Series: Texts in Applied Mathematics, Vol. 65
1st ed. 2016, XIV, 550 p. 134 illus., 60 illus.
in color.
Printed book
Hardcover
ISBN 978-1-4939-6387-4
* Includes ample commentary on exercises to help explain their
significance and provide a deeper understanding of content
* Detailed appendices gives readers self-study opportunities
* Supports practical uses of subject matter and broader scientific
awareness
This book develops the theory of ordinary differential equations (ODEs), starting from an
introductory level (with no prior experience in ODEs assumed) through to a graduate-level
treatment of the qualitative theory, including bifurcation theory (but not chaos). While
proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-toface
interactions.
A unique fea
ture of this book is the integration of rigorous theory with numerous
applications of scientific interest. Besides providing motivation, this synthesis clarifies the
theory and enhances scientific literacy. Other features include: (i) a wealth of exercises
at various levels, along with commentary that explains why they matter; (ii) figures with
consistent color conventions to identify nullclines, periodic orbits, stable and unstable
manifolds; and (iii) a dedicated website with software templates, problem solutions, and
other resources supporting the text.
Given its many applications, the book may be used comfortably in science and
engineering courses as well as in mathematics courses. Its level is accessible to upperlevel
undergraduates but still appropriate for graduate students. The thoughtful
presentation, which anticipates many confusions of beginning students, makes the
book suitable for a teaching environment that emphasizes self-directed, active learning
(including the so-called inverted classroom).
1st ed. 2016, X, 470 p. 16 illus., 15 illus. in
color.
A product of Birkhauser Basel
Printed book
Hardcover
ISBN 978-3-319-40517-9
Series: Progress in Probability, Vol. 71
* Gives a unique view on the mathematical methods used by experts to
establish high dimensional results
* Displays the wide scope of the types of problems to which these
methods can be successfully applied
* Provides not only a valuable introduction to what is meant by high
dimensional probability, but also exposes fruitful new areas of
research
This volume collects selected papers from the 7th High Dimensional Probability meeting
held at the Institut d'Etudes Scientifiques de Cargese (IESC) in Corsica, France.
High Dimensional Probability (HDP) is an area of mathematics that includes the study of
probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert
spaces and Banach spaces. The most remarkable feature of this area is that it has resulted
in the creation of powerful new tools and perspectives, whose range of application has
led to interactions with other subfields of mathematics, statistics, and computer science.
These include random matrices, nonparametric statistics, empirical processes, statistical
learning theory, concentration of measure phenomena, strong and weak approximations,
functional estimation, combinatorial optimization, and random graphs.
The contributions in this volume show that HDP theory continues to thrive and develop
new tools, methods, techniques and perspectives to analyze random phenomena.
Series: History of Mathematics Subseries, Vol. 2162
1st ed. 2016, X, 228 p. 20 illus.
Printed book
Softcover
ISBN 978-3-319-42311-1
* Presents, through the works of the pioneers, the sophisticated
evolution of one of the most important notions of geometry and
topology
* Features many illustrations which aid the understanding of the more
complicated constructions
* Excepting M. Audin's novel La formule de Stokes, there are no similar
booksExplains many connections between analysis, algebra, number
theory, geometry and topology
Exploring several of the evolutionary branches of the mathematical notion of genus, this
book traces the idea from its prehistory in problems of integration, through algebraic
curves and their associated Riemann surfaces, into algebraic surfaces, and finally into
higher dimensions. Its importance in analysis, algebraic geometry, number theory and
topology is emphasized through many theorems. Almost every chapter is organized
around excerpts from a research paper in which a new perspective was brought on the
genus or on one of the objects to which this notion applies. The author was motivated by
the belief that a subject may best be understood and communicated by studying its broad
lines of development, feeling the way one arrives at the definitions of its fundamental
notions, and appreciating the amount of effort spent in order to explore its phenomena.
Series: C.I.M.E. Foundation Subseries, Vol. 2166
1st ed. 2016, X, 134 p.
Printed book
Softcover
ISBN 978-3-319-42350-0
* Offers a basic introduction to the subjects
* Gives detailed and careful explanations of the topics
* Presents four different and very important aspects of the
applications of Ricci flow
Presenting some impressive recent achievements in differential geometry and topology,
this volume focuses on results obtained using techniques based on Ricci flow. These
ideas are at the core of the study of differentiable manifolds. Several very important open
problems and conjectures come from this area and the techniques described herein are
used to face and solve some of them.
The book’s four chapters are based on lectures given by leading researchers in the field
of geometric analysis and low-dimensional geometry/topology, respectively offering an
introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-
manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and
Kahler?Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers
interested in differential manifolds.
Series: C.I.M.E. Foundation Subseries, Vol. 2167
1st ed. 2016, X, 340 p. 111 illus., 78 illus. in
color.
Printed book
Softcover
ISBN 978-3-319-42678-5
* Provides an overview of different mathematical models and methods
applied to cell and tissue behaviour
* Gives many examples of application
* Includes more than 200 explanatory figures
The aim of these lecture notes is to give an introduction to several mathematical models
and methods that can be used to describe the behaviour of living systems. This emerging
field of application intrinsically requires the handling of phenomena occurring at different
spatial scales and hence the use of multiscale methods.
Modelling and simulating the mechanisms that cells use to move, self-organise
and develop in tissues is not only fundamental to an understanding of embryonic
development, but is also relevant in tissue engineering and in other environmental
and industrial processes involving the growth and homeostasis of biological systems.
Growth and organization processes are also important in many tissue degeneration and
regeneration processes, such as tumour growth, tissue vascularization, heart and muscle
functionality, and cardio-vascular diseases.