringerBriefs in Mathematics
1st ed. 2017, XI, 55 p. 19 illus.
Printed book
Softcover
ISBN 978-3-319-57516-2
* Covers metric diffusion along compact foliations
* Reinforces basic principles in foliations, holonomy, and heat diffusion
* Clarifies the metrization of weak topology
Up-to-date research in metric diffusion along compact foliations is presented in this book.
Beginning with fundamentals from the optimal transportation theory and the theory
of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality
Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric
diffusion is defined, the topology of the metric space is studied and the limits of diffused
metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat
diffusion, and compact foliations are detailed and vital technical lemmas are proved to
aide understanding.
Graduate students and researchers in geometry, topology and dynamics of foliations
and laminations will find this supplement useful as it presents facts about the metric
diffusion along non-compact foliation and provides a full description of the limit for
metrics diffused along foliation with at least one compact leaf on the two dimensions.
1st ed. 2017, XII, 507 p. 15 illus., 14 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-57302-1
* Presents extended basic theory of linear algebra
* Includes programs in MATLAB that provide students with experience
in implementation and evaluation of numerical algorithms
* Perfect for a one or two semester course at the advanced
undergraduate or graduate level
This book combines a solid theoretical background in linear algebra with practical
algorithms for numerical solution of linear algebra problems. Developed from a number
of courses taught repeatedly by the authors, the material extensively covers topics
like matrix algebra, theory for linear systems of equations, spectral theory, vector
and matrix norms combined with main direct and iterative numerical methods, least
squares problems, and eigenproblems. Numerical algorithms illustrated by computer
programs written in MATLAB are also provided in the Appendix to give the reader a
better understanding of professional numerical software for the solution of real-life
problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix
computation, and large sparse matrices, this text will interest students at the advanced
undergraduate or graduate level.