Series: C.I.M.E. Foundation Subseries, Vol. 2172
* Provides an up-to-date survey of results on rationality of algebraic
varieties
* Gives a comprehensive introduction to the subject, accessible to nonspecialists
* Each chapter includes a large bibliography
Providing an overview of the state of the art on rationality questions in algebraic
geometry, this volume gives an update on the most recent developments. It offers
a comprehensive introduction to this fascinating topic, and will certainly become
an essential reference for anybody working in the field. Rationality problems are of
fundamental importance both in algebra and algebraic geometry. Historically, rationality
problems motivated significant developments in the theory of abelian integrals, Riemann
surfaces and the Abel*Jacobi map, among other areas, and they have strong links with
modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived
categories. This text is aimed at researchers and graduate students in algebraic geometry.
1st ed. 2016, XII, 140 p.
Softcover
ISBN 978-3-319-46208-0
Series: Springer Texts in Statistics
* Offers accessible coverage on statistical learning procedures for
practitioners
* Examines a wide array of real applications
* Presents intuitive explanations and visual representation of
underlying statistical concepts
This textbook considers statistical learning applications when interest centers on the
conditional distribution of the response variable, given a set of predictors, and when
it is important to characterize how the predictors are related to the response. As a first
approximation, this can be seen as an extension of nonparametric regression.
This fully revised new edition includes important developments over the past 8 years.
Consistent with modern data analytics, it emphasizes that a proper statistical learning
data analysis derives from sound data collection, intelligent data management,
appropriate statistical procedures, and an accessible interpretation of results. A continued
emphasis on the implications for practice runs through the text. Among the statistical
learning procedures examined are bagging, random forests, boosting, support vector
machines and neural networks. Response variables may be quantitative or categorical. As
in the first edition, a unifying theme is supervised learning that can be treated as a form of
regression analysis.
Key concepts and procedures are illustrated with real applications, especially those with
practical implications. A principal instance is the need to explicitly take into account
asymmetric costs in the fitting process. For example, in some situations false positives
may be far less costly than false negatives. Also provided is helpful craft lore such as
not automatically ceding data analysis decisions to a fitting algorithm. In many settings,
subject-matter knowledge should trump formal fitting criteria. Yet another important
message is to appreciate the limitation of onefs data and not apply statistical learning
procedures that require more than the data can provide.
The material is written for upper undergraduate level and graduate students in the social
and life sciences and for researchers who want to apply statistical learning procedures
to scientific and policy problems. The author uses this book in a course on modern
regression for the social, behavioral, and biological sciences. Intuitive explanations and
visual representations are prominent. All of the analyses included are done in R with code
routinely provided.
2nd ed. 2016, XXIII, 347 p. 120 illus., 91 illus. in color.
Hardcover
ISBN 978-3-319-44047-7
Series: Graduate Texts in Mathematics, Vol. 173
* Standard textbook of modern graph theory
* Covers all the basic material in full detail
* Introduces and illustrates the more advanced methods of that field
This standard textbook of modern graph theory, now in its fifth edition, combines the
authority of a classic with the engaging freshness of style that is the hallmark of active
mathematics. It covers the core material of the subject with concise yet reliably complete
proofs, while offering glimpses of more advanced methods in each field by one or two
deeper results, again with proofs given in full detail.
The book can be used as a reliable text for an introductory course, as a graduate text, and
for self-study.
gThis outstanding book cannot be substituted with any other book on the present
textbook market. It has every chance of becoming the standard textbook for graph
theory.h Acta Scientiarum Mathematiciarum
gDeep, clear, wonderful. This is a serious book about the heart of graph theory. It has
depth and integrity.h Persi Diaconis & Ron Graham, SIAM Review
gThe book has received a very enthusiastic reception, which it amply deserves. A masterly
elucidation of modern graph theory.h
Bulletin of the Institute of Combinatorics and its Applications
gSucceeds dramatically ... a hell of a good book.h MAA Reviews
gA highlight of the book is what is by far the best account in print of the Seymour-
Robertson theory of graph minors.h Mathematika
g ... like listening to someone explain mathematics.h Bulletin of the AMS
5th ed. 2017, X, 433 p. 119 illus.
Printed book
Hardcover
ISBN 978-3-662-53621-6
Series: Springer Undergraduate Mathematics Series
* Presents fundamental topics of ordinary differential equations in a
compact volume
* Provides numerous examples and exercises
* Includes extra material on special topics in analysis and topology in
an added appendix
This textbook is a comprehensive treatment of ordinary differential equations, concisely
presenting basic and essential results in a rigorous manner.
Including various examples from physics, mechanics, natural sciences, engineering
and automatic theory, Differential Equations is a bridge between the abstract theory of
differential equations and applied systems theory. Particular attention is given to the
existence and uniqueness of the Cauchy problem, linear differential systems, stability
theory and applications to first-order partial differential equations.
Upper undergraduate students and researchers in applied mathematics and systems
theory with a background in advanced calculus will find this book particularly useful.
Supplementary topics are covered in an appendix enabling the book to be completely
self-contained.
1st ed. 2016, XI, 213 p. 16 illus.
Softcover
ISBN 978-3-319-45260-9
Series: Birkhauser Advanced Texts Basler Lehrbucher
* Provides an up-to-date description of nonlinear boundary value
problemsTheory of periodic solutions of ODEs are treatedPermits
to fastly reach advanced scientific results and open problems in the
field
This book provides an up-to-date description of the methods needed to face the existence
of solutions to some nonlinear boundary value problems. All important and interesting
aspects of the theory of periodic solutions of ordinary differential equations related to the
physical and mathematical question of resonance are treated. The author has chosen as
a model example the periodic problem for a second order scalar differential equation. In
a paedagogical style the author takes the reader step by step from the basics to the most
advanced existence results in the field.
1st ed. 2016, Approx. 310 p. 9 illus., 8 illus. in color.
Hardcover
ISBN 978-3-319-47089-4
Series: Lecture Notes in Mathematics, Vol. 2169
* Numerous step-by-step tutorials help the reader to learn quicklyA
special chapter on next generation Flash prepares readers for the
futureIncludes ten tips on how to protect flash sites from hackers
As in the previous Seminar Notes, the current volume reflects general trends in the study
of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical
theme in the Local Theory of Banach Spaces which is well represented in this volume
is the identification of lower-dimensional structures in high-dimensional objects. More
recent applications of high-dimensionality are manifested by contributions in Random
Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian
measure plays a central role in many of these topics, and is also studied in this volume;
in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is
revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well
apparent in several contributions. The classical relation to both the primal and dual Brunn-
Minkowski theories is also well represented, and related algebraic structures pertaining
to valuations and valent functions are discussed. All contributions are original research
papers and were subject to the usual refereeing standards.
1st ed. 2016, X, 370 p. 10 illus., 5 illus. in color.
Softcover
ISBN 978-3-319-45281-4