* Sixth edition has been revised, updated and expanded
* Reference book providing rapid access to formulae, data, and
concepts of applied mathematics
* Famous and classic reference book for engineers, physicists, and
applied mathematicians worldwide
This guide book to mathematics contains in handbook form the fundamental working
knowledge of mathematics which is needed as an everyday guide for working scientists
and engineers, as well as for students. Easy to understand, and convenient to use, this
guide book gives concisely the information necessary to evaluate most problems which
occur in concrete applications. In the newer editions emphasis was laid on those fields
of mathematics that became more important for the formulation and modeling of
technical and natural processes, namely Numerical Mathematics, Probability Theory
and Statistics, as well as Information Processing. Besides many enhancements and new
paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions
and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.
6th ed. 2015, XLIV, 1207 p. 799 illus. With
Original German edition published by Verlag Europa-Lehrmittel, Haan-Gruiten,2012.
Softcover
ISBN 978-3-662-46220-1
Series: Encyclopaedia of Mathematical Sciences, Vol. 130
* Excellent presentations of topics one cannot find in books elsewhere
* Presents not only various algorithms and computer-based methods,
but also some theoretical results
* Detailed discussion of the notion of a Grobner basis
* Covers a lot of illustrating and instructing examples
* With two new appendices by V.L. Popov and an Addendum by N. A'Campo and V.L. Popov
This book is about the computational aspects of invariant theory. Of central interest is the
question how the invariant ring of a given group action can be calculated. Algorithms
for this purpose form the main pillars around which the book is built. There are two
introductory chapters, one on Grobner basis methods and one on the basic concepts
of invariant theory, which prepare the ground for the algorithms. Then algorithms for
computing invariants of finite and reductive groups are discussed. Particular emphasis
lies on interrelations between structural properties of invariant rings and computational
methods. Finally, the book contains a chapter on applications of invariant theory, covering
fields as disparate as graph theory, coding theory, dynamical systems, and computer
vision.
The book is intended for postgraduate students as well as researchers in geometry,
computer algebra, and, of course, invariant theory. The text is enriched with numerous
explicit examples which illustrate the theory and should be of more than passing interest.
More than ten years after the first publication of the book, the second edition now
provides a major update and covers many recent developments in the field. Among the
roughly 100 added pages there are two appendices, authored by Vladimir Popov, and an
addendum by Norbert A'Campo and Vladimir Popov.
2015, X, 320 p. 13 illus.
Printed book
Hardcover
ISBN 978-3-662-48420-3
Series: Problem Books in Mathematics
* Contains a wide variety of top-notch methods and results of Cptheory
and general topology presented with detailed proofs
* Presents and classifies 100 open problems in Cp-theory explaining
their relationship with previous research
* Introduces the reader to the theories of u-equivalent spaces and lequivalent
spaces
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete
coverage of the theory of functional equivalencies through 500 carefully selected
problems and exercises. By systematically introducing each of the major topics of
Cp-theory, the book is intended to bring a dedicated reader from basic topological
principles to the frontiers of modern research. The book presents complete and up-todate
information on the preservation of topological properties by homeomorphisms of
function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent
spaces is developed from scratch. The reader will also find introductions to the theory
of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse
systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of
Hilbert's Problem 13 is included as it is needed for the presentation of the theory of lequivalent
spaces. This volume contains the most important classical results on functional
equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of
compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and
the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.
From the reviews of Special Features of Function Spaces: “This is a well-written and very
interesting book from several points of view and can be used as a textbook for courses in
both Cp-theory and general topology as well as a reference guide for specialists working
in Cp-theory and related topics. Additionally, the material can also be considered as an
introduction to advanced set theory and descriptive set theory. …I hope that this book
becomes the right hand of students and researchers in mathematics.” ( Mathematical
Reviews)
From the reviews of Topological and Function Spaces: “It is designed to bring a dedicated
reader from basic topological principles to the frontiers of modern research. The only
background needed is some knowledge of set theory and real numbers.
1st ed. 2015, X, 670 p.
Hardcover
ISBN 978-3-319-24383-2
Series: Springer Texts in Statistics
* Inexpensive paperback that presents the essentials
* Emphasis on issues in measurement that are critical in quality control
The rich set of examples and problems integrated throughout this book will help readers
gain a better understanding of where and how to apply Statistical Quality Control
(SQC) tools. Real projects, cases and data sets show clearly how SQC tools are used in
practice. Topics are covered in the right amount of detail to give insight into their relative
importance in modern quality assurance and the ability to immediately use them.
2nd ed. 2016, X, 410 p.
Printed book
Softcover
ISBN 978-0-387-79105-0
Series: Lecture Notes in Mathematics, Vol. 2152
This book introduces a theory of higher matrix factorizations for regular sequences
and uses it to describe the minimal free resolutions of high syzygy modules over
complete intersections. Such resolutions have attracted attention ever since the elegant
construction of the minimal free resolution of the residue field by Tate in 1957.
The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by
Eisenbud in 1980, which yields a description of the eventual structure of minimal free
resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a
wide range of mathematical fields, from singularity theory to mathematical physics.
1st ed. 2016, Approx. 120 p.
Printed book
Softcover
ISBN 978-3-319-26436-3
Series: Lecture Notes in Mathematics, Vol. 2156
Presenting the first systematic treatment of the behavior of Neron models under ramified
base change, this book can be read as an introduction to various subtle invariants and
constructions related to Neron models of semi-abelian varieties, motivated by concrete
research problems and complemented with explicit examples.
Neron models of abelian and semi-abelian varieties have become an indispensable tool
in algebraic and arithmetic geometry since Neron introduced them in his seminal 1964
paper. Applications range from the theory of heights in Diophantine geometry to Hodge
theory.
We focus specifically on Neron component groups, Edixhoven’s filtration and the base
change conductor of Chai and Yu, and we study these invariants using various techniques
such as models of curves, sheaves on Grothendieck sites and non-archimedean
uniformization. We then apply our results to the study of motivic zeta functions of abelian
varieties. The final chapter contains a list of challenging open questions. This book is
aimed towards researchers with a background in algebraic and arithmetic geometry
1st ed. 2016, Approx. 170 p.
Printed book
Softcover
ISBN 978-3-319-26637-4